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atom.xml
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<?xml version="1.0" encoding="utf-8"?>
<feed xmlns="http://www.w3.org/2005/Atom">
<title>Kahvia`s Home</title>
<subtitle>你站在桥上看风景，看风景人在楼上看你。</subtitle>
<link href="https://blog.kahvia.cn/atom.xml" rel="self"/>
<link href="https://blog.kahvia.cn/"/>
<updated>2024-08-28T14:59:15.065Z</updated>
<id>https://blog.kahvia.cn/</id>
<author>
<name>Kahvia</name>
</author>
<generator uri="https://hexo.io/">Hexo</generator>
<entry>
<title>Linux小知识</title>
<link href="https://blog.kahvia.cn/2024/08/28/LinuxOperations.html"/>
<id>https://blog.kahvia.cn/2024/08/28/LinuxOperations.html</id>
<published>2024-08-28T07:12:03.408Z</published>
<updated>2024-08-28T14:59:15.065Z</updated>
<content type="html"><![CDATA[<h3 id="添加用户"><a class="markdownIt-Anchor" href="#添加用户"></a> 添加用户</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">adduser xxx</span><br></pre></td></tr></table></figure><h3 id="为用户赋予去除sudo权限"><a class="markdownIt-Anchor" href="#为用户赋予去除sudo权限"></a> 为用户赋予/去除sudo权限</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">sudo usermod -a -G sudo username</span><br></pre></td></tr></table></figure><p><code>sudo usermod -a -G sudo username</code> 这是一个Linux命令，用于管理用户组权限。它表示将用户（username）添加到sudo用户组。</p><ul><li><code>usermod</code>: 用户管理工具</li><li><code>-a</code>: 表示追加（append），即如果该用户已经存在于其他组，不会将其移除</li><li><code>-G</code>: 指定用户应加入的组名，这里是<code>sudo</code></li><li><code>username</code>: 需要修改权限的用户名</li></ul><p>执行这个命令后，指定的用户会获得sudo权限，允许他们使用sudo命令来执行需要管理员权限的操作。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">sudo usermod -G usergroup username</span><br></pre></td></tr></table></figure><p>将用户转移到 usergroup 用户组中，即移出 sudo 用户群。</p><h3 id="安装zsh"><a class="markdownIt-Anchor" href="#安装zsh"></a> 安装Zsh</h3><p><a href="https://www.zsh.org/">Zsh</a>是 bash 的平替，有着如诸如输入目录名称自动 cd ，以及目录名自动更正等功能。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">sudo apt update</span><br><span class="line">sudo apt install zsh</span><br></pre></td></tr></table></figure><h3 id="安装homebrew"><a class="markdownIt-Anchor" href="#安装homebrew"></a> 安装HomeBrew</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">#官方</span></span><br><span class="line">/bin/bash -c <span class="string">"<span class="subst">$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh)</span>"</span></span><br><span class="line"><span class="comment">#非官方</span></span><br><span class="line">/bin/zsh -c <span class="string">"<span class="subst">$(curl -fsSL https://gitee.com/cunkai/HomebrewCN/raw/master/Homebrew.sh)</span>"</span></span><br></pre></td></tr></table></figure><h3 id="安装nodejs"><a class="markdownIt-Anchor" href="#安装nodejs"></a> 安装Nodejs</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">brew install node@20</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h3 id="添加用户"><a class="markdownIt-Anchor" href="#添加用户"></a> 添加用户</h3>
<figure class="highlight bash"><table><tr><td class="gutter"><pre><sp</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="Linux" scheme="https://blog.kahvia.cn/tags/Linux/"/>
</entry>
<entry>
<title>Python常用语法</title>
<link href="https://blog.kahvia.cn/2024/07/16/PythonGrammar.html"/>
<id>https://blog.kahvia.cn/2024/07/16/PythonGrammar.html</id>
<published>2024-07-16T02:05:01.856Z</published>
<updated>2024-07-16T05:16:26.059Z</updated>
<content type="html"><![CDATA[<h3 id="字符串格式化"><a class="markdownIt-Anchor" href="#字符串格式化"></a> 字符串格式化</h3><p>格式化的过程中，如果遇到数字，可以使用 <code>:[格式]</code>来指定数字的格式。</p><ol><li>采用 f 前缀进行格式化。</li></ol><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">name = <span class="string">'Kahvia'</span></span><br><span class="line">money = <span class="number">143.257</span></span><br><span class="line">dialog = <span class="string">f'Hello <span class="subst">{name}</span>, your money is <span class="subst">{money:<span class="number">.2</span>f}</span>.'</span></span><br><span class="line"><span class="built_in">print</span>(dialog)</span><br></pre></td></tr></table></figure><blockquote><p>Hello Kahvia, your money is 143.26.</p></blockquote><ol start="2"><li>采用 format 方法</li></ol><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line">name = <span class="string">'Kahvia'</span></span><br><span class="line">name2 = <span class="string">'Adong'</span></span><br><span class="line">dialog = <span class="string">'Hello {0}, and {1}.'</span>.<span class="built_in">format</span>(name, name2)</span><br><span class="line"><span class="built_in">print</span>(dialog)</span><br><span class="line">dialog = <span class="string">'Hello {n1}, and {n2}.'</span>.<span class="built_in">format</span>(n1=name, n2=name2)</span><br><span class="line"><span class="built_in">print</span>(dialog)</span><br></pre></td></tr></table></figure><blockquote><p>Hello Kahvia, and Adong.<br />Hello Kahvia, and Adong.</p></blockquote><h3 id="自定义函数"><a class="markdownIt-Anchor" href="#自定义函数"></a> 自定义函数</h3><p>采用关键词 def 来定义函数，并跟随<code>:</code>表示下面的缩进行是函数体。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">def</span> <span class="title function_">make_friends</span>(<span class="params">name1, name2</span>):</span><br><span class="line"> <span class="built_in">print</span>(<span class="string">f"<span class="subst">{name1}</span> and <span class="subst">{name2}</span> are friends now!"</span>)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">name = <span class="string">'Kahvia'</span></span><br><span class="line">name2 = <span class="string">'Adong'</span></span><br><span class="line">make_friends(name, name2)</span><br></pre></td></tr></table></figure><blockquote><p>Kahvia and Adong are friends now!</p></blockquote><h3 id="引入模块"><a class="markdownIt-Anchor" href="#引入模块"></a> 引入模块</h3><p>采用 import 引入一个模块中的方法和变量。</p><ol><li><code>import statistics</code>,使用模块中的方法时，采用<code>statistics.median([1,2,3])</code></li><li><code>from statistics import median, mean</code>,使用方法时，采用<code>median([1,2,3])</code></li><li><code>from statistics import *</code>,使用方法同2。但是容易造成模块之间的方法或者变量冲突。</li></ol><p>常使用第一种和第二种。第三方模块可以在网站<a href="https://pypi.org/">PyPI · The Python Package Index</a>上进行查看。</p><h3 id="类"><a class="markdownIt-Anchor" href="#类"></a> 类</h3><h4 id="定义"><a class="markdownIt-Anchor" href="#定义"></a> 定义</h4><p>采用 class 关键词定义一个类，并在对应的代码块中采用<code>_init_</code>来定义初始化对象的构造函数。定义其它方法时，也必须要将 self 作为第一个形参。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Person</span>:</span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">__init__</span>(<span class="params">self, name</span>):</span><br><span class="line"> self.name = name</span><br><span class="line"></span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">say_hello</span>(<span class="params">self</span>):</span><br><span class="line"> <span class="built_in">print</span>(<span class="string">f'Hello my name is <span class="subst">{self.name}</span>.'</span>)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">Kahvia = Person(<span class="string">'Kahvia'</span>)</span><br><span class="line">Kahvia.say_hello()</span><br><span class="line"></span><br></pre></td></tr></table></figure><blockquote><p>Hello my name is Kahvia.</p></blockquote><h4 id="继承"><a class="markdownIt-Anchor" href="#继承"></a> 继承</h4><p>定义类的时候，后接括号包裹父类。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Teacher</span>(<span class="title class_ inherited__">Person</span>):</span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">__init__</span>(<span class="params">self, name, level</span>):</span><br><span class="line"> <span class="built_in">super</span>().__init__(name)</span><br><span class="line"> self.level = level</span><br><span class="line"></span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">teach</span>(<span class="params">self</span>):</span><br><span class="line"> <span class="built_in">print</span>(<span class="string">f"I am <span class="subst">{self.name}</span>, a teacher."</span>)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">class</span> <span class="title class_">Student</span>(<span class="title class_ inherited__">Person</span>):</span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">__init__</span>(<span class="params">self, name, class_no</span>):</span><br><span class="line"> <span class="built_in">super</span>().__init__(name)</span><br><span class="line"> self.class_no = class_no</span><br><span class="line"></span><br><span class="line"> <span class="keyword">def</span> <span class="title function_">study</span>(<span class="params">self</span>):</span><br><span class="line"> <span class="built_in">print</span>(<span class="string">f"I am <span class="subst">{self.name}</span>, a student."</span>)</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">t1 = Teacher(<span class="string">"Kahvia"</span>, <span class="number">6</span>)</span><br><span class="line">s1 = Student(<span class="string">"Adong"</span>, <span class="number">1</span>)</span><br><span class="line">t1.teach()</span><br><span class="line">s1.study()</span><br></pre></td></tr></table></figure><blockquote><p>I am Kahvia, a teacher.<br />I am Adong, a student.</p></blockquote><h3 id="文件读写"><a class="markdownIt-Anchor" href="#文件读写"></a> 文件读写</h3><p>注意，读模式打开文件时，若是文件不存在，会报错。</p><h4 id="readline"><a class="markdownIt-Anchor" href="#readline"></a> readline</h4><p>一次只读一行，内容包括换行符。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line">file = <span class="built_in">open</span>(<span class="string">'book.txt'</span>, <span class="string">'r'</span>, encoding=<span class="string">'utf-8'</span>)</span><br><span class="line"></span><br><span class="line"><span class="comment"># 像下面这样写是不对的，python不允许在条件语句中进行赋值操作，这是为了防止出现在比较中将 == 写成 = 的低级错误，这种错误不容易发现，因为可以运行。</span></span><br><span class="line"><span class="comment"># while (line = file.readline()) != "":</span></span><br><span class="line"><span class="comment"># print(line)</span></span><br><span class="line"></span><br><span class="line">line = file.readline()</span><br><span class="line"><span class="keyword">while</span> line != <span class="string">""</span>:</span><br><span class="line"> <span class="comment"># 打印的end设置为空，防止默认的换行与文件中的换行叠加。</span></span><br><span class="line"> <span class="built_in">print</span>(line, end=<span class="string">""</span>)</span><br><span class="line"> line = file.readline()</span><br><span class="line">file.close()</span><br></pre></td></tr></table></figure><blockquote><p>你存在<br />我深深的脑海里<br />我的心里</p></blockquote><h4 id="read"><a class="markdownIt-Anchor" href="#read"></a> read</h4><p>一次全读出来，不适合对大文件使用。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">file = <span class="built_in">open</span>(<span class="string">'book.txt'</span>, <span class="string">'r'</span>, encoding=<span class="string">'utf-8'</span>)</span><br><span class="line"><span class="comment"># 注意打印结尾有print默认的换行</span></span><br><span class="line"><span class="built_in">print</span>(file.read())</span><br><span class="line">file.close()</span><br></pre></td></tr></table></figure><blockquote><p>你存在<br />我深深的脑海里<br />我的心里</p></blockquote><h4 id="readlines"><a class="markdownIt-Anchor" href="#readlines"></a> readlines</h4><p>读出文件中所有行，放在列表中并返回。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">file = <span class="built_in">open</span>(<span class="string">'book.txt'</span>, <span class="string">'r'</span>, encoding=<span class="string">'utf-8'</span>)</span><br><span class="line"><span class="built_in">print</span>(file.readlines())</span><br><span class="line">file.close()</span><br></pre></td></tr></table></figure><blockquote><p>[‘你存在\n’, ‘我深深的脑海里\n’, ‘我的心里’]</p></blockquote><h4 id="with-open-as"><a class="markdownIt-Anchor" href="#with-open-as"></a> with open … as …</h4><p>这种写法可以不用close，执行完毕即close。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">'book.txt'</span>, <span class="string">'r'</span>, encoding=<span class="string">'utf-8'</span>) <span class="keyword">as</span> file:</span><br><span class="line"> <span class="comment"># 注意打印结尾有print默认的换行</span></span><br><span class="line"> <span class="built_in">print</span>(file.read())</span><br></pre></td></tr></table></figure><h4 id="write"><a class="markdownIt-Anchor" href="#write"></a> write</h4><p>write不会自动添加换行符，要换行只能自己补充<code>\n</code>。使用 w 模式打开时，若无文件会自动创建，有则清空。若是不希望清空，则需指定为 a 模式，即append，意为追加。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">with</span> <span class="built_in">open</span>(<span class="string">'book.txt'</span>, <span class="string">'w'</span>, encoding=<span class="string">'utf-8'</span>) <span class="keyword">as</span> file:</span><br><span class="line"> file.write(<span class="string">"Hello World"</span>)</span><br></pre></td></tr></table></figure><h4 id="同时读写"><a class="markdownIt-Anchor" href="#同时读写"></a> 同时读写</h4><p>正常情况下，指定打开模式为 r 时，只能读，指定 w 时，只能写。若要既能读又能写，则需要指定为<code>r+</code>，此时write语句会以追加的形式写入到文件后面，同append。</p><h3 id="异常处理"><a class="markdownIt-Anchor" href="#异常处理"></a> 异常处理</h3><p>使用 try…except…else… 来处理异常。</p><h3 id="代码测试"><a class="markdownIt-Anchor" href="#代码测试"></a> 代码测试</h3><p>使用 unittest 。</p><h3 id="高阶函数和匿名函数"><a class="markdownIt-Anchor" href="#高阶函数和匿名函数"></a> 高阶函数和匿名函数</h3><p>高阶函数：将另一个函数作为参数的函数。</p><p>匿名函数(lambda函数)：<code>lambda para1, para2, ... : para1 op para2 op ...</code>，比如<code>lambda num: num * 5</code>就是一个表达式，传入一个数字，返回五倍的数字。</p><p>lambda 表达式可用于高阶函数作为实参传递。</p>]]></content>
<summary type="html"><h3 id="字符串格式化"><a class="markdownIt-Anchor" href="#字符串格式化"></a> 字符串格式化</h3>
<p>格式化的过程中，如果遇到数字，可以使用 <code>:[格式]</code>来指定数字的格式。</p>
<ol>
<li</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="python" scheme="https://blog.kahvia.cn/tags/python/"/>
</entry>
<entry>
<title>LaTeX语法</title>
<link href="https://blog.kahvia.cn/2024/06/21/LaTeX.html"/>
<id>https://blog.kahvia.cn/2024/06/21/LaTeX.html</id>
<published>2024-06-21T10:03:10.459Z</published>
<updated>2024-07-17T16:07:06.530Z</updated>
<content type="html"><![CDATA[<h3 id="anzhiyu主题配置数学公式"><a class="markdownIt-Anchor" href="#anzhiyu主题配置数学公式"></a> Anzhiyu主题配置数学公式</h3><p>有两种方法。</p><p>方法一，参考<a href="https://www.yyyzyyyz.cn/posts/654d8712aff4/#4-%E4%BD%BF%E7%94%A8pandoc%E8%8E%B7%E5%BE%97%E6%9B%B4%E5%A5%BD%E7%9A%84mathjax%E6%94%AF%E6%8C%81">为hexo博客更换pandoc渲染</a>，使用<em>mathjax</em>无论是前端渲染还是后端渲染公式块都无法正常换行。</p><p>方法二，参考<a href="https://blog.windsky.tech/2021/01/30/Hexo-Katex/">Hexo博客渲染KaTeX数学公式</a>，可以正常渲染。</p><p>最终采用了第二种渲染方法。步骤如下所示。</p><ol><li><p>关闭主题自带的 mathjax 和 katex 。因为方法二采用的是自己启用 katex 。</p><figure class="highlight yaml"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># Math (数学)</span></span><br><span class="line"><span class="comment"># --------------------------------------</span></span><br><span class="line"><span class="comment"># About the per_page</span></span><br><span class="line"><span class="comment"># if you set it to true, it will load mathjax/katex script in each page (true 表示每一页都加载js)</span></span><br><span class="line"><span class="comment"># if you set it to false, it will load mathjax/katex script according to your setting (add the 'mathjax: true' in page's front-matter)</span></span><br><span class="line"><span class="comment"># (false 需要时加载，须在使用的 Markdown Front-matter 加上 mathjax: true)</span></span><br><span class="line"></span><br><span class="line"><span class="comment"># MathJax</span></span><br><span class="line"><span class="attr">mathjax:</span></span><br><span class="line"> <span class="attr">enable:</span> <span class="literal">false</span></span><br><span class="line"> <span class="attr">per_page:</span> <span class="literal">false</span></span><br><span class="line"></span><br><span class="line"><span class="comment"># KaTeX</span></span><br><span class="line"><span class="attr">katex:</span></span><br><span class="line"> <span class="attr">enable:</span> <span class="literal">false</span></span><br><span class="line"> <span class="attr">per_page:</span> <span class="literal">false</span></span><br><span class="line"> <span class="attr">hide_scrollbar:</span> <span class="literal">true</span></span><br></pre></td></tr></table></figure><p>为什么不用主题自带的 mathjax ，因为无法正确换行。<br />为什么不用主题自带的 katex ，因为渲染经常失灵，本地渲染成功后部署到 github 以后才是正常的，不过经常本地都渲染失败，根据我多方查找资料，这跟 pjax 有关，关掉主题中的 pjax 或许有效，但会影响其它功能。至于 pjax 如何使渲染失效，我不清楚，因为<a href="https://blog.pai233.top/20210930/hexo-katex/">路人甲</a>也不清楚，<a href="https://blog.aqcoder.cn/posts/6e665e82/#%E8%A7%A3%E5%86%B3%E8%BF%87%E7%A8%8B">路人乙</a>也不是很清楚。但终归是找到的方法二这样的解决方法。</p></li><li><p>卸载hexo自带的渲染渲染器，因为它渲染不了数学公式。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm uni hexo-renderer-marked</span><br></pre></td></tr></table></figure><p>安装 hexo-renderer-markdown-it-plus 渲染器。此渲染器默认包含且开启了 <code>@iktakahiro/markdown-it-katex</code> 插件，可渲染 11.1 版本以前的 KaTeXKATEX 公式。但 KaTeXKATEX 自 13.0 开始渲染机制发生了变化，需要更换为 <code>@andatoshiki/markdown-it-katex</code> 插件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">npm i hexo-renderer-markdown-it-plus</span><br><span class="line">npm install katex</span><br><span class="line">npm install @andatoshiki/markdown-it-katex</span><br></pre></td></tr></table></figure><p>在<code>_config.yml</code>中配置 markdown_it_plus 渲染器，即关闭其自带的 <code>@iktakahiro/markdown-it-katex</code> 插件，启用新版插件 <code>@andatoshiki/markdown-it-katex</code>。</p><figure class="highlight yaml"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="attr">markdown_it_plus:</span></span><br><span class="line"> <span class="comment"># ...</span></span><br><span class="line"> <span class="attr">plugins:</span></span><br><span class="line"> <span class="bullet">-</span> <span class="attr">plugin:</span></span><br><span class="line"> <span class="attr">name:</span> <span class="string">'@iktakahiro/markdown-it-katex'</span></span><br><span class="line"> <span class="attr">enable:</span> <span class="literal">false</span></span><br><span class="line"> <span class="bullet">-</span> <span class="attr">plugin:</span></span><br><span class="line"> <span class="attr">name:</span> <span class="string">'@andatoshiki/markdown-it-katex'</span></span><br><span class="line"> <span class="attr">enable:</span> <span class="literal">true</span></span><br></pre></td></tr></table></figure></li><li><p>在主题配置文件中，引入katex的css文件。</p><figure class="highlight yaml"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="attr">inject:</span></span><br><span class="line"> <span class="attr">head:</span></span><br><span class="line"> <span class="comment"># 自定义css</span></span><br><span class="line"> <span class="comment"># - <link rel="stylesheet" href="/css/custom.css" media="defer" onload="this.media='all'"></span></span><br><span class="line"> <span class="bullet">-</span> <span class="string"><link</span> <span class="string">rel="stylesheet"</span> <span class="string">href="https://lib.baomitu.com/KaTeX/latest/katex.min.css"></span></span><br></pre></td></tr></table></figure></li><li><p><code>hexo cl</code>、<code>hexo g</code>、<code>hexo s</code>，小三连查看效果，确认生效后<code>hexo cl</code>、<code>hexo g -d</code>，部署到云端。</p></li></ol><h3 id="分数"><a class="markdownIt-Anchor" href="#分数"></a> 分数</h3><p>frac ：fraction，分数。</p><figure class="highlight latex"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">\frac</span>{son}{mother}</span><br></pre></td></tr></table></figure><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi>s</mi><mi>o</mi><mi>n</mi></mrow><mrow><mi>m</mi><mi>o</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>r</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{son}{mother}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.7935600000000003em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.10756em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><h3 id="偏导"><a class="markdownIt-Anchor" href="#偏导"></a> 偏导</h3><p>partial ：偏爱的。</p><figure class="highlight latex"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">\frac</span>{<span class="keyword">\partial</span> f}{<span class="keyword">\partial</span> x}</span><br></pre></td></tr></table></figure><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>f</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\partial f}{\partial x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0574399999999997em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714399999999998em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><h3 id="向量"><a class="markdownIt-Anchor" href="#向量"></a> 向量</h3><p>vec ：vector，向量。</p><p>overrightarrow：上方右箭头。</p><p>overleftarrow：上方左箭头。</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mspace width="1em"/><mover accent="true"><mi>x</mi><mo stretchy="true">→</mo></mover><mspace width="1em"/><mover accent="true"><mi>y</mi><mo stretchy="true">←</mo></mover></mrow><annotation encoding="application/x-tex">\vec x \quad \overrightarrow x \quad \overleftarrow y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.147em;vertical-align:-0.19444em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9525600000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span class="svg-align" style="top:-3.43056em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:0.888em;"><svg width='400em' height='0.522em' viewBox='0 0 400000 522' preserveAspectRatio='xMaxYMin slice'><path d='M0 241v40h399891c-47.3 35.3-84 78-110 128-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/></svg></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9525600000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span><span class="svg-align" style="top:-3.43056em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:0.888em;"><svg width='400em' height='0.522em' viewBox='0 0 400000 522' preserveAspectRatio='xMinYMin slice'><path d='M400000 241H110l3-3c68.7-52.7 113.7-120 135-202 4-14.7 6-23 6-25 0-7.3-7-11-21-11-8 0-13.2.8-15.5 2.5-2.3 1.7-4.2 5.8-5.5 12.5-1.3 4.7-2.7 10.3-4 17-12 48.7-34.8 92-68.5 130S65.3 228.3 18 247c-10 4-16 7.7-18 11 0 8.7 6 14.3 18 17 47.3 18.7 87.8 47 121.5 85S196 441.3 208 490c.7 2 1.3 5 2 9s1.2 6.7 1.5 8c.3 1.3 1 3.3 2 6s2.2 4.5 3.5 5.5c1.3 1 3.3 1.8 6 2.5s6 1 10 1c14 0 21-3.7 21-11 0-2-2-10.3-6-25-20-79.3-65-146.7-135-202 l-3-3h399890zM100 241v40h399900v-40z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span></span></span></span></p><h3 id="点乘"><a class="markdownIt-Anchor" href="#点乘"></a> 点乘</h3><p>cdot：circle dot，圆点。</p><figure class="highlight latex"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">\vec</span> x <span class="keyword">\cdot</span> <span class="keyword">\vec</span> y</span><br></pre></td></tr></table></figure><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mo>⋅</mo><mover accent="true"><mi>y</mi><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec x \cdot \vec y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.9084399999999999em;vertical-align:-0.19444em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.17994em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span></span></span></span></p>]]></content>
<summary type="html"><h3 id="anzhiyu主题配置数学公式"><a class="markdownIt-Anchor" href="#anzhiyu主题配置数学公式"></a> Anzhiyu主题配置数学公式</h3>
<p>有两种方法。</p>
<p>方法一，参考<a href="http</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="latex" scheme="https://blog.kahvia.cn/tags/latex/"/>
</entry>
<entry>
<title>机器学习</title>
<link href="https://blog.kahvia.cn/2024/06/21/MachineLearning.html"/>
<id>https://blog.kahvia.cn/2024/06/21/MachineLearning.html</id>
<published>2024-06-21T07:47:15.746Z</published>
<updated>2024-06-25T17:49:53.153Z</updated>
<content type="html"><![CDATA[<h3 id="机器学习分类"><a class="markdownIt-Anchor" href="#机器学习分类"></a> 机器学习分类</h3><p>机器学习分为监督学习和非监督学习。</p><p>监督学习：输入数据得到“正确的”输出，输入与输出是映射关系。回归算法（Regression），比如用线性回归来预测房价；分类算法（Classification），比如输入肿瘤信息将其分类为良性、恶性等类别。</p><p>非监督学习：输入数据得到的输出没有“正确”的概念，常用于寻找数据中的结构。聚类算法（Clustering），将相似的数据归类在一起；异常检测（Anomaly Detection），找出不寻常的数据；降维（Dimensionality Reduction），将大数据集压缩成小数据集并尽可能减少信息丢失。</p><h3 id="线性回归"><a class="markdownIt-Anchor" href="#线性回归"></a> 线性回归</h3><p>x -> f -> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span></span></span> 。</p><ul><li>x 是输入变量（input variable），又称特征（feature）。</li><li>y 是输出变量（output variable），又称目标变量（target variable），是训练集（training set）中的实际真实值。</li><li>m 是训练样本数，数据集的大小。number of training examples。</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span></span></span> 是模型（model）预测值</li></ul><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>s</mi><mi>i</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi>e</mi><mspace width="1em"/><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>i</mi><mi>n</mi><mi>g</mi><mspace width="1em"/><mi>e</mi><mi>x</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mspace linebreak="newline"></mspace><mspace linebreak="newline"></mspace><mo stretchy="false">(</mo><msup><mi>x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo separator="true">,</mo><msup><mi>y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><msup><mi>i</mi><mrow><mi>t</mi><mi>h</mi></mrow></msup><mspace width="1em"/><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>i</mi><mi>n</mi><mi>g</mi><mspace width="1em"/><mi>e</mi><mi>x</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">(x,y) = single \quad training \quad example \\\\(x^{(i)},y^{(i)}) = i^{th} \quad training \quad example</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">a</span><span class="mord mathnormal">m</span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span></span><span class="mspace newline"></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.188em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">i</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">h</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">a</span><span class="mord mathnormal">m</span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span></span></span></span></span></p><p>通过训练集训练模型（model），然后给模型输入x，模型输出 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span></span></span> 作为预测值。</p><h4 id="单输入线性回归linear-regression-with-one-variable"><a class="markdownIt-Anchor" href="#单输入线性回归linear-regression-with-one-variable"></a> 单输入线性回归（Linear regression with one variable）</h4><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>o</mi><mi>d</mi><mi>e</mi><mi>l</mi><mo>:</mo><msub><mi>f</mi><mrow><mi>w</mi><mo separator="true">,</mo><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>w</mi><mi>x</mi><mo>+</mo><mi>b</mi></mrow><annotation encoding="application/x-tex">model : f_{w,b}(x) = wx + b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">b</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span></span></span></span></p><p>w 代表权重（weight），b 代表基础值（base value）。</p><h5 id="代价函数"><a class="markdownIt-Anchor" href="#代价函数"></a> 代价函数</h5><p>Cost function : Squared error cost function.</p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>J</mi><mo stretchy="false">(</mo><mi>w</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></msubsup><mo stretchy="false">(</mo><msup><mover accent="true"><mi>y</mi><mo>^</mo></mover><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo>−</mo><msup><mi>y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></msubsup><mo stretchy="false">(</mo><msub><mi>f</mi><mrow><mi>w</mi><mo separator="true">,</mo><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><msup><mi>x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>−</mo><msup><mi>y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">J(w,b) = \frac{1}{2m} \sum\limits_{i=1}^{m}(\hat{y}^{(i)} - y^{(i)})^2 = \frac1{2m} \sum\limits_{i=1}^m(f_{w,b}(x^{(i)}) - y^{(i)})^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.329066em;vertical-align:-0.9776689999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.19444em;"><span class="mord">^</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.329066em;vertical-align:-0.9776689999999999em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3513970000000004em;"><span style="top:-2.122331em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9776689999999999em;"><span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">b</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8879999999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></p><p>训练集的代价越小，模型越符合预期。代价函数中的 2 是为了梯度下降中求偏导时使公式更加简洁，因为 J 求偏导时外函数的导数会产生乘 2 ，正好抵消。</p><h5 id="梯度下降gradient-descent-algorithm"><a class="markdownIt-Anchor" href="#梯度下降gradient-descent-algorithm"></a> 梯度下降（Gradient descent algorithm）</h5><p>用于最小化代价函数的一种算法。参考<a href="https://www.bilibili.com/video/BV19f421Q7CL/?spm_id_from=333.337.search-card.all.click&vd_source=c1d0ac10ebe4bb4e8cf6648904e6ed40">不至于吧，梯度下降简单得有点离谱了啊</a>。</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>w</mi><mo>=</mo><mi>w</mi><mo>−</mo><mi>α</mi><mfrac><mi mathvariant="normal">∂</mi><mrow><mi mathvariant="normal">∂</mi><mi>w</mi></mrow></mfrac><mi>J</mi><mo stretchy="false">(</mo><mi>w</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo><mspace linebreak="newline"></mspace><mspace linebreak="newline"></mspace><mi>b</mi><mo>=</mo><mi>b</mi><mo>−</mo><mi>α</mi><mfrac><mi mathvariant="normal">∂</mi><mrow><mi mathvariant="normal">∂</mi><mi>b</mi></mrow></mfrac><mi>J</mi><mo stretchy="false">(</mo><mi>w</mi><mo separator="true">,</mo><mi>b</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">w = w - \alpha \frac{\partial}{\partial w} J(w,b) \\\\b = b - \alpha \frac{\partial}{\partial b} J(w,b)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span></span><span class="mspace newline"></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.05744em;vertical-align:-0.686em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.37144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">b</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">b</span><span class="mclose">)</span></span></span></span></span></p><p>其中，α 代表学习率，用于控制步长，防止步长过大导致 J 在最小值附近反复横跳而无法收敛。因此学习率的合适取值很重要。</p><p>偏导则作为方向以及基本步长。梯度是偏导数构成的向量。</p><h4 id="多元线性回归multiple-linear-regression"><a class="markdownIt-Anchor" href="#多元线性回归multiple-linear-regression"></a> 多元线性回归（Multiple linear regression）</h4><p>注：不是多元回归（Multivariate regression）。</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>x</mi><mi>j</mi></msub><mo>=</mo><msup><mi>j</mi><mrow><mi>t</mi><mi>h</mi></mrow></msup><mi>f</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi><mspace linebreak="newline"></mspace><mi>n</mi><mo>=</mo><mi>n</mi><mi>u</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mspace width="1em"/><mi>o</mi><mi>f</mi><mspace width="1em"/><mi>f</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi><mi>s</mi><mspace linebreak="newline"></mspace><msup><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo>=</mo><mi>f</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi><mi>s</mi><mspace width="1em"/><mi>o</mi><mi>f</mi><mspace width="1em"/><msup><mi>i</mi><mrow><mi>t</mi><mi>h</mi></mrow></msup><mspace width="1em"/><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>i</mi><mi>n</mi><mi>g</mi><mspace width="1em"/><mi>e</mi><mi>x</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi><mspace linebreak="newline"></mspace><msubsup><mi>x</mi><mi>j</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><mi>v</mi><mi>a</mi><mi>l</mi><mi>u</mi><mi>e</mi><mspace width="1em"/><mi>o</mi><mi>f</mi><mspace width="1em"/><mi>f</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi><mspace width="1em"/><mi>j</mi><mspace width="1em"/><mi>i</mi><mi>n</mi><mspace width="1em"/><msup><mi>i</mi><mrow><mi>t</mi><mi>h</mi></mrow></msup><mspace width="1em"/><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi><mi>i</mi><mi>n</mi><mi>g</mi><mspace width="1em"/><mi>e</mi><mi>x</mi><mi>a</mi><mi>m</mi><mi>p</mi><mi>l</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">x_j = j^{th}feature \\n = number \quad of \quad features \\\vec x^{(i)} = features \quad of \quad i^{th} \quad training \quad example \\x^{(i)}_j = value \quad of \quad feature \quad j \quad in \quad i^{th} \quad training \quad example</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">h</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">e</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">n</span><span class="mord mathnormal">u</span><span class="mord mathnormal">m</span><span class="mord mathnormal">b</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.938em;vertical-align:0em;"></span><span class="mord"><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093548em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal">i</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">h</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">a</span><span class="mord mathnormal">m</span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:1.4577719999999998em;vertical-align:-0.412972em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.4231360000000004em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.412972em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093548em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">u</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">e</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal">i</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">h</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:1em;"></span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">a</span><span class="mord mathnormal">m</span><span class="mord mathnormal">p</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span></span></span></span></span></p><p>现引入多个特征值x，每个x的下标不同。每个特征值都有对应的权重。</p><p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>f</mi><mrow><mover accent="true"><mi>w</mi><mo>⃗</mo></mover><mo separator="true">,</mo><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mo stretchy="false">)</mo><mo>=</mo><msub><mi>w</mi><mn>1</mn></msub><msub><mi>x</mi><mn>1</mn></msub><mo>+</mo><msub><mi>w</mi><mn>2</mn></msub><msub><mi>x</mi><mn>2</mn></msub><mo>+</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>+</mo><msub><mi>w</mi><mi>n</mi></msub><msub><mi>x</mi><mi>n</mi></msub><mo>+</mo><mi>b</mi><mo>=</mo><mover accent="true"><mi>w</mi><mo>⃗</mo></mover><mo>⋅</mo><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mo>+</mo><mi>b</mi><mspace linebreak="newline"></mspace><mover accent="true"><mi>w</mi><mo>⃗</mo></mover><mo>=</mo><mo stretchy="false">[</mo><msub><mi>w</mi><mn>1</mn></msub><mspace width="1em"/><msub><mi>w</mi><mn>2</mn></msub><mspace width="1em"/><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mspace width="1em"/><msub><mi>w</mi><mi>n</mi></msub><mo stretchy="false">]</mo><mspace linebreak="newline"></mspace><mover accent="true"><mi>x</mi><mo>⃗</mo></mover><mo>=</mo><mo stretchy="false">[</mo><msub><mi>x</mi><mn>1</mn></msub><mspace width="1em"/><msub><mi>x</mi><mn>2</mn></msub><mspace width="1em"/><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mspace width="1em"/><msub><mi>x</mi><mi>n</mi></msub><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f_{\vec w,b}(\vec x) = w_1x_1 + w_2x_2 + ... + w_nx_n + b = \vec w \cdot \vec x + b \\\vec w = [w_1 \quad w_2 \quad ... \quad w_n] \\\vec x = [x_1 \quad x_2 \quad ... \quad x_n]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.041108em;vertical-align:-0.2911079999999999em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.5450000000000004em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord accent mtight"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-2.714em;"><span class="pstrut" style="height:2.714em;"></span><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span><span style="top:-2.714em;"><span class="pstrut" style="height:2.714em;"></span><span class="accent-body" style="left:-0.15216em;"><span class="overlay mtight" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">b</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2911079999999999em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.73333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.15216em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.79733em;vertical-align:-0.08333em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal">b</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.15216em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span></span><span class="mspace newline"></span><span class="base"><span class="strut" style="height:0.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">x</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.20772em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 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style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:1em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">]</span></span></span></span></span></p><h5 id="向量化"><a class="markdownIt-Anchor" href="#向量化"></a> 向量化</h5><p>在 python 中，我们常使用 numpy 库来进行科学计算。</p><p>通过<code>np.array()</code>初始化一维数组，通过<code>np.dot()</code>方法调用点乘运算。点乘方法比单纯的循环遍历相乘之和更加快速，特别是数据量大的情况下，因为 numpy 方法可以使用一些硬件来实现加速计算，比如分成多个部分并行计算？这比单纯的循环或许快上许多。</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line">w = np.array([<span class="number">1.0</span>, <span class="number">2.0</span>, <span class="number">3.0</span>])</span><br><span class="line">x = np.array([<span class="number">10</span>, <span class="number">20</span>, <span class="number">30</span>])</span><br><span class="line">b = <span class="number">2</span></span><br><span class="line"><span class="comment"># 通过点乘的方式来简化运算</span></span><br><span class="line">f = np.dot(w,x) + b</span><br></pre></td></tr></table></figure><h5 id="特征缩放"><a class="markdownIt-Anchor" href="#特征缩放"></a> 特征缩放</h5><p>在使用梯度下降求解模型参数以最小化代价函数时，有时因为不同参数的取值范围不同，特别是一个范围特别大，一个范围特别小的情况下，会导致不同参数在各自方向上的下降步子相差较大。如果说梯度下降最好的情况是不同方向上的步子一致，经过合成后迈出的一步刚好是去往最低点的方向，那么上面提到的情况就是走得有点斜，相比较之下就是饶了圈子，虽然也能到达最低点，但是由于走的距离变长，需要的步子也就变多，即迭代次数变多。如下图所示，较优的是步子较少的路线，绕远路的则是较差路线。</p><p><img src="https://pics.kahvia.cn/img/%E7%89%B9%E5%BE%81%E7%BC%A9%E6%94%BE%E8%83%8C%E6%99%AF%E7%A4%BA%E4%BE%8B.png" alt="特征缩放背景图例" /></p><p>为了尽可能减少迭代次数，通过“特征缩放”可以协调不同方向上的下降距离，以优化梯度下降。而特征缩放的做法就是：对数据集的各个特征值进行处理，使得不同的特征具有相似的取值范围。下面有两种简单方法。</p><ol><li><strong>均值归一化（Mean normalization）</strong>：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>μ</mi><mi>i</mi></msub></mrow><mrow><msub><mi>x</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_i = \frac {x_i - \mu_i} {x_{max} - x_{min}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.2995389999999998em;vertical-align:-0.44509999999999994em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.854439em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">μ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.44509999999999994em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>，其中 μ 代表某个特征中的平均值，这是缩放到 0 的周围。</li><li><strong>最小-最大值归一化（min-max normalization）</strong>：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><mrow><msub><mi>x</mi><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mo>−</mo><msub><mi>x</mi><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">x_i = \frac {x_i - x_{min}} {x_{max} - x_{min}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.263531em;vertical-align:-0.44509999999999994em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8184309999999999em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.44509999999999994em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>，这是缩放到 [0,1] 区间。</li></ol>]]></content>
<summary type="html"><h3 id="机器学习分类"><a class="markdownIt-Anchor" href="#机器学习分类"></a> 机器学习分类</h3>
<p>机器学习分为监督学习和非监督学习。</p>
<p>监督学习：输入数据得到“正确的”输出，输入与输出是映射关系。回归算法（</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="MachineLeaning" scheme="https://blog.kahvia.cn/tags/MachineLeaning/"/>
</entry>
<entry>
<title>Anaconda</title>
<link href="https://blog.kahvia.cn/2024/06/05/Anaconda.html"/>
<id>https://blog.kahvia.cn/2024/06/05/Anaconda.html</id>
<published>2024-06-05T15:18:40.580Z</published>
<updated>2024-06-06T06:59:45.873Z</updated>
<content type="html"><![CDATA[<h3 id="删除conda源"><a class="markdownIt-Anchor" href="#删除conda源"></a> 删除conda源</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">conda config --remove-key channels</span><br></pre></td></tr></table></figure><h3 id="conda配置"><a class="markdownIt-Anchor" href="#conda配置"></a> conda配置</h3><p><a href="https://mirrors4.tuna.tsinghua.edu.cn/help/anaconda/">anaconda | 镜像站使用帮助 | 清华大学开源软件镜像站</a></p><p>修改<code>C:\Users\用户名\.condarc</code>文件内容为下面内容。其中envs_dirs是指定conda环境的安装位置。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line">channels:</span><br><span class="line"> - defaults</span><br><span class="line">show_channel_urls: <span class="literal">true</span></span><br><span class="line">default_channels:</span><br><span class="line"> - https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/main</span><br><span class="line"> - https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/r</span><br><span class="line"> - https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/msys2</span><br><span class="line">custom_channels:</span><br><span class="line"> conda-forge: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> msys2: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> bioconda: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> menpo: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> pytorch: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> pytorch-lts: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> simpleitk: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud</span><br><span class="line"> deepmodeling: https://mirrors.tuna.tsinghua.edu.cn/anaconda/cloud/</span><br><span class="line">envs_dirs:</span><br><span class="line"> - D://Anaconda//envs</span><br><span class="line"> </span><br></pre></td></tr></table></figure><p>通过<code>conda info</code>查看conda信息。看到D:\Anaconda\envs在envs directories的第一位，就代表虚拟环境默认安装位置设置好了。通过channel URLs也可以看见清华镜像源也设置好了。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br></pre></td><td class="code"><pre><span class="line">(adong) PS C:\WINDOWS\system32> conda info</span><br><span class="line"></span><br><span class="line"> active environment : adong</span><br><span class="line"> active <span class="built_in">env</span> location : D:\Anaconda\envs\adong</span><br><span class="line"> shell level : 2</span><br><span class="line"> user config file : C:\Users\91430\.condarc</span><br><span class="line"> populated config files : C:\Users\91430\.condarc</span><br><span class="line"> conda version : 24.1.2</span><br><span class="line"> conda-build version : 24.1.2</span><br><span class="line"> python version : 3.11.7.final.0</span><br><span class="line"> solver : libmamba (default)</span><br><span class="line"> virtual packages : __archspec=1=x86_64</span><br><span class="line"> __conda=24.1.2=0</span><br><span class="line"> __cuda=12.3=0</span><br><span class="line"> __win=0=0</span><br><span class="line"> base environment : D:\Anaconda (writable)</span><br><span class="line"> conda av data <span class="built_in">dir</span> : D:\Anaconda\etc\conda</span><br><span class="line"> conda av metadata url : None</span><br><span class="line"> channel URLs : https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/main/win-64</span><br><span class="line"> https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/main/noarch</span><br><span class="line"> https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/r/win-64</span><br><span class="line"> https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/r/noarch</span><br><span class="line"> https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/msys2/win-64</span><br><span class="line"> https://mirrors.tuna.tsinghua.edu.cn/anaconda/pkgs/msys2/noarch</span><br><span class="line"> package cache : D:\Anaconda\pkgs</span><br><span class="line"> C:\Users\91430\.conda\pkgs</span><br><span class="line"> C:\Users\91430\AppData\Local\conda\conda\pkgs</span><br><span class="line"> envs directories : D:\Anaconda\envs</span><br><span class="line"> C:\Users\91430\.conda\envs</span><br><span class="line"> C:\Users\91430\AppData\Local\conda\conda\envs</span><br><span class="line"> platform : win-64</span><br><span class="line"> user-agent : conda/24.1.2 requests/2.31.0 CPython/3.11.7 Windows/10 Windows/10.0.22000 solver/libmamba conda-libmamba-solver/24.1.0 libmambapy/1.5.6 aau/0.4.3 c/2cby9s0faIgGPUHiAZNUZA s/l8VpJfZM5eNDkpX7Ia9NMQ e/678Mj-yGtTUNyUgyuxwmKw</span><br><span class="line"> administrator : True</span><br><span class="line"> netrc file : None</span><br><span class="line"> offline mode : False</span><br></pre></td></tr></table></figure><h3 id="吴恩达机器学习optional-labs环境配置"><a class="markdownIt-Anchor" href="#吴恩达机器学习optional-labs环境配置"></a> 吴恩达机器学习Optional Labs环境配置</h3><p>采用的是JupyterNotebook、JupyterLab，以及lab的一些插件。</p><p>由于安装的anaconda的base环境自带一套Jupyter，在Jupyter以及lab插件的版本上，或许存在兼容问题，比如我在base环境下查看拓展。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line">(base) C:\Users\91430>jupyter labextension list</span><br><span class="line">JupyterLab v4.0.13</span><br><span class="line">D:\Anaconda\share\jupyter\labextensions</span><br><span class="line"> jupyter-matplotlib v0.11.4 enabled ok</span><br><span class="line"> jupyterlab-plotly v5.15.0 enabled X</span><br><span class="line"> @jupyter-notebook/lab-extension v7.0.8 enabled ok</span><br><span class="line"> @jupyter-widgets/jupyterlab-manager v5.0.11 enabled ok (python, jupyterlab_widgets)</span><br><span class="line"> @lckr/jupyterlab_variableinspector v3.1.0 enabled ok (python, lckr_jupyterlab_variableinspector)</span><br><span class="line"> @pyviz/jupyterlab_pyviz v3.0.0 enabled ok</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> The following extensions are outdated:</span><br><span class="line"> jupyterlab-plotly</span><br><span class="line"></span><br><span class="line"> Consider checking <span class="keyword">if</span> an update is available <span class="keyword">for</span> these packages.</span><br></pre></td></tr></table></figure><p>可以看到 plotly 的版本是有问题的。刚安装anaconda的时候，Lab的版本和plotly的版本比现在还高，后来，我参考了<a href="https://github.com/jupyterlab/jupyterlab/issues/14590">这个Issue</a>，将 Lab 和 plotly 进行降级，期望能兼容，然而并没有，结果如上所示。</p><p>所以我新建了一个conda环境<code>conda create -n adong python=3.7</code>，其中n代表name，adong则是我取的环境名，后面可以接环境要安装的包，这里安装的python3.7。</p><p>安装完成后，通过<code>conda activate adong</code>切换到新环境，输入<code>conda install "jupyterlab>=3" "ipywidgets>=7.6"</code>安装 jupyterlab 和插件ipywidgets。此后，缺啥装啥就行了，通过<code>conda install xxx</code>进行安装即可。</p><p>有一些必要的，比如<code>numpy matplotlib ipympl</code>。安装完成后，在该环境下通过输入命令<code>jupyter notebook</code>，即可正常使用相关功能，效果如下所示。</p><p><img src="https://pics.kahvia.cn/img/jupyterlab%E5%B1%95%E7%A4%BA.gif" alt="效果展示" /></p>]]></content>
<summary type="html"><h3 id="删除conda源"><a class="markdownIt-Anchor" href="#删除conda源"></a> 删除conda源</h3>
<figure class="highlight bash"><table><tr><td class="gutt</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="Anaconda" scheme="https://blog.kahvia.cn/tags/Anaconda/"/>
</entry>
<entry>
<title>SSH连接问题</title>
<link href="https://blog.kahvia.cn/2024/06/02/SshProblems.html"/>
<id>https://blog.kahvia.cn/2024/06/02/SshProblems.html</id>
<published>2024-06-02T05:52:50.144Z</published>
<updated>2024-06-02T06:26:36.246Z</updated>
<content type="html"><![CDATA[<h3 id="问题描述"><a class="markdownIt-Anchor" href="#问题描述"></a> 问题描述</h3><p>不知从哪一天开始，xshell突然无法连接我的云服务器。在那一天之前，一切正常。</p><h3 id="故障原因"><a class="markdownIt-Anchor" href="#故障原因"></a> 故障原因</h3><p>在参考其他人博客内容进行故障排错无果后，我突发奇想，将校园网换成热点试了一下，结果成功了。所以故障原因大概率是校园网。去网上搜了一下，可能是校园网设置了ssh拦截，所以校园网不管连接哪个服务器的22端口都不行。解决方法参考<a href="https://blog.csdn.net/Gaowumao/article/details/118272547">该博客文章</a>。</p><h3 id="解决方法"><a class="markdownIt-Anchor" href="#解决方法"></a> 解决方法</h3><ol><li><code>vim /etc/ssh/sshd_config</code>打开配置修改页面</li><li>添加自定义端口<code>Port 1022</code></li><li><code>systemctl restart sshd</code>重启sshd服务(centos7写法)</li><li><code>firewall-cmd --zone=public --add-port=1022/tcp --permanent</code>为防火墙打开对应的端口（未开启防火墙则省略这一步）</li><li><code>firewall-cmd --reload</code>防火墙重新加载配置（未开启防火墙则省略这一步）</li><li><code>firewall-cmd --list-all</code>查看已开放端口列表（未开启防火墙则省略这一步），出现1022则成功</li><li>去服务器服务商设置安全策略（或者有的地方叫安全组），入口规则添加1022，即允许外部访问服务器1022端口</li></ol><p>这样一套小连招下来，我的Xshell就能通过1022端口正常连接服务器了。</p><h3 id="参考博客"><a class="markdownIt-Anchor" href="#参考博客"></a> 参考博客</h3><p><a href="https://blog.csdn.net/qq_45782768/article/details/130174381">校园网SSH连接不上阿里云_校园网 用不了ssh-CSDN博客</a></p><p><a href="https://www.cnblogs.com/yizhipanghu/p/11171211.html">Centos7 防火墙开放端口，查看状态，查看开放端口 - 香菜哥哥 - 博客园 (cnblogs.com)</a></p><p><a href="https://blog.csdn.net/Gaowumao/article/details/118272547">XShell 无法连接云服务器的那些坑_为什么连校园网无法用xshell-CSDN博客</a></p><p><a href="https://blog.csdn.net/qq_50956771/article/details/136628785?utm_medium=distribute.pc_relevant.none-task-blog-2~default~baidujs_baidulandingword~default-0-136628785-blog-118272547.235%5Ev43%5Epc_blog_bottom_relevance_base6&spm=1001.2101.3001.4242.1&utm_relevant_index=3">踩坑：xshell连接阿里云失败 “Could not connect to ‘xxxxxxxxx‘: Connection failed.“,校园网_could not connect to ‘116.63.168.95’ (port 2673): -CSDN博客</a></p>]]></content>
<summary type="html"><h3 id="问题描述"><a class="markdownIt-Anchor" href="#问题描述"></a> 问题描述</h3>
<p>不知从哪一天开始，xshell突然无法连接我的云服务器。在那一天之前，一切正常。</p>
<h3 id="故障原因"><a clas</summary>
<category term="小问题" scheme="https://blog.kahvia.cn/categories/%E5%B0%8F%E9%97%AE%E9%A2%98/"/>
<category term="ssh centos7 xshell" scheme="https://blog.kahvia.cn/tags/ssh-centos7-xshell/"/>
</entry>
<entry>
<title>DaisyUI指南</title>
<link href="https://blog.kahvia.cn/2024/04/19/DaisyUI.html"/>
<id>https://blog.kahvia.cn/2024/04/19/DaisyUI.html</id>
<published>2024-04-19T15:29:10.512Z</published>
<updated>2024-04-21T10:01:19.246Z</updated>
<content type="html"><![CDATA[<h3 id="主题切换"><a class="markdownIt-Anchor" href="#主题切换"></a> 主题切换</h3><p>参考<a href="https://daisyui.com/components/theme-controller/">主题控制器</a>。以下甄选了几个好看的主题。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">/** <span class="doctag">@type</span> {<span class="type">import('tailwindcss').Config</span>} */</span></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">content</span>: [<span class="string">"./src/**/*.{html,js,vue}"</span>],</span><br><span class="line"> <span class="attr">theme</span>: {</span><br><span class="line"> <span class="attr">extend</span>: {},</span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [<span class="built_in">require</span>(<span class="string">"daisyui"</span>)],</span><br><span class="line"> <span class="attr">daisyui</span>: {</span><br><span class="line"> <span class="attr">themes</span>: [</span><br><span class="line"> <span class="string">"light"</span>,</span><br><span class="line"> <span class="string">"dark"</span>,</span><br><span class="line"> <span class="string">"halloween"</span>,</span><br><span class="line"> <span class="string">"garden"</span>,</span><br><span class="line"> <span class="string">"forest"</span>,</span><br><span class="line"> <span class="string">"lofi"</span>,</span><br><span class="line"> <span class="string">"pastel"</span>,</span><br><span class="line"> <span class="string">"fantasy"</span>,</span><br><span class="line"> <span class="string">"wireframe"</span>,</span><br><span class="line"> <span class="string">"dracula"</span>,</span><br><span class="line"> <span class="string">"cmyk"</span>,</span><br><span class="line"> <span class="string">"autumn"</span>,</span><br><span class="line"> ], <span class="comment">// false: only light + dark | true: all themes | array: specific themes like this ["light", "dark", "cupcake"]</span></span><br><span class="line"> <span class="attr">darkTheme</span>: <span class="string">"dark"</span>, <span class="comment">// name of one of the included themes for dark mode</span></span><br><span class="line"> <span class="attr">base</span>: <span class="literal">true</span>, <span class="comment">// applies background color and foreground color for root element by default</span></span><br><span class="line"> <span class="attr">styled</span>: <span class="literal">true</span>, <span class="comment">// include daisyUI colors and design decisions for all components</span></span><br><span class="line"> <span class="attr">utils</span>: <span class="literal">true</span>, <span class="comment">// adds responsive and modifier utility classes</span></span><br><span class="line"> <span class="attr">prefix</span>: <span class="string">""</span>, <span class="comment">// prefix for daisyUI classnames (components, modifiers and responsive class names. Not colors)</span></span><br><span class="line"> <span class="attr">logs</span>: <span class="literal">true</span>, <span class="comment">// Shows info about daisyUI version and used config in the console when building your CSS</span></span><br><span class="line"> <span class="attr">themeRoot</span>: <span class="string">":root"</span>, <span class="comment">// The element that receives theme color CSS variables</span></span><br><span class="line"> },</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"></span><br></pre></td></tr></table></figure><h4 id="我的主题切换器"><a class="markdownIt-Anchor" href="#我的主题切换器"></a> 我的主题切换器</h4><p>其中 tabindex=“0” 代表元素能否通过进行聚焦（用点的或者Tab键），此处第一个tabindex="0"不能省略，因为下面的ul的dropdown-content的底层css样式写的就是：上面那个Theme div聚焦了，下面这个列表才显示。至于第二个ul的聚焦，没啥用，可以删掉，因为input能直接聚焦。</p><p>通过 <strong>:checked=“index == themeIndex”</strong>来初始化主题选择器的<strong>radio</strong>的选项默认选中。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <div class="dropdown"></span><br><span class="line"> <div tabindex="0" role="button" class="btn m-1"></span><br><span class="line"> Theme</span><br><span class="line"> <svg width="12px" height="12px" class="h-2 w-2 fill-current opacity-60 inline-block"</span><br><span class="line"> xmlns="http://www.w3.org/2000/svg" viewBox="0 0 2048 2048"></span><br><span class="line"> <path d="M1799 349l242 241-1017 1017L7 590l242-241 775 775 775-775z"></path></span><br><span class="line"> </svg></span><br><span class="line"> </div></span><br><span class="line"> <ul tabindex="0" class="dropdown-content z-[1] p-2 shadow-2xl bg-base-300 rounded-box w-52"></span><br><span class="line"> <li v-for="(theme, index) in themeList" @click="changeTheme(index, theme)"></span><br><span class="line"> <input type="radio" name="theme-dropdown"</span><br><span class="line"> class="theme-controller btn btn-sm btn-block btn-ghost justify-start" :aria-label="theme"</span><br><span class="line"> :value="theme" :checked="index == themeIndex" /></span><br><span class="line"> </li></span><br><span class="line"> </ul></span><br><span class="line"> </div></span><br><span class="line"></template></span><br><span class="line"></span><br><span class="line"><script setup></span><br><span class="line">import { ref, onMounted } from 'vue';</span><br><span class="line">import { useThemeStore } from '@/stores/themeStore';</span><br><span class="line"></span><br><span class="line">const { changeThemeTo, getCurrentThemeIndex } = useThemeStore();</span><br><span class="line"></span><br><span class="line">const themeIndex = ref(0);</span><br><span class="line">const themeList = ref([</span><br><span class="line"> "light",</span><br><span class="line"> "dark",</span><br><span class="line"> "halloween",</span><br><span class="line"> "garden",</span><br><span class="line"> "forest",</span><br><span class="line"> "lofi",</span><br><span class="line"> "pastel",</span><br><span class="line"> "fantasy",</span><br><span class="line"> "wireframe",</span><br><span class="line"> "black",</span><br><span class="line"> "luxury",</span><br><span class="line"> "dracula",</span><br><span class="line"> "cmyk",</span><br><span class="line"> "autumn",</span><br><span class="line">])</span><br><span class="line"></span><br><span class="line">function changeTheme(index, themeName) {</span><br><span class="line"> themeIndex.value = index;</span><br><span class="line"> changeThemeTo(index, themeName);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">onMounted(() => {</span><br><span class="line"> themeIndex.value = getCurrentThemeIndex();</span><br><span class="line">})</span><br><span class="line"></span><br><span class="line"></script></span><br><span class="line"></span><br><span class="line"><style scoped></style></span><br></pre></td></tr></table></figure><p>以下是pinia持久化的内容。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//themeStore.js</span></span><br><span class="line"><span class="keyword">import</span> { ref } <span class="keyword">from</span> <span class="string">'vue'</span></span><br><span class="line"><span class="keyword">import</span> { defineStore } <span class="keyword">from</span> <span class="string">'pinia'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> useThemeStore = <span class="title function_">defineStore</span>(<span class="string">'theme'</span>, <span class="function">() =></span> {</span><br><span class="line"> <span class="keyword">const</span> theme = <span class="title function_">ref</span>(<span class="string">'light'</span>);</span><br><span class="line"> <span class="keyword">const</span> themeIndex = <span class="title function_">ref</span>(<span class="number">0</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">initialTheme</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">let</span> html = <span class="variable language_">document</span>.<span class="title function_">getElementsByTagName</span>(<span class="string">'html'</span>)[<span class="number">0</span>];</span><br><span class="line"> html.<span class="title function_">setAttribute</span>(<span class="string">'data-theme'</span>, theme.<span class="property">value</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">changeThemeTo</span>(<span class="params">index, themeName</span>) {</span><br><span class="line"> themeIndex.<span class="property">value</span> = index;</span><br><span class="line"> theme.<span class="property">value</span> = themeName;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">getCurrentThemeIndex</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">return</span> themeIndex.<span class="property">value</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> { theme, themeIndex, initialTheme, changeThemeTo, getCurrentThemeIndex }</span><br><span class="line">}, {</span><br><span class="line"> <span class="attr">persist</span>: <span class="literal">true</span></span><br><span class="line">})</span><br><span class="line"></span><br></pre></td></tr></table></figure><p>即便在控制器中初始化了默认<strong>radio</strong>的默认选中，但是在App.vue的onMounted函数中调用初始化主题仍然是必要的。因为主题控制器大多在导航栏中，而有的登陆界面中没有导航栏，意味着主题控制器未生效，此时需要根据本地数据主动初始化主题。</p><h3 id="封装好的popingalert"><a class="markdownIt-Anchor" href="#封装好的popingalert"></a> 封装好的PopingAlert</h3><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="tag"><<span class="name">div</span> <span class="attr">ref</span>=<span class="string">"alert"</span> <span class="attr">role</span>=<span class="string">"alert"</span> <span class="attr">class</span>=<span class="string">"alert w-fit absolute left-1/2 -translate-x-1/2 transition-all duration-1000"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">:class</span>=<span class="string">"{ 'opacity-0 invisible -top-3': !visible, 'opacity-100 top-3': visible, [alertTypeClass]: true }"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">v-if</span>=<span class="string">"type == 'default'"</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">class</span>=<span class="string">"stroke-info shrink-0 w-6 h-6"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M13 16h-1v-4h-1m1-4h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"</span>></span><span class="tag"></<span class="name">path</span>></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">v-if</span>=<span class="string">"type == 'info'"</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">class</span>=<span class="string">"stroke-current shrink-0 w-6 h-6"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M13 16h-1v-4h-1m1-4h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"</span>></span><span class="tag"></<span class="name">path</span>></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">v-if</span>=<span class="string">"type == 'success'"</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">class</span>=<span class="string">"stroke-current shrink-0 h-6 w-6"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z"</span> /></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">v-if</span>=<span class="string">"type == 'warning'"</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">class</span>=<span class="string">"stroke-current shrink-0 h-6 w-6"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M12 9v2m0 4h.01m-6.938 4h13.856c1.54 0 2.502-1.667 1.732-3L13.732 4c-.77-1.333-2.694-1.333-3.464 0L3.34 16c-.77 1.333.192 3 1.732 3z"</span> /></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">v-if</span>=<span class="string">"type == 'error'"</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">class</span>=<span class="string">"stroke-current shrink-0 h-6 w-6"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M10 14l2-2m0 0l2-2m-2 2l-2-2m2 2l2 2m7-2a9 9 0 11-18 0 9 9 0 0118 0z"</span> /></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="tag"><<span class="name">span</span>></span>{{ messgae }}<span class="tag"></<span class="name">span</span>></span></span><br><span class="line"><span class="tag"></<span class="name">div</span>></span></span><br></pre></td></tr></table></figure><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { ref, computed } <span class="keyword">from</span> <span class="string">'vue'</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> alert = <span class="title function_">ref</span>(<span class="literal">null</span>);</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> type = <span class="title function_">ref</span>(<span class="string">"default"</span>)</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> messgae = <span class="title function_">ref</span>(<span class="string">"Hello world."</span>);</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> visible = <span class="title function_">ref</span>(<span class="literal">false</span>);</span><br><span class="line"></span><br><span class="line"><span class="keyword">function</span> <span class="title function_">showAlert</span>(<span class="params">msg, typeName = <span class="string">"default"</span></span>) {</span><br><span class="line"> messgae.<span class="property">value</span> = msg;</span><br><span class="line"> type.<span class="property">value</span> = typeName;</span><br><span class="line"> visible.<span class="property">value</span> = <span class="literal">true</span>;</span><br><span class="line"> <span class="built_in">setTimeout</span>(<span class="function">() =></span> visible.<span class="property">value</span> = <span class="literal">false</span>, <span class="number">2000</span>);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="title function_">defineExpose</span>({ showAlert });</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> alertTypeClass = <span class="title function_">computed</span>(<span class="function">() =></span> {</span><br><span class="line"> <span class="keyword">let</span> typeClass = <span class="string">"default"</span>;</span><br><span class="line"> <span class="keyword">switch</span> (type.<span class="property">value</span>) {</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'info'</span>:</span><br><span class="line"> typeClass = <span class="string">'alert-info'</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'success'</span>:</span><br><span class="line"> typeClass = <span class="string">'alert-success'</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'warning'</span>:</span><br><span class="line"> typeClass = <span class="string">'alert-warning'</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> <span class="keyword">case</span> <span class="string">'error'</span>:</span><br><span class="line"> typeClass = <span class="string">'alert-error'</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"></span><br><span class="line"> <span class="attr">default</span>:</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> typeClass;</span><br><span class="line">})</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h3 id="主题切换"><a class="markdownIt-Anchor" href="#主题切换"></a> 主题切换</h3>
<p>参考<a href="https://daisyui.com/components/theme-controller/">主题控制器</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="DaisyUI Tailwind" scheme="https://blog.kahvia.cn/tags/DaisyUI-Tailwind/"/>
</entry>
<entry>
<title>VueUse</title>
<link href="https://blog.kahvia.cn/2024/03/16/Vue-use.html"/>
<id>https://blog.kahvia.cn/2024/03/16/Vue-use.html</id>
<published>2024-03-16T11:00:29.186Z</published>
<updated>2024-03-16T11:12:39.088Z</updated>
<content type="html"><![CDATA[<p>这是 Vue 的一个第三方库，提供了许多意想不到的功能。比如异步 computed 。</p><h3 id="computedasync"><a class="markdownIt-Anchor" href="#computedasync"></a> <a href="https://vueuse.org/core/computedAsync/#computedasync">computedAsync</a></h3><p>Vue 官方的 computed 是同步的，有时并不能满足开发需求。比如我根据“县名”异步查询行政区下的“乡镇”，在 resolve 之前，我希望有个默认值。当然了，我可以定义一个 ref 变量来存放默认值，异步查询后更改 ref 的值。这意味着，我要在选择县之后的回调函数中，手动调用异步函数，然后等待异步函数 resolve ，再修改 ref 的值。这显然很麻烦。</p><p>但是这个库函数，直接传入异步函数和默认值，组件直接使用 computed 的结果即可，自然是方便很多。</p><p>比如。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">const</span> towns = <span class="title function_">computedAsync</span>(</span><br><span class="line"> <span class="keyword">async</span> () => {</span><br><span class="line"> <span class="keyword">if</span> (country.<span class="property">value</span>) {</span><br><span class="line"> <span class="keyword">let</span> towns = <span class="keyword">await</span> <span class="title function_">getTowns</span>((country.<span class="property">value</span> <span class="keyword">as</span> <span class="built_in">any</span>).<span class="property">name</span>);</span><br><span class="line"> <span class="keyword">return</span> <span class="title function_">addIdToDistinct</span>(towns <span class="keyword">as</span> <span class="built_in">any</span>);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> [{ <span class="attr">id</span>: <span class="number">0</span>, <span class="attr">name</span>: <span class="string">''</span> }];</span><br><span class="line"> },</span><br><span class="line"> [{ <span class="attr">id</span>: <span class="number">0</span>, <span class="attr">name</span>: <span class="string">''</span> }],</span><br><span class="line"> { <span class="attr">lazy</span>: <span class="literal">true</span> }</span><br><span class="line">)</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><p>这是 Vue 的一个第三方库，提供了许多意想不到的功能。比如异步 computed 。</p>
<h3 id="computedasync"><a class="markdownIt-Anchor" href="#computedasync"></a> <a href="h</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="uniapp" scheme="https://blog.kahvia.cn/tags/uniapp/"/>
</entry>
<entry>
<title>项目过程中积累的css技巧</title>
<link href="https://blog.kahvia.cn/2024/03/11/css-skills.html"/>
<id>https://blog.kahvia.cn/2024/03/11/css-skills.html</id>
<published>2024-03-11T11:12:59.343Z</published>
<updated>2024-05-06T07:35:25.758Z</updated>
<content type="html"><![CDATA[<h3 id="flex布局设置多行首对齐且整体居中"><a class="markdownIt-Anchor" href="#flex布局设置多行首对齐且整体居中"></a> Flex布局设置多行首对齐且整体居中</h3><p>假定项目中的待展示元素宽高固定，每一行要求左对齐，一行最多五个，在此基础上，依据设备的不同，每一行多余的屏幕空间不同。如何将每行排满后多余的屏幕空间分配给该行的每个元素？</p><p>答：采用一个空盒子对展示元素进行包裹。对于空盒子，采用<strong> flex-bias </strong>设置一行内所占空间为 20% ，同时空盒子也进行 flex 布局，对展示元素进行水平和垂直的居中处理。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <div class="categories"></span><br><span class="line"> <div class="wrapper" v-for="category in categories"></span><br><span class="line"> <navigator class="navigator-item" url="/pages/index/index" open-type="navigate"</span><br><span class="line"> hover-class="navigator-hover"></span><br><span class="line"> <image class="icon" :src="category.icon_data" /></span><br><span class="line"> <text>{{ category.name }}</text></span><br><span class="line"> </navigator></span><br><span class="line"> </div></span><br><span class="line"> </div></span><br><span class="line"></template></span><br><span class="line"></span><br><span class="line"><script setup></span><br><span class="line">import { ref, onMounted } from 'vue'</span><br><span class="line">import { getCats } from '@/services/product';</span><br><span class="line">import { useProductStore } from '@/stores/piniaStores';</span><br><span class="line">import { storeToRefs } from 'pinia';</span><br><span class="line"></span><br><span class="line">const { categories } = storeToRefs(useProductStore());</span><br><span class="line"></span><br><span class="line">onMounted(() => {</span><br><span class="line"> getCats();</span><br><span class="line">})</span><br><span class="line"></span><br><span class="line"></script></span><br><span class="line"></span><br><span class="line"><style scoped></span><br><span class="line">.categories {</span><br><span class="line"> width: 100%;</span><br><span class="line"> display: flex;</span><br><span class="line"> flex-wrap: wrap;</span><br><span class="line"> justify-content: flex-start;</span><br><span class="line"> margin-top: 10px;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">.wrapper {</span><br><span class="line"> flex-basis: 20%;</span><br><span class="line"> display: flex;</span><br><span class="line"> justify-content: center;</span><br><span class="line"> align-items: center;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">.navigator-item {</span><br><span class="line"> position: relative;</span><br><span class="line"> width: 50px;</span><br><span class="line"> height: 50px;</span><br><span class="line"> margin-bottom: 25px;</span><br><span class="line"> background-color: #6196A6;</span><br><span class="line"> border-radius: 10px;</span><br><span class="line"> display: flex;</span><br><span class="line"> flex-direction: column;</span><br><span class="line"> align-items: center;</span><br><span class="line"> justify-content: center;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">.navigator-item text {</span><br><span class="line"> position: absolute;</span><br><span class="line"> bottom: -20px;</span><br><span class="line"> font-size: x-small;</span><br><span class="line"> font-weight: 500;</span><br><span class="line"> color: black;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">image {</span><br><span class="line"> width: 30px;</span><br><span class="line"> height: 30px;</span><br><span class="line"></span><br><span class="line">}</span><br><span class="line"></style></span><br></pre></td></tr></table></figure><p><img src="https://pics.kahvia.cn/img/20240311193512.png" alt="效果图" /></p><h3 id="淡入淡出动画"><a class="markdownIt-Anchor" href="#淡入淡出动画"></a> 淡入淡出动画</h3><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="tag"><<span class="name">div</span> <span class="attr">ref</span>=<span class="string">"alert"</span> <span class="attr">role</span>=<span class="string">"alert"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">class</span>=<span class="string">"alert w-fit absolute top-0 left-1/2 -translate-x-1/2 transition-all duration-1000"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">:class</span>=<span class="string">"{ 'opacity-0 invisible': !visible, 'opacity-100': visible }"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">svg</span> <span class="attr">xmlns</span>=<span class="string">"http://www.w3.org/2000/svg"</span> <span class="attr">fill</span>=<span class="string">"none"</span> <span class="attr">viewBox</span>=<span class="string">"0 0 24 24"</span> <span class="attr">class</span>=<span class="string">"stroke-info shrink-0 w-6 h-6"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">path</span> <span class="attr">stroke-linecap</span>=<span class="string">"round"</span> <span class="attr">stroke-linejoin</span>=<span class="string">"round"</span> <span class="attr">stroke-width</span>=<span class="string">"2"</span></span></span><br><span class="line"><span class="tag"> <span class="attr">d</span>=<span class="string">"M13 16h-1v-4h-1m1-4h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"</span>></span><span class="tag"></<span class="name">path</span>></span></span><br><span class="line"> <span class="tag"></<span class="name">svg</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">span</span>></span>{{ messgae }}<span class="tag"></<span class="name">span</span>></span></span><br><span class="line"><span class="tag"></<span class="name">div</span>></span></span><br></pre></td></tr></table></figure><p>在添加 transition 的情况下，<strong>visibility</strong> 的 visible 到 hidden 是 duration 结束后的突变，并不会有过渡效果，而 hidden 到 visible 是 duration 刚开始就突变的。</p><p>这意味着元素在获得 hidden 的时候是会因为 duration 而延迟，延迟期间仍然可以进行交互（包括看见、点击、拖拽等等），直到 visibility : hidden被添加。</p><p>同样意味着元素在获得 visible 的时候是瞬间生效的，不会因为 duration 有任何的延迟。</p><p>这样一来，当我们点击按钮让它显示的时候，它是瞬间出现的。再次点击按钮让它消失的时候，它会等待 duration 度过，然后瞬间消失。</p><p>我们只需要添加 opacity 不透明度的变化，让元素在 duration 期间淡入淡出，即可实现视觉和交互层面的淡入淡出。</p><p><img src="https://pics.kahvia.cn/img/MS%E6%B8%90%E5%85%A5%E6%B8%90%E5%87%BA.gif" alt="渐入渐出" /></p><h3 id="flex布局未溢出时居中溢出时start"><a class="markdownIt-Anchor" href="#flex布局未溢出时居中溢出时start"></a> Flex布局未溢出时居中，溢出时start</h3><p><a href="https://stackoverflow.com/questions/34184535/change-justify-content-value-when-flex-items-overflow-container">参考问答</a></p><p>问题描述：通过 <code>justify-content:center</code>，可以设置 Flex 布局主轴居中，但是溢出设置滚动时，会导致滚动内容异常（居中导致的）。期望效果：未溢出时主轴居中，溢出时 flex-start 的效果。</p><p>解决方法：为 flex 盒子添加 before 和 after 伪元素，分别设置外边距 <code>margin:auto</code>。在未溢出的时候，自动外边距会占据剩余的空间，将元素居中。在溢出的时候，该属性会被忽略，正常溢出，无不良效果，即普通的靠左的从左到右依次排列，溢出滚动。</p><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="selector-class">.iconSelector</span><span class="selector-pseudo">::before</span>,</span><br><span class="line"><span class="selector-class">.iconSelector</span><span class="selector-pseudo">::after</span> {</span><br><span class="line"> <span class="attribute">content</span>: <span class="string">''</span>;</span><br><span class="line"> <span class="comment">/* Insert pseudo-element */</span></span><br><span class="line"> <span class="attribute">margin</span>: auto;</span><br><span class="line"> <span class="comment">/* Make it push flex items to the center */</span></span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h3 id="flex布局设置多行首对齐且整体居中"><a class="markdownIt-Anchor" href="#flex布局设置多行首对齐且整体居中"></a> Flex布局设置多行首对齐且整体居中</h3>
<p>假定项目中的待展示元素宽高固定，每一行要求左对齐</summary>
<category term="经验" scheme="https://blog.kahvia.cn/categories/%E7%BB%8F%E9%AA%8C/"/>
<category term="css" scheme="https://blog.kahvia.cn/tags/css/"/>
</entry>
<entry>
<title>vue3知识点</title>
<link href="https://blog.kahvia.cn/2024/03/09/vue3Knowledge.html"/>
<id>https://blog.kahvia.cn/2024/03/09/vue3Knowledge.html</id>
<published>2024-03-09T10:28:17.575Z</published>
<updated>2024-03-16T11:57:50.279Z</updated>
<content type="html"><![CDATA[<h3 id="样式穿透"><a class="markdownIt-Anchor" href="#样式穿透"></a> 样式穿透</h3><p>使用样式穿透，可以穿透子组件影响到下面的类的样式，做到对第三方组件的样式自定义。</p><h4 id="采用"><a class="markdownIt-Anchor" href="#采用"></a> 采用>>></h4><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line">uni-data-picker>>><span class="selector-class">.input-value-border</span> {</span><br><span class="line"> <span class="attribute">border</span>: <span class="number">1px</span> solid black;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100px</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">50px</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="采用-deep"><a class="markdownIt-Anchor" href="#采用-deep"></a> 采用 /deep/</h4><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line">uni-data-picker /deep/ <span class="selector-class">.input-value-border</span> {</span><br><span class="line"> <span class="attribute">border</span>: <span class="number">1px</span> solid red;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100px</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">50px</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="采用-v-deep"><a class="markdownIt-Anchor" href="#采用-v-deep"></a> 采用 ::v-deep</h4><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line">uni-data-picker::v-deep .input-value-border {</span><br><span class="line"> <span class="attribute">border</span>: <span class="number">3px</span> solid orange;</span><br><span class="line"> <span class="attribute">width</span>: <span class="number">100px</span>;</span><br><span class="line"> <span class="attribute">height</span>: <span class="number">50px</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="父组件获取子组件属性"><a class="markdownIt-Anchor" href="#父组件获取子组件属性"></a> 父组件获取子组件属性</h3><p>根据<a href="https://cn.vuejs.org/api/sfc-script-setup.html#defineexpose">官方文档</a>，采用组合式 api 编写的组件，内部定义的属性、方法，都是不对外开放的。可以调用 defineExpose() 方法，暴露需要的属性和方法。外部通过 ref 进行模板引用，即可访问暴露出来的属性和方法。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <uni-popup ref="popPage" type="bottom" background-color="#f7f7f7"></span><br><span class="line"> <div class="boxBack"></span><br><span class="line"> <div class="box"></span><br><span class="line"> <input type="nickname" placeholder="请输入分类名称" v-model="catName"></span><br><span class="line"> <button ref="nickBtn" @click="">确认</button></span><br><span class="line"> </div></span><br><span class="line"> </div></span><br><span class="line"> </uni-popup></span><br><span class="line"></template></span><br><span class="line"></span><br><span class="line"><script setup lang="ts"></span><br><span class="line">import { ref } from 'vue';</span><br><span class="line"></span><br><span class="line">const popPage = ref(null);</span><br><span class="line">const catName = ref("");</span><br><span class="line"></span><br><span class="line">function popUp() {</span><br><span class="line"> console.log(popPage.value);</span><br><span class="line"> (popPage.value as any).open();</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">defineExpose({</span><br><span class="line"> popUp</span><br><span class="line">})</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"></script></span><br><span class="line"></span><br><span class="line"><!-- 弹出层样式 --></span><br><span class="line"><style scoped></span><br><span class="line"></style></span><br></pre></td></tr></table></figure><h3 id="props设置默认值"><a class="markdownIt-Anchor" href="#props设置默认值"></a> props设置默认值</h3><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//Boolean 类型的未传递 prop 将被转换为 false。————官方文档</span></span><br><span class="line"><span class="keyword">let</span> props = <span class="title function_">defineProps</span>({</span><br><span class="line"> <span class="attr">title</span>: <span class="title class_">String</span>,</span><br><span class="line"> <span class="attr">showBack</span>: {</span><br><span class="line"> <span class="attr">type</span>: <span class="title class_">Boolean</span>,</span><br><span class="line"> <span class="attr">default</span>: <span class="literal">true</span></span><br><span class="line"> }</span><br><span class="line">});</span><br></pre></td></tr></table></figure><h3 id="watch-props的值"><a class="markdownIt-Anchor" href="#watch-props的值"></a> watch props的值</h3><p>要使用 getter 函数。此处的 props.catName 是一个外部传入常量，如果给 watch 这个东西，那么 watch 调用，生成监视的时候，收到的参数是一个常量，这不对。要给 watch 一个getter 函数，让它自己调用函数去看，这样监视器看到返回值跟之前不一样了，才知道发生了变化。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="title function_">watch</span>(<span class="function">() =></span> props.<span class="property">catName</span>, <span class="keyword">async</span> (oldCatName, newCatName) => {</span><br><span class="line"> <span class="keyword">if</span> ((productsMap.<span class="property">value</span> <span class="keyword">as</span> <span class="built_in">any</span>)[props.<span class="property">catName</span>].<span class="property">length</span> == <span class="number">0</span>)</span><br><span class="line"> <span class="title function_">getProsByCatName</span>();</span><br><span class="line">})</span><br></pre></td></tr></table></figure><blockquote><p><a href="https://cn.vuejs.org/guide/essentials/watchers.html#watch-source-types">侦听器 | Vue.js (vuejs.org)</a></p></blockquote>]]></content>
<summary type="html"><h3 id="样式穿透"><a class="markdownIt-Anchor" href="#样式穿透"></a> 样式穿透</h3>
<p>使用样式穿透，可以穿透子组件影响到下面的类的样式，做到对第三方组件的样式自定义。</p>
<h4 id="采用"><a class=</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="vue" scheme="https://blog.kahvia.cn/tags/vue/"/>
</entry>
<entry>
<title>MemFireDb</title>
<link href="https://blog.kahvia.cn/2024/03/06/MemFireDb.html"/>
<id>https://blog.kahvia.cn/2024/03/06/MemFireDb.html</id>
<published>2024-03-06T04:41:35.603Z</published>
<updated>2024-05-04T08:54:02.957Z</updated>
<content type="html"><![CDATA[<h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3><p>以最近的 uniapp 开发微信小程序为例。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">npm install @supabase/supabase-js</span><br><span class="line">npm install supabase-wechat-stable-v2</span><br></pre></td></tr></table></figure><h3 id="配置数据库连接"><a class="markdownIt-Anchor" href="#配置数据库连接"></a> 配置数据库连接</h3><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//fireDb.ts</span></span><br><span class="line"><span class="keyword">import</span> { createClient } <span class="keyword">from</span> <span class="string">"supabase-wechat-stable-v2"</span></span><br><span class="line"></span><br><span class="line"><span class="comment">//这两个常量可以在MemFireDb官网数据库的api中找到</span></span><br><span class="line"><span class="keyword">const</span> supabaseUrl = <span class="string">"https://xxxx.baseapi.memfiredb.com"</span>;</span><br><span class="line"><span class="keyword">const</span> publicAnonKey = <span class="string">"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx"</span>;</span><br><span class="line"><span class="comment">// Create a single supabase client for interacting with your database</span></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> supabase = <span class="title function_">createClient</span>(supabaseUrl, publicAnonKey);</span><br></pre></td></tr></table></figure><h3 id="微信授权手机号一键登陆"><a class="markdownIt-Anchor" href="#微信授权手机号一键登陆"></a> 微信授权手机号一键登陆</h3><p>在 uniapp 中，设置 button 的 open-type 为 getPhoneNumber，并监听事件getPhoneNumber。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"><button class="btn" open-type="getPhoneNumber" @getphonenumber="wxLogin"></span><br><span class="line"> <image</span><br><span class="line"> src="data:image/svg+xml;base64,xxx" /></span><br><span class="line"> <text>微信快捷登录</text></span><br><span class="line"> </button></span><br><span class="line"></template></span><br></pre></td></tr></table></figure><p>监听事件发生时，调用 wxLogin 函数，传入一个事件对象，根据 code 值判断是否获取到电话号码。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> <span class="title function_">wxLogin</span> = <span class="keyword">async</span> (<span class="params">e: <span class="built_in">any</span></span>) => {</span><br><span class="line"> wx.<span class="title function_">login</span>({</span><br><span class="line"> <span class="attr">success</span>: <span class="keyword">async</span> res => {</span><br><span class="line"> <span class="comment">//在getPhoneNumber事件中,如果code为undefined，则用户未授权，否则用户已经授权，获取到手机号码</span></span><br><span class="line"> <span class="keyword">if</span> (!e.<span class="property">detail</span>.<span class="property">code</span>) {</span><br><span class="line"> wx.<span class="title function_">showToast</span>({</span><br><span class="line"> <span class="attr">title</span>: <span class="string">"授权失败"</span>,</span><br><span class="line"> <span class="attr">icon</span>: <span class="string">"none"</span>,</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">2000</span></span><br><span class="line"> })</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//微信登录，新用户则自动注册</span></span><br><span class="line"> <span class="keyword">const</span> { data, error } = <span class="keyword">await</span> supabase.<span class="property">auth</span>.<span class="title function_">signInWithWechat</span>({ <span class="attr">code</span>: res.<span class="property">code</span> })</span><br><span class="line"> <span class="keyword">let</span> { <span class="attr">user</span>: { <span class="attr">data</span>: { user } } } = data <span class="keyword">as</span> <span class="built_in">any</span>;</span><br><span class="line"> <span class="title function_">setProfile</span>(user);</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="keyword">if</span> (error) {</span><br><span class="line"> wx.<span class="title function_">showToast</span>({</span><br><span class="line"> <span class="attr">title</span>: <span class="title class_">JSON</span>.<span class="title function_">stringify</span>(error) || error?.<span class="property">message</span>,</span><br><span class="line"> <span class="attr">icon</span>: <span class="string">"none"</span>,</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">2000</span></span><br><span class="line"> })</span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> (data) {</span><br><span class="line"> <span class="comment">//获取到用户信息后，绑定电话号码到小程序用户上</span></span><br><span class="line"> <span class="keyword">const</span> { data, error } = <span class="keyword">await</span> supabase.<span class="property">auth</span>.<span class="title function_">wechatBindPhone</span>({</span><br><span class="line"> <span class="attr">code</span>: e.<span class="property">detail</span>.<span class="property">code</span>,</span><br><span class="line"> })</span><br><span class="line"> <span class="keyword">if</span> (error) {</span><br><span class="line"> wx.<span class="title function_">showToast</span>({</span><br><span class="line"> <span class="attr">title</span>: <span class="title class_">JSON</span>.<span class="title function_">stringify</span>(error) || error?.<span class="property">message</span>,</span><br><span class="line"> <span class="attr">icon</span>: <span class="string">"none"</span>,</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">2000</span></span><br><span class="line"> })</span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> (data) {</span><br><span class="line"> wx.<span class="title function_">showToast</span>({</span><br><span class="line"> <span class="attr">title</span>: <span class="string">'登录成功！'</span>,</span><br><span class="line"> <span class="attr">icon</span>: <span class="string">"none"</span>,</span><br><span class="line"> <span class="attr">duration</span>: <span class="number">1000</span></span><br><span class="line"> })</span><br><span class="line"> wx.<span class="title function_">switchTab</span>({</span><br><span class="line"> <span class="attr">url</span>: <span class="string">'/pages/index/index'</span></span><br><span class="line"> })</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> },</span><br><span class="line"> })</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></table></figure><h3 id="获取微信头像"><a class="markdownIt-Anchor" href="#获取微信头像"></a> 获取微信头像</h3><p>操作与获取手机号码类似。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><button class="avatarCoverBtn" open-type="chooseAvatar" @chooseavatar="chooseAvatar"></span><br><span class="line"><image class="avatar" :src="profile.avatar" mode="scaleToFill" /></span><br><span class="line"></button></span><br></pre></td></tr></table></figure><p>在获取到头像的本地路径后，需要转存到对象存储的存储桶中，获取对应的网络地址，然后更新数据库中的头像信息和小程序本地的头像信息。我采用 Pinia 进行状态管理，因此在 updateAvatar 函数中，对 userStore 里的头像信息进行了更新。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> <span class="title function_">chooseAvatar</span> = (<span class="params">e: <span class="built_in">any</span></span>) => {</span><br><span class="line"> <span class="keyword">let</span> { avatarUrl } = e.<span class="property">detail</span></span><br><span class="line"> wx.<span class="title function_">getImageInfo</span>({</span><br><span class="line"> <span class="attr">src</span>: avatarUrl, <span class="comment">// 图片路径，必须是本地路径，可以相对路径或绝对路径</span></span><br><span class="line"> <span class="attr">success</span>: <span class="keyword">async</span> <span class="keyword">function</span> (<span class="params">res</span>) {</span><br><span class="line"> <span class="keyword">const</span> file = { <span class="attr">fileType</span>: <span class="string">"image"</span>, <span class="attr">width</span>: res.<span class="property">width</span>, <span class="attr">height</span>: res.<span class="property">height</span>, <span class="attr">tempFilePath</span>: avatarUrl }</span><br><span class="line"> <span class="keyword">const</span> fileExt = avatarUrl.<span class="title function_">split</span>(<span class="string">'.'</span>).<span class="title function_">pop</span>()</span><br><span class="line"> <span class="keyword">const</span> fileName = <span class="string">`<span class="subst">${<span class="built_in">Math</span>.random()}</span>.<span class="subst">${fileExt}</span>`</span></span><br><span class="line"> <span class="keyword">const</span> filePath = <span class="string">`<span class="subst">${profile.value.id}</span>/<span class="subst">${fileName}</span>`</span></span><br><span class="line"> <span class="keyword">let</span> { <span class="attr">error</span>: uploadError } = <span class="keyword">await</span> supabase.<span class="property">storage</span></span><br><span class="line"> .<span class="title function_">from</span>(<span class="string">'avatars'</span>)</span><br><span class="line"> .<span class="title function_">upload</span>(filePath, file <span class="keyword">as</span> <span class="built_in">any</span>)</span><br><span class="line"> <span class="keyword">if</span> (uploadError) {</span><br><span class="line"> <span class="keyword">throw</span> uploadError</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//获取具有一年期限的头像url</span></span><br><span class="line"> <span class="keyword">const</span> { data } = <span class="keyword">await</span> supabase</span><br><span class="line"> .<span class="property">storage</span></span><br><span class="line"> .<span class="title function_">from</span>(<span class="string">'avatars'</span>)</span><br><span class="line"> .<span class="title function_">createSignedUrl</span>(filePath, <span class="number">31556952</span>);</span><br><span class="line"> <span class="comment">//更新头像</span></span><br><span class="line"> <span class="title function_">updateAvatar</span>(data!.<span class="property">signedUrl</span>);</span><br><span class="line"> }</span><br><span class="line"> })</span><br><span class="line">};</span><br></pre></td></tr></table></figure><p>注：存储桶我设置为私有，且设置了行级安全策略，因此在存储头像的时候，需要存入对应 uid 文件夹下，否则没有权限。</p><blockquote><p><a href="https://document.memfiredb.com/docs/guides/storage#%E5%85%B1%E6%9C%89%E6%A1%B6%E5%92%8C%E7%A7%81%E6%9C%89%E6%A1%B6">存储桶的私有和共有</a>，详细描述了二者的区别，以及对应的获取资源 url 的方式。</p></blockquote><h3 id="自己维护users的信息"><a class="markdownIt-Anchor" href="#自己维护users的信息"></a> 自己维护users的信息</h3><p>在 public 中新建 users 表。为其创建两个触发器，分别在 auth.users 插入和更新时触发，用以同步 users 中的变化。</p><figure class="highlight postgresql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">CREATE</span> <span class="keyword">TABLE</span> USERS (</span><br><span class="line"> id <span class="type">uuid</span> <span class="keyword">references</span> auth.users <span class="keyword">not</span> <span class="keyword">null</span> <span class="keyword">primary key</span>,</span><br><span class="line"> <span class="keyword">role</span> <span class="type">text</span>,</span><br><span class="line"> email <span class="type">text</span>,</span><br><span class="line"> last_sign_in_at <span class="type">text</span>,</span><br><span class="line"> raw_app_meta_data <span class="type">jsonb</span>,</span><br><span class="line"> raw_user_meta_data <span class="type">jsonb</span></span><br><span class="line">);</span><br><span class="line"><span class="keyword">create</span> <span class="keyword">or replace</span> <span class="keyword">function</span> <span class="built_in">public</span>.handle_new_user()</span><br><span class="line"><span class="keyword">returns</span> <span class="type">trigger</span> <span class="keyword">as</span> $$<span class="language-pgsql"></span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">begin</span></span></span><br><span class="line"><span class="language-pgsql"> <span class="keyword">insert</span> <span class="keyword">into</span> <span class="built_in">public</span>.users (id, <span class="keyword">role</span>, email,last_sign_in_at,raw_app_meta_data,raw_user_meta_data)</span></span><br><span class="line"><span class="language-pgsql"> <span class="keyword">values</span> (<span class="built_in">new</span>.id,<span class="built_in">new</span>.<span class="keyword">role</span>, <span class="built_in">new</span>.email,<span class="built_in">new</span>.last_sign_in_at,<span class="built_in">new</span>.raw_app_meta_data,<span class="built_in">new</span>.raw_user_meta_data);</span></span><br><span class="line"><span class="language-pgsql"> <span class="keyword">return</span> <span class="built_in">new</span>;</span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">end</span>;</span></span><br><span class="line"><span class="language-pgsql">$$</span> <span class="keyword">language</span> plpgsql <span class="keyword">security</span> <span class="keyword">definer</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">create</span> <span class="keyword">trigger</span> on_new_user</span><br><span class="line"><span class="keyword">after</span> <span class="keyword">insert</span> <span class="keyword">on</span> auth.users <span class="keyword">for</span> <span class="keyword">each</span> <span class="keyword">row</span></span><br><span class="line"><span class="keyword">execute</span> <span class="keyword">procedure</span> <span class="built_in">public</span>.handle_new_user ();</span><br><span class="line"></span><br><span class="line"><span class="keyword">create</span> <span class="keyword">or replace</span> <span class="keyword">function</span> <span class="built_in">public</span>.update_user()</span><br><span class="line"><span class="keyword">returns</span> <span class="type">trigger</span> <span class="keyword">as</span> $$<span class="language-pgsql"></span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">begin</span></span></span><br><span class="line"><span class="language-pgsql"> <span class="keyword">UPDATE</span> <span class="built_in">public</span>.users</span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">SET</span> <span class="keyword">role</span> = <span class="built_in">new</span>.<span class="keyword">role</span>, </span></span><br><span class="line"><span class="language-pgsql"> email = <span class="built_in">new</span>.email,</span></span><br><span class="line"><span class="language-pgsql"> last_sign_in_at = <span class="built_in">new</span>.last_sign_in_at,</span></span><br><span class="line"><span class="language-pgsql"> raw_app_meta_data = <span class="built_in">new</span>.raw_app_meta_data,</span></span><br><span class="line"><span class="language-pgsql"> raw_user_meta_data = <span class="built_in">new</span>.raw_user_meta_data</span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">WHERE</span> id = <span class="built_in">new</span>.id;</span></span><br><span class="line"><span class="language-pgsql"></span></span><br><span class="line"><span class="language-pgsql"> <span class="keyword">return</span> <span class="built_in">new</span>;</span></span><br><span class="line"><span class="language-pgsql"><span class="keyword">end</span>;</span></span><br><span class="line"><span class="language-pgsql">$$</span> <span class="keyword">language</span> plpgsql <span class="keyword">security</span> <span class="keyword">definer</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">create</span> <span class="keyword">trigger</span> on_update_user</span><br><span class="line"><span class="keyword">after</span> <span class="keyword">update</span> <span class="keyword">on</span> auth.users <span class="keyword">for</span> <span class="keyword">each</span> <span class="keyword">row</span></span><br><span class="line"><span class="keyword">execute</span> <span class="keyword">procedure</span> <span class="built_in">public</span>.update_user ();</span><br></pre></td></tr></table></figure><p>为其设定行级安全策略，仅超级管理员可以访问。</p><figure class="highlight postgresql"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">(get_my_claim(<span class="string">'role'</span>::<span class="type">text</span>) = <span class="string">'"super_admin"'</span>::<span class="type">jsonb</span>)</span><br></pre></td></tr></table></figure><h3 id="查询行数"><a class="markdownIt-Anchor" href="#查询行数"></a> 查询行数</h3><p>其中 head 表示是否只获取每一行的开头，而不获取具体数据。设置为 true 时，返回的 data 为 null 。estimated 是指在行数小的时候返回具体值，行数多的时候返回估计值。注意不能使用 range ，不然 count 的结果就是 range 的范围了。</p><figure class="highlight postgresql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line">export const getUsersNum = () => {</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">new</span> Promise(async (resolve, reject) => {</span><br><span class="line"> const { data, count, error } = await supabase</span><br><span class="line"> .<span class="keyword">from</span>(<span class="string">'users'</span>)</span><br><span class="line"> .<span class="keyword">select</span>(<span class="string">'*'</span>, { count: <span class="string">'estimated'</span>, head: <span class="keyword">true</span> })</span><br><span class="line"> <span class="keyword">if</span> (count)</span><br><span class="line"> resolve(count);</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> reject();</span><br><span class="line"> })</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="input失焦空查询"><a class="markdownIt-Anchor" href="#input失焦空查询"></a> input失焦空查询</h3><p>当为一个input输入框添加失去焦点时的事件函数 blur 时，如果是调用的异步查询函数，比如 supabase 的 select 时，会在查询时添加奇怪的参数，导致查询结果为空数组。</p><p><img src="https://pics.kahvia.cn/img/supabase%E7%9A%84input%E5%A4%B1%E7%84%A6%E7%A9%BA%E6%9F%A5%E8%AF%A21.png" alt="不正常的参数" /></p><p>为了正常查询，在 blur 触发的时候去调用同步函数，通过同步函数去调用异步查询函数即可，就像这样：<code>@blur="()=>getOrders()"</code></p><p><img src="https://pics.kahvia.cn/img/supabase%E7%9A%84input%E5%A4%B1%E7%84%A6%E7%A9%BA%E6%9F%A5%E8%AF%A22.png" alt="正常查询" /></p><p>可以看见奇怪的事件参数消失了，数据正常查询。</p><h3 id="请求未发送"><a class="markdownIt-Anchor" href="#请求未发送"></a> 请求未发送</h3><p>在对数据库进行一个字段更新的异步操作时，发现请求未成功发送。<code>supabase.from('address').update({ 'default': false }).eq('id', *fromAid*);</code></p><p>经过查阅<a href="https://www.reddit.com/r/Supabase/comments/13jsbv1/comment/jkilyj5/?utm_source=reddit&utm_medium=web2x&context=3">资料</a>得知，supabase <strong>自己封装的链式调用</strong>，在不需 await 的情况下，需要用 .then() 来表示请求的构造完成。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">supabase.<span class="title function_">from</span>(<span class="string">'address'</span>).<span class="title function_">update</span>({ <span class="string">'default'</span>: <span class="literal">true</span> }).<span class="title function_">eq</span>(<span class="string">'id'</span>, fromAid).<span class="title function_">then</span>();</span><br></pre></td></tr></table></figure><p>这样就可以在使用其自定义链式调用的情况下，正常发送无需等待的异步请求。</p>]]></content>
<summary type="html"><h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3>
<p>以最近的 uniapp 开发微信小程序为例。</p>
<figure class="highlight bash"><table><tr><td</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="PostgreSQL" scheme="https://blog.kahvia.cn/tags/PostgreSQL/"/>
</entry>
<entry>
<title>TypeScript</title>
<link href="https://blog.kahvia.cn/2024/02/29/TypeScript.html"/>
<id>https://blog.kahvia.cn/2024/02/29/TypeScript.html</id>
<published>2024-02-29T05:43:41.729Z</published>
<updated>2024-03-07T09:23:51.225Z</updated>
<content type="html"><![CDATA[<h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i -g typescript</span><br></pre></td></tr></table></figure><h3 id="编译ts文件"><a class="markdownIt-Anchor" href="#编译ts文件"></a> 编译ts文件</h3><p>使用该命令可以将 ts 文件转换成可执行的 js 文件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">tsc xxx.ts</span><br></pre></td></tr></table></figure><p>通过 node 命令执行相应的 js 文件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">node xxx.js</span><br></pre></td></tr></table></figure><h3 id="直接运行ts文件"><a class="markdownIt-Anchor" href="#直接运行ts文件"></a> 直接运行ts文件</h3><p>先安装所需工具包。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i -g ts-node</span><br></pre></td></tr></table></figure><p>使用该工具包直接执行 ts 文件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">ts-node xxx.ts</span><br></pre></td></tr></table></figure><h3 id="使用时的一些小问题"><a class="markdownIt-Anchor" href="#使用时的一些小问题"></a> 使用时的一些小问题</h3><h4 id="类型本身定义是错误的"><a class="markdownIt-Anchor" href="#类型本身定义是错误的"></a> 类型本身定义是错误的</h4><p>比如，在使用 MemFireDB 的微信SDK开发小程序的时候，我使用了一个方法用于获取用户信息。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">const</span> { <span class="attr">data</span>: { user } } = <span class="keyword">await</span> supabase.<span class="property">auth</span>.<span class="title function_">getUser</span>();</span><br></pre></td></tr></table></figure><p>对于 user 对应的官方 type 是 User，如下所示。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">interface</span> <span class="title class_">User</span> {</span><br><span class="line"> <span class="attr">id</span>: <span class="built_in">string</span></span><br><span class="line"> <span class="attr">app_metadata</span>: <span class="title class_">UserAppMetadata</span></span><br><span class="line"> <span class="attr">user_metadata</span>: <span class="title class_">UserMetadata</span></span><br><span class="line"> <span class="attr">aud</span>: <span class="built_in">string</span></span><br><span class="line"> confirmation_sent_at?: <span class="built_in">string</span></span><br><span class="line"> recovery_sent_at?: <span class="built_in">string</span></span><br><span class="line"> email_change_sent_at?: <span class="built_in">string</span></span><br><span class="line"> new_email?: <span class="built_in">string</span></span><br><span class="line"> new_phone?: <span class="built_in">string</span></span><br><span class="line"> invited_at?: <span class="built_in">string</span></span><br><span class="line"> action_link?: <span class="built_in">string</span></span><br><span class="line"> email?: <span class="built_in">string</span></span><br><span class="line"> phone?: <span class="built_in">string</span></span><br><span class="line"> <span class="attr">created_at</span>: <span class="built_in">string</span></span><br><span class="line"> confirmed_at?: <span class="built_in">string</span></span><br><span class="line"> email_confirmed_at?: <span class="built_in">string</span></span><br><span class="line"> phone_confirmed_at?: <span class="built_in">string</span></span><br><span class="line"> last_sign_in_at?: <span class="built_in">string</span></span><br><span class="line"> role?: <span class="built_in">string</span></span><br><span class="line"> updated_at?: <span class="built_in">string</span></span><br><span class="line"> identities?: <span class="title class_">UserIdentity</span>[]</span><br><span class="line"> factors?: <span class="title class_">Factor</span>[]</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>然而经过实际打印输出我发现，这个 user 的数据结构如下所示。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"data"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"id"</span><span class="punctuation">:</span><span class="string">"xxx"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"app_metadata"</span><span class="punctuation">:</span><span class="punctuation">{</span><span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"xxx"</span><span class="punctuation">:</span><span class="string">"xxxx"</span></span><br><span class="line"> <span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>所以正确的的 User 定义应该是下面这样的。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">interface</span> <span class="title class_">User</span> {</span><br><span class="line"> <span class="attr">data</span>:{</span><br><span class="line"> <span class="attr">id</span>: <span class="built_in">string</span></span><br><span class="line"> <span class="attr">app_metadata</span>: <span class="title class_">UserAppMetadata</span></span><br><span class="line"> <span class="attr">xxx</span>:xxxx</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>虽然我发现了错误，但我业务做一半，也不能不用这个了吧。所以我自己定义了一个 type ，如下所示。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">interface</span> <span class="title class_">MyUser</span> {</span><br><span class="line"> <span class="attr">data</span>: <span class="title class_">User</span>,</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>然后使用断言 as 进行强制类型转换，先取消原有的类型声明，再声明为新的类型。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">let</span> myUser = user <span class="keyword">as</span> <span class="built_in">unknown</span> <span class="keyword">as</span> <span class="title class_">MyUser</span>;</span><br></pre></td></tr></table></figure><p>这样一来，我就可以通过 <a href="http://myUser.data.id">myUser.data.id</a> 这种形式，正常使用数据。</p>]]></content>
<summary type="html"><h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3>
<figure class="highlight bash"><table><tr><td class="gutter"><pre><span cla</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="ts" scheme="https://blog.kahvia.cn/tags/ts/"/>
</entry>
<entry>
<title>uniapp知识点</title>
<link href="https://blog.kahvia.cn/2024/02/29/Uniapp.html"/>
<id>https://blog.kahvia.cn/2024/02/29/Uniapp.html</id>
<published>2024-02-29T01:47:57.745Z</published>
<updated>2024-05-15T07:59:03.276Z</updated>
<content type="html"><![CDATA[<h3 id="在vscode中开发uniapp"><a class="markdownIt-Anchor" href="#在vscode中开发uniapp"></a> 在vscode中开发uniapp</h3><h4 id="使用命令行创建uniapp项目"><a class="markdownIt-Anchor" href="#使用命令行创建uniapp项目"></a> 使用命令行创建uniapp项目</h4><p>此处是vue3+ts。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npx degit dcloudio/uni-preset-vue<span class="comment">#vite-ts my-vue3-project</span></span><br></pre></td></tr></table></figure><h4 id="安装插件"><a class="markdownIt-Anchor" href="#安装插件"></a> 安装插件</h4><ul><li>uni-create-view</li><li>uni-helper</li><li>uniapp小程序扩展</li></ul><h4 id="ts相关"><a class="markdownIt-Anchor" href="#ts相关"></a> TS相关</h4><p>在根目录创建 <code>tsconfig.json</code> 文件，并进行个性化配置，个性化配置是可选的，没有<code>tsconfig.json</code>时会自动使用默认配置运行。推荐配置如下：</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// tsconfig.json</span></span><br><span class="line"><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"compilerOptions"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"target"</span><span class="punctuation">:</span> <span class="string">"esnext"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"module"</span><span class="punctuation">:</span> <span class="string">"esnext"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"strict"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"jsx"</span><span class="punctuation">:</span> <span class="string">"preserve"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"moduleResolution"</span><span class="punctuation">:</span> <span class="string">"node"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"esModuleInterop"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"sourceMap"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"skipLibCheck"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"importHelpers"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"allowSyntheticDefaultImports"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"useDefineForClassFields"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"resolveJsonModule"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"lib"</span><span class="punctuation">:</span> <span class="punctuation">[</span></span><br><span class="line"> <span class="string">"esnext"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"dom"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"types"</span><span class="punctuation">:</span> <span class="punctuation">[</span></span><br><span class="line"> <span class="string">"@dcloudio/types"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"@types/wechat-miniprogram"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"@uni-helper/uni-app-types"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"@uni-helper/uni-ui-types"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"baseUrl"</span><span class="punctuation">:</span> <span class="string">"./"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"paths"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"@/*"</span><span class="punctuation">:</span> <span class="punctuation">[</span></span><br><span class="line"> <span class="string">"src/*"</span></span><br><span class="line"> <span class="punctuation">]</span></span><br><span class="line"> <span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"vueCompilerOptions"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"nativeTags"</span><span class="punctuation">:</span> <span class="punctuation">[</span></span><br><span class="line"> <span class="string">"block"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"component"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"template"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"slot"</span></span><br><span class="line"> <span class="punctuation">]</span></span><br><span class="line"> <span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"exclude"</span><span class="punctuation">:</span> <span class="punctuation">[</span></span><br><span class="line"> <span class="string">"node_modules"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"unpackage"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="string">"src/**/*.nvue"</span></span><br><span class="line"> <span class="punctuation">]</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><blockquote><p>vueCompilerOptions以及nativeTags的配置是必须的。否则uniapp的标签比如view会出现<strong><a href="https://blog.csdn.net/weixin_41844140/article/details/134901640?spm=1001.2101.3001.6650.1&utm_medium=distribute.pc_relevant.none-task-blog-2~default~CTRLIST~Rate-1-134901640-blog-134186772.235%5Ev43%5Epc_blog_bottom_relevance_base3&depth_1-utm_source=distribute.pc_relevant.none-task-blog-2~default~CTRLIST~Rate-1-134901640-blog-134186772.235%5Ev43%5Epc_blog_bottom_relevance_base3&utm_relevant_index=2">类型错误</a></strong>。</p><p>baseUrl 和 paths 用于映射@/开头的 import 路径。详情参考<a href="https://www.typescriptlang.org/zh/tsconfig#paths">TypeScript: TSConfig</a>。</p></blockquote><p>安装TS类型支持包。前者是微信小程序组件的TS类型，后者是uniapp组件的TS类型。这些类型已在上方配置文件中的types添加。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i -D @types/wechat-miniprogram @uni-helper/uni-app-types</span><br></pre></td></tr></table></figure><h4 id="json文件相关"><a class="markdownIt-Anchor" href="#json文件相关"></a> json文件相关</h4><p>在 uniapp 项目中，我们可能会在 json 文件中有注释，vscode 识别 json 文件时，不允许有注释在其中，会报错，如下图所示。</p><p><img src="https://pics.kahvia.cn/img/20240301171803.png" alt="json文件内注释报错" /></p><p>解决方法：在 vscode 的设置中，搜索 associations ，添加文件关联键值对，即<strong> xxx.json jsonc </strong>。如下图所示，报错已消失。</p><p>注：.json 文件是标准的 json 格式，除了不允许有注释以外，还有其它的一些严格规则。.jsonc 文件则是拓展的 json 格式，能有注释在其中，以及可以省略 key 的引号等等。像 package.json 这种文件，最好还是不要加注释在里面。</p><p><img src="https://pics.kahvia.cn/img/20240301174049.png" alt="vscode文件关联" /></p><h3 id="uni-ui"><a class="markdownIt-Anchor" href="#uni-ui"></a> uni-ui</h3><p><a href="https://uniapp.dcloud.net.cn/component/uniui/uni-ui.html">uni-ui 介绍 | uni-app官网 (dcloud.net.cn)</a></p><h4 id="安装-uni-ui-所需的-sass-预处理器和加载器"><a class="markdownIt-Anchor" href="#安装-uni-ui-所需的-sass-预处理器和加载器"></a> 安装 uni-ui 所需的 sass 预处理器和加载器</h4><p>安装 sass</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i sass -D 或 yarn add sass -D </span><br></pre></td></tr></table></figure><p>安装 sass-loader</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i sass-loader@10.1.1 -D 或 yarn add sass-loader@10.1.1 -D</span><br></pre></td></tr></table></figure><h4 id="安装uni-ui"><a class="markdownIt-Anchor" href="#安装uni-ui"></a> 安装uni-ui</h4><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i @dcloudio/uni-ui 或 yarn add @dcloudio/uni-ui</span><br></pre></td></tr></table></figure><h4 id="配置uni-ui组件自动导入"><a class="markdownIt-Anchor" href="#配置uni-ui组件自动导入"></a> 配置uni-ui组件自动导入</h4><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// pages.json</span></span><br><span class="line"><span class="punctuation">{</span></span><br><span class="line"><span class="attr">"easycom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="attr">"autoscan"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"custom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="comment">// uni-ui 规则如下配置</span></span><br><span class="line"><span class="attr">"^uni-(.*)"</span><span class="punctuation">:</span> <span class="string">"@dcloudio/uni-ui/lib/uni-$1/uni-$1.vue"</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"></span><br><span class="line"><span class="comment">// 其他内容</span></span><br><span class="line">pages<span class="punctuation">:</span><span class="punctuation">[</span></span><br><span class="line"><span class="comment">// ...</span></span><br><span class="line"><span class="punctuation">]</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"></span><br></pre></td></tr></table></figure><h4 id="安装-uni-ui-的-ts-类型包"><a class="markdownIt-Anchor" href="#安装-uni-ui-的-ts-类型包"></a> 安装 uni-ui 的 ts 类型包</h4><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i -D @uni-helper/uni-ui-types</span><br></pre></td></tr></table></figure><p>然后在 tsconfig.json 中的 types 里写上对应的类型。现在就可以在 uni-ui 的组件标签上看到对应的类型了。</p><h3 id="pinia"><a class="markdownIt-Anchor" href="#pinia"></a> Pinia</h3><h4 id="pinia本体"><a class="markdownIt-Anchor" href="#pinia本体"></a> pinia本体</h4><p>本人采用 vue 版本 3.4.21, pinia 版本 2.0.36，不会发生依赖冲突以及各种报错。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i pinia@2.0.36</span><br></pre></td></tr></table></figure><p>创建 pinia 实例。</p><figure class="highlight tsx"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { createApp } <span class="keyword">from</span> <span class="string">'vue'</span></span><br><span class="line"><span class="keyword">import</span> { createPinia } <span class="keyword">from</span> <span class="string">'pinia'</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">App</span> <span class="keyword">from</span> <span class="string">'./App.vue'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> pinia = <span class="title function_">createPinia</span>()</span><br><span class="line"><span class="keyword">const</span> app = <span class="title function_">createApp</span>(<span class="title class_">App</span>)</span><br><span class="line"></span><br><span class="line">app.<span class="title function_">use</span>(pinia)</span><br><span class="line">app.<span class="title function_">mount</span>(<span class="string">'#app'</span>)</span><br></pre></td></tr></table></figure><h5 id="常用操作"><a class="markdownIt-Anchor" href="#常用操作"></a> 常用操作</h5><p>使用 <a href="https://pinia.vuejs.org/zh/core-concepts/#using-the-store">storeToRefs()</a> 取出 store 中的响应式数据。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { useUserStore } <span class="keyword">from</span> <span class="string">'../../stores/piniaStores'</span></span><br><span class="line"><span class="keyword">import</span> { storeToRefs } <span class="keyword">from</span> <span class="string">'pinia'</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> userStore = <span class="title function_">useUserStore</span>();</span><br><span class="line"><span class="keyword">const</span> {nickName} = <span class="title function_">storeToRefs</span>(userStore);</span><br></pre></td></tr></table></figure><h4 id="pinia的持久化插件"><a class="markdownIt-Anchor" href="#pinia的持久化插件"></a> pinia的持久化插件</h4><p><a href="https://prazdevs.github.io/pinia-plugin-persistedstate/">Home | pinia-plugin-persistedstate (prazdevs.github.io)</a></p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i pinia-plugin-persistedstate</span><br></pre></td></tr></table></figure><p>注意：是 pinia-plugin-persistedstate 这个插件，而非 <a href="https://seb-l.github.io/pinia-plugin-persist/">pinia-plugin-persist</a> 这个坑比插件。后者使用自定义 Storage 的时候，比如我是用的 uni 的storage，会报错说没有sessionStorage，这让我研究了一下午自己的官方文档，怀疑是自己的问题，最后得出结论是插件官方的问题。</p><p>在 main.ts 中配置持久化。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { createPinia } <span class="keyword">from</span> <span class="string">'pinia'</span></span><br><span class="line"><span class="keyword">import</span> piniaPluginPersistedstate <span class="keyword">from</span> <span class="string">'pinia-plugin-persistedstate'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> pinia = <span class="title function_">createPinia</span>()</span><br><span class="line">pinia.<span class="title function_">use</span>(piniaPluginPersistedstate)</span><br></pre></td></tr></table></figure><p>我配置完成后是如下所示。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { createSSRApp } <span class="keyword">from</span> <span class="string">"vue"</span>;</span><br><span class="line"><span class="keyword">import</span> <span class="title class_">App</span> <span class="keyword">from</span> <span class="string">"./App.vue"</span>;</span><br><span class="line"><span class="keyword">import</span> * <span class="keyword">as</span> <span class="title class_">Pinia</span> <span class="keyword">from</span> <span class="string">'pinia'</span>;</span><br><span class="line"><span class="keyword">import</span> piniaPluginPersistedstate <span class="keyword">from</span> <span class="string">'pinia-plugin-persistedstate'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">function</span> <span class="title function_">createApp</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="keyword">const</span> app = <span class="title function_">createSSRApp</span>(<span class="title class_">App</span>);</span><br><span class="line"> <span class="keyword">const</span> pinia = <span class="title class_">Pinia</span>.<span class="title function_">createPinia</span>();</span><br><span class="line"> pinia.<span class="title function_">use</span>(piniaPluginPersistedstate);</span><br><span class="line"> app.<span class="title function_">use</span>(pinia);</span><br><span class="line"> </span><br><span class="line"> <span class="keyword">return</span> {</span><br><span class="line"> app,</span><br><span class="line"> <span class="title class_">Pinia</span>,</span><br><span class="line"> };</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></table></figure><p>因为是为了 uniapp 采用的 pinia ，而 uniapp 没有 sessionStorage ，所以在定义 store 的时候需要自定义 storage。参考代码如下。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> { defineStore } <span class="keyword">from</span> <span class="string">'pinia'</span></span><br><span class="line"><span class="keyword">import</span> { <span class="title class_">StorageLike</span> } <span class="keyword">from</span> <span class="string">'pinia-plugin-persistedstate'</span>;</span><br><span class="line"><span class="keyword">import</span> { ref } <span class="keyword">from</span> <span class="string">'vue'</span></span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> <span class="attr">uniStorege</span>: <span class="title class_">StorageLike</span> = {</span><br><span class="line"> <span class="title function_">setItem</span>(<span class="params">key, value</span>) {</span><br><span class="line"> uni.<span class="title function_">setStorageSync</span>(key, value);</span><br><span class="line"> },</span><br><span class="line"> <span class="title function_">getItem</span>(<span class="params">key</span>) {</span><br><span class="line"> <span class="keyword">return</span> uni.<span class="title function_">getStorageSync</span>(key);</span><br><span class="line"> },</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">// 你可以对 `defineStore()` 的返回值进行任意命名，但最好使用 store 的名字，同时以 `use` 开头且以 `Store` 结尾。(比如 `useUserStore`，`useCartStore`，`useProductStore`)</span></span><br><span class="line"><span class="comment">// 第一个参数是你的应用中 Store 的唯一 ID。</span></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> useUserStore = <span class="title function_">defineStore</span>(<span class="string">'user'</span>, <span class="function">() =></span> {</span><br><span class="line"> <span class="keyword">const</span> nickName = <span class="title function_">ref</span>(<span class="string">"Kahvia"</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">function</span> <span class="title function_">setName</span>(<span class="params">name: <span class="built_in">string</span></span>) {</span><br><span class="line"> nickName.<span class="property">value</span> = name;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> { nickName, setName };</span><br><span class="line">}, {</span><br><span class="line"> <span class="attr">persist</span>: {</span><br><span class="line"> <span class="attr">storage</span>: uniStorege,</span><br><span class="line"> },</span><br><span class="line">})</span><br><span class="line"></span><br></pre></td></tr></table></figure><p>关于插件的其它可选配置，可以参照官方文档。</p><h3 id="为-uniapp-的请求添加拦截器"><a class="markdownIt-Anchor" href="#为-uniapp-的请求添加拦截器"></a> 为 uniapp 的请求添加拦截器</h3><p>拦截器的作用是，在请求发送前拦截请求，或收到请求结果后拦截结果，对请求或结果作一定的处理后，再放行。常用于简化操作，比如发送请求前统一添加域名前缀，或收到请求结果后提取关键数据、展示错误信息等。减少了代码的冗余。ps：比如我以前做项目的时候，都是在一个 js 文件中定义常量 baseUrl，在有请求的页面引入该 js 文件，采用 baseUrl + ‘/user/upload’ 这种形式的代码，这意味着我有多少个请求，我就写了多少个这样的拼接代码，的确写了很多无用代码。</p><p>以下代码块则展示了如何添加请求发送前的拦截器。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//utils/http.ts</span></span><br><span class="line"><span class="keyword">import</span> { useUserStore } <span class="keyword">from</span> <span class="string">"@/stores/piniaStores"</span>;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> <span class="attr">baseUrl</span>: <span class="built_in">string</span> = <span class="string">"https://www.kahvia.cn"</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> httpInterceptor = {</span><br><span class="line"> <span class="title function_">invoke</span>(<span class="params">options: UniApp.RequestOptions</span>) {</span><br><span class="line"> <span class="comment">//请求添加前缀</span></span><br><span class="line"> <span class="keyword">if</span> (!options.<span class="property">url</span>.<span class="title function_">startsWith</span>(<span class="string">"http"</span>))</span><br><span class="line"> options.<span class="property">url</span> = baseUrl + options.<span class="property">url</span>;</span><br><span class="line"> <span class="comment">//设置超时时间</span></span><br><span class="line"> options.<span class="property">timeout</span> = <span class="number">10000</span>;</span><br><span class="line"> <span class="comment">//设置请求头</span></span><br><span class="line"> options.<span class="property">header</span> = {</span><br><span class="line"> <span class="comment">//保留原有请求头</span></span><br><span class="line"> ...options.<span class="property">header</span>,</span><br><span class="line"> <span class="comment">//添加请求来源</span></span><br><span class="line"> <span class="string">'source-client'</span>: <span class="string">'miniapp'</span></span><br><span class="line"> };</span><br><span class="line"> <span class="keyword">const</span> userStore = <span class="title function_">useUserStore</span>();</span><br><span class="line"> <span class="keyword">const</span> token = userStore.<span class="property">profile</span>?.<span class="property">token</span>;</span><br><span class="line"> <span class="keyword">if</span> (token)</span><br><span class="line"> options.<span class="property">header</span>.<span class="property">Authorization</span> = token;</span><br><span class="line"></span><br><span class="line"> },</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line">uni.<span class="title function_">addInterceptor</span>(<span class="string">"request"</span>, httpInterceptor);</span><br><span class="line">uni.<span class="title function_">addInterceptor</span>(<span class="string">"uploadFile"</span>, httpInterceptor);</span><br></pre></td></tr></table></figure><p>uniapp 中没有关于请求结果的拦截器，得用 Promise 手动封装。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//utils/http.ts</span></span><br><span class="line"><span class="comment">//接上个拦截器代码块</span></span><br><span class="line"></span><br><span class="line"><span class="comment">//自己封装的数据类型</span></span><br><span class="line"><span class="keyword">interface</span> <span class="title class_">Data</span><T> {</span><br><span class="line"> <span class="attr">code</span>: <span class="built_in">number</span>,</span><br><span class="line"> <span class="attr">msg</span>: <span class="built_in">string</span>,</span><br><span class="line"> <span class="attr">data</span>: T</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="comment">//封装uni-request，对数据结果进行统一处理，即拦截请求结果。上面的interceptor是请求发送前拦截。</span></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">const</span> http = <T><span class="function">(<span class="params">options: UniApp.RequestOptions</span>) =></span> {</span><br><span class="line"> <span class="keyword">return</span> <span class="keyword">new</span> <span class="title class_">Promise</span><<span class="title class_">Data</span><T>>(<span class="function">(<span class="params">resolve, reject</span>) =></span> {</span><br><span class="line"> uni.<span class="title function_">request</span>({</span><br><span class="line"> ...options,</span><br><span class="line"> <span class="comment">//服务器有响应结果，不管状态码是200还是401亦或是500，都会走success函数。</span></span><br><span class="line"> <span class="title function_">success</span>(<span class="params">res</span>) {</span><br><span class="line"> <span class="comment">//状态码正常，则resolve，axios内部也是如此实现的。</span></span><br><span class="line"> <span class="keyword">if</span> (res.<span class="property">statusCode</span> >= <span class="number">200</span> && res.<span class="property">statusCode</span> < <span class="number">300</span>) {</span><br><span class="line"> <span class="comment">//用as对返回类型进行断言</span></span><br><span class="line"> <span class="title function_">resolve</span>(res.<span class="property">data</span> <span class="keyword">as</span> <span class="title class_">Data</span><T>);</span><br><span class="line"> } <span class="keyword">else</span> <span class="keyword">if</span> (res.<span class="property">statusCode</span> == <span class="number">401</span>) {</span><br><span class="line"> <span class="comment">//401代表token无效，身份验证失败</span></span><br><span class="line"> <span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"Authorization error"</span>);</span><br><span class="line"> uni.<span class="title function_">showToast</span>({ <span class="attr">title</span>: <span class="string">"身份验证失效，请重新登录"</span> });</span><br><span class="line"> <span class="title function_">reject</span>(res);</span><br><span class="line"> } <span class="keyword">else</span> {</span><br><span class="line"> uni.<span class="title function_">showToast</span>({ <span class="attr">title</span>: <span class="string">"服务器异常"</span> });</span><br><span class="line"> <span class="title function_">reject</span>(res);</span><br><span class="line"> }</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//服务器没有返回结果，代表请求未成功发送，即网络异常。</span></span><br><span class="line"> <span class="title function_">fail</span>(<span class="params">err</span>) {</span><br><span class="line"> uni.<span class="title function_">showToast</span>({ <span class="attr">title</span>: <span class="string">"网络异常，请检查网络"</span> })</span><br><span class="line"> <span class="title function_">reject</span>(err);</span><br><span class="line"> },</span><br><span class="line"> })</span><br><span class="line"> })</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>这样一来，自己封装的网络请求模块就完成了。在需要的地方导入使用即可。</p><p>注：泛型 T 的使用是为了更好地处理数据。每个请求返回的 data 部分都是变化的，有的是字符数组，有的是对象数组，根据选择使用。</p><figure class="highlight ts"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> {http} <span class="keyword">from</span> <span class="string">'@/utils/http'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">async</span> <span class="keyword">function</span> <span class="title function_">clickTest</span>(<span class="params"></span>){</span><br><span class="line"> userStore.<span class="title function_">setName</span>(<span class="string">"Adong"</span>);</span><br><span class="line"> <span class="keyword">const</span> res = <span class="keyword">await</span> http<<span class="built_in">string</span>[]>({</span><br><span class="line"> <span class="attr">method</span>:<span class="string">"GET"</span>,</span><br><span class="line"> <span class="attr">url</span>:<span class="string">"/test"</span></span><br><span class="line"> })</span><br><span class="line"> <span class="variable language_">console</span>.<span class="title function_">log</span>(res);</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>当请求的结果有效，即 resolve 后，该 Promise 对象的状态会变成 fulfilled（已兑现），变量 res 有了有效值，继续执行下面的 log 语句。当请求的结果无效，即 reject 后，该 Promise 对象的状态变为 rejected（已拒绝），此时异步函数直接结束，不会执行下面的 log 语句。</p><p>注：Promise 对象的初始状态为 pending（待定）。</p><h3 id="uniapp知识点"><a class="markdownIt-Anchor" href="#uniapp知识点"></a> uniapp知识点</h3><h4 id="svg"><a class="markdownIt-Anchor" href="#svg"></a> svg</h4><p>uniapp 中不支持 svg 标签，所以涉及到的 svg 图片可以转换成 base64 进行使用。</p><p><a href="https://www.zhangxinxu.com/sp/svgo/">SVG在线工具</a>。通过这个工具我们可以实现上述操作。我就用这个工具将 iconfont 上面的图标转换成了 base64 ，用 img 标签进行了插入。</p><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="tag"><<span class="name">img</span> <span class="attr">class</span>=<span class="string">"searchIcon"</span> <span class="attr">src</span>=<span class="string">"data:image/svg+xml;base64,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"</span>></span></span><br></pre></td></tr></table></figure><h4 id="自定义导航栏"><a class="markdownIt-Anchor" href="#自定义导航栏"></a> 自定义导航栏</h4><p>设置 navigationStyle 为 custom 以取消默认导航栏。然后手写导航栏组件添加到页面中使用即可。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br></pre></td><td class="code"><pre><span class="line"><span class="punctuation">{</span></span><br><span class="line"><span class="attr">"easycom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="attr">"autoscan"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"custom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="comment">// uni-ui 规则如下配置</span></span><br><span class="line"><span class="attr">"^uni-(.*)"</span><span class="punctuation">:</span> <span class="string">"@dcloudio/uni-ui/lib/uni-$1/uni-$1.vue"</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"pages"</span><span class="punctuation">:</span> <span class="punctuation">[</span> <span class="comment">//pages数组中第一项表示应用启动页，参考：https://uniapp.dcloud.io/collocation/pages</span></span><br><span class="line"><span class="punctuation">{</span></span><br><span class="line"><span class="attr">"path"</span><span class="punctuation">:</span> <span class="string">"pages/index/index"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"style"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="comment">//取消默认导航栏</span></span><br><span class="line"><span class="attr">"navigationStyle"</span><span class="punctuation">:</span> <span class="string">"custom"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"navigationBarTitleText"</span><span class="punctuation">:</span> <span class="string">"首页"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"navigationBarTextStyle"</span><span class="punctuation">:</span> <span class="string">"white"</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">]</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"globalStyle"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="attr">"navigationBarTextStyle"</span><span class="punctuation">:</span> <span class="string">"white"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"navigationBarTitleText"</span><span class="punctuation">:</span> <span class="string">"uni-app"</span><span class="punctuation">,</span></span><br><span class="line"><span class="comment">// "navigationBarBackgroundColor": "#F8F8F8",</span></span><br><span class="line"><span class="comment">// "backgroundColor": "#F8F8F8"</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><h4 id="image标签"><a class="markdownIt-Anchor" href="#image标签"></a> image标签</h4><p>uniapp 中不能使用 img 标签。使用 img 标签后，会被解析成 image 标签，导致为 img 写的 css 样式失效。</p><h4 id="样式隔离"><a class="markdownIt-Anchor" href="#样式隔离"></a> 样式隔离</h4><p>在某些情况下，比如我写了一个组件，里面用到了 uniapp 提供的内置组件，如 uni-file-picker ，当我尝试通过 vue 的样式穿透去修改内置组件的样式时，怎么改都不行，用上 !important 也不行，在调试的时候看穿透的样式根本没修改成功。这时候或许就是 uniapp 自带的样式隔离起了作用。使用以下代码进行样式隔离的取消，可以解决问题。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><script lang="ts"></span><br><span class="line">export default {</span><br><span class="line"> options: {</span><br><span class="line"> styleIsolation: 'shared'</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></script></span><br></pre></td></tr></table></figure><p>非常傻逼的一个问题。<a href="https://developers.weixin.qq.com/miniprogram/dev/framework/custom-component/wxml-wxss.html#%E7%BB%84%E4%BB%B6%E6%A0%B7%E5%BC%8F%E9%9A%94%E7%A6%BB">样式隔离。</a>这个文档是微信官方文档，因此推断是微信小程序的特有设定。</p><h4 id="禁止手指滑动"><a class="markdownIt-Anchor" href="#禁止手指滑动"></a> 禁止手指滑动</h4><p>在自定义的加载遮罩显示时，需要禁止手指滑动，以防下面的页面被滑动。</p><p>在最外层添加 @touchmove.stop.prevent=“() => { }” 。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><template></span><br><span class="line"> <div @touchmove.stop.prevent="() => { }" class="loading" :class="{ alignTop: ifAlignTop, alignBottom: !ifAlignTop }"</span><br><span class="line"> v-if="isLoading"></span><br><span class="line"> <uni-load-more icon-type="circle" color="white" status="loading" :icon-size="30"</span><br><span class="line"> :content-text="{ contentrefresh: content, contentdown: '', contentnomore: '' }" /></span><br><span class="line"> </div></span><br><span class="line"></template></span><br></pre></td></tr></table></figure><h4 id="自定义遮罩的位置问题"><a class="markdownIt-Anchor" href="#自定义遮罩的位置问题"></a> 自定义遮罩的位置问题</h4><p>在 uniapp 中，App.vue 文件中并不能写 template ，所以全局遮罩并不方便实现。 所以需要定义一个遮罩组件，在每个页面分别引入使用。</p><p>然而，遮罩放在每个页面的根节点下有时也并不方便。举个例子，遮罩的高度一般是100vh，假设我通过绝对定位对页面进行上左对齐，当页面可以滚动的时候，即页面高度大于100vh的时候，如果我在页面底部触发了遮罩，由于遮罩高度不够，页面底部就是无遮罩状态。如果我对遮罩的高度预设成300vh，可以达到遮住底部的效果，但是遮罩中间的加载用的提示信息又跑到了别处，而不在屏幕中间。想要动态控制遮罩的高度或者其中的文字位置是不现实的，每个页面的高度都不一样，而 uniapp 中又不容易获取滚动高度。</p><p><s>因此，固定遮罩的高度为100vh，尝试调整遮罩的引入位置以及对齐位置才是更合理的做法。比如我在页面底部触发了从底部弹出的弹出层，那么封装一个组件，引入弹出层和遮罩层，将自定义组件标记为相对定位，遮罩层标记为绝对定位，并使遮罩下左对齐。</s></p><h4 id="scroll-view-滚动条问题"><a class="markdownIt-Anchor" href="#scroll-view-滚动条问题"></a> scroll-view 滚动条问题</h4><p>在微信小程序中，仅设置 show-scrollbar = “false” 是没用的，同时还要设置 enhanced = “true”。</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><scroll-view :scroll-y="true" class="cats" :show-scrollbar="false" :enhanced="true"></span><br><span class="line"> <div :key="index" v-for="(cat, index) in categories" class="cat" :class="{ catActive: catIsActive(index) }"</span><br><span class="line"> @click=setActive(index)></span><br><span class="line"> <text>{{ cat.name }}</text></span><br><span class="line"> </div></span><br><span class="line"></scroll-view></span><br></pre></td></tr></table></figure><p>别用uniapp的这个组件写 flex 布局。因为flex布局中的 align-content 会无效，调了一下午没吊用。🐕都不用。自己写的 flex 布局盒子好用的一批。</p><h4 id="第三方组件引入问题"><a class="markdownIt-Anchor" href="#第三方组件引入问题"></a> 第三方组件引入问题</h4><p>以 NutUi 为例，配置 easycom 自动导入的代码如下所示。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="attr">"easycom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="attr">"autoscan"</span><span class="punctuation">:</span> <span class="literal"><span class="keyword">true</span></span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"custom"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"><span class="comment">// uni-ui 规则如下配置</span></span><br><span class="line"><span class="attr">"^uni-(.*)"</span><span class="punctuation">:</span> <span class="string">"@dcloudio/uni-ui/lib/uni-$1/uni-$1.vue"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"^nut-(.*)?-(.*)"</span><span class="punctuation">:</span> <span class="string">"nutui-uniapp/components/$1$2/$1$2.vue"</span><span class="punctuation">,</span></span><br><span class="line"><span class="attr">"^nut-(.*)"</span><span class="punctuation">:</span> <span class="string">"nutui-uniapp/components/$1/$1.vue"</span></span><br><span class="line"><span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>可以看到引入规则中的组件名称是短横线命名法。因此在使用组件时，也应使用短横线命名，因为大驼峰命名会导致自动引入出问题，我甚至曾怀疑是 uniapp 的问题，毕竟是真不太好用。</p><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"><!-- 有效 --></span></span><br><span class="line"><span class="tag"><<span class="name">nut-button</span> <span class="attr">type</span>=<span class="string">"danger"</span>></span>TEST<span class="tag"></<span class="name">nut-button</span>></span></span><br><span class="line"><span class="comment"><!-- 无效 --></span></span><br><span class="line"><span class="comment"><!-- <NutButton type="danger">TEST</NutButton> --></span></span><br></pre></td></tr></table></figure><p>当然有时也会出现大驼峰名称能用的情况，这种情况通常是短横线名称的组件以意想不到的方式被引入了。比如上面代码中两种写法，如果同时存在，你会发现大驼峰形式的也能正常用，因为短横线写法已经引入了这个组件。至于为什么大驼峰不能正常引入组件，我只能猜测 easycom 就是浅显地凭借所写标签名称进行自动引入的。</p>]]></content>
<summary type="html"><h3 id="在vscode中开发uniapp"><a class="markdownIt-Anchor" href="#在vscode中开发uniapp"></a> 在vscode中开发uniapp</h3>
<h4 id="使用命令行创建uniapp项目"><a class</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="uniapp" scheme="https://blog.kahvia.cn/tags/uniapp/"/>
</entry>
<entry>
<title>使用nrm管理npm镜像源</title>
<link href="https://blog.kahvia.cn/2024/02/04/NpmMirrorManage.html"/>
<id>https://blog.kahvia.cn/2024/02/04/NpmMirrorManage.html</id>
<published>2024-02-04T09:58:19.119Z</published>
<updated>2024-06-22T06:00:26.310Z</updated>
<content type="html"><![CDATA[<h3 id="安装nrm"><a class="markdownIt-Anchor" href="#安装nrm"></a> 安装nrm</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm install -g nrm</span><br></pre></td></tr></table></figure><h3 id="查看镜像源"><a class="markdownIt-Anchor" href="#查看镜像源"></a> 查看镜像源</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">nrm <span class="built_in">ls</span></span><br></pre></td></tr></table></figure><h3 id="选用镜像源"><a class="markdownIt-Anchor" href="#选用镜像源"></a> 选用镜像源</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">nrm use xxx</span><br></pre></td></tr></table></figure><p>比如<strong>nrm use taobao</strong>。当 npm 命令卡进度的时候，请先查看当前源是否是镜像源，因为在2024年6月22日这天突然发现变回了默认源，切换为镜像源后恢复正常。</p>]]></content>
<summary type="html"><h3 id="安装nrm"><a class="markdownIt-Anchor" href="#安装nrm"></a> 安装nrm</h3>
<figure class="highlight bash"><table><tr><td class="gutter"><pre></summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="node.js" scheme="https://blog.kahvia.cn/tags/node-js/"/>
</entry>
<entry>
<title>基础算法</title>
<link href="https://blog.kahvia.cn/2024/01/15/AlgorithmAcBase1.html"/>
<id>https://blog.kahvia.cn/2024/01/15/AlgorithmAcBase1.html</id>
<published>2024-01-15T10:16:23.498Z</published>
<updated>2024-01-28T14:27:25.713Z</updated>
<content type="html"><![CDATA[<h3 id="快速排序"><a class="markdownIt-Anchor" href="#快速排序"></a> 快速排序</h3><ol><li>选取基准值（分界值）x，可以是数组的第一个元素，也可以是数组的最后一个元素，中间元素亦可。</li><li>使用双指针<strong> i </strong>和 <strong>j</strong> 从数组的两端开始扫描，从左端找到一个<strong>>=x</strong>的值a，从右端找到一个<strong><=x</strong>的值b，交换ab的值，交换后<strong>i以及i之前的元素</strong>都小于等于x，<strong>j以及j之后的元素</strong>都大于等于x。交换后i应递增，j应递减，继续查找可以交换的值，知道ij相遇甚至错开（i > j）。</li><li>当数组成功划分两部分，左部分小于等于x，右部分大于等于x的时候，左右两部分分别递归调用快速排序。</li></ol><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/4.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"><span class="type">int</span> t[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">quick_sort</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(l >= r) <span class="keyword">return</span>;</span><br><span class="line"> <span class="type">int</span> i = l - <span class="number">1</span>, j = r + <span class="number">1</span>, x = t[(l + r) / <span class="number">2</span>];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(i < j){</span><br><span class="line"> <span class="comment">//基准值元素也可以交换，在左区间或者右区间都可以，因此while (t[i] < x);没有等号=。</span></span><br><span class="line"> <span class="comment">//如果是不能交换，即while (t[i] <= x);</span></span><br><span class="line"> <span class="comment">//那么比如6 2 3，基准值为2时。从左边找到了一个比2大的值6，但是从右边找不到比2小的，j--会一直执行，死循环了。</span></span><br><span class="line"> <span class="keyword">do</span> i++; <span class="keyword">while</span> (t[i] < x);</span><br><span class="line"> <span class="keyword">do</span> j--; <span class="keyword">while</span> (t[j] > x);</span><br><span class="line"> <span class="keyword">if</span>(i < j) <span class="built_in">swap</span>(t[i],t[j]);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">/*在划分区间递归调用快排的时候，i==j或者i>j</span></span><br><span class="line"><span class="comment"> ①当i==j时，举例数组为2 1. l==0，r==1。区间为[0,1]。</span></span><br><span class="line"><span class="comment"> x = t[(l + r) / 2];取值为x=2，相当于取数组首元素为基准值，经过循环后i==j==0。</span></span><br><span class="line"><span class="comment"> 正确的分法：划分区间应为[0,0]和[1,1]，即[l, j]和[j + 1, r]，或者将j换成i。</span></span><br><span class="line"><span class="comment"> 也就是将相遇处的元素划分给右区间。</span></span><br><span class="line"><span class="comment"> 错误的分法：如果划分给左区间，即[l, j - 1]和[j, r]的话，区间为[0,-1]和[0,1]。</span></span><br><span class="line"><span class="comment"> 右区间的快排与当前快排区间相同，导致右区间递归与当前相同，陷入死循环。</span></span><br><span class="line"><span class="comment"> 若想使得该分法正确，应当x = t[(l + r + 1) / 2]，即取数组尾元素为基准值。</span></span><br><span class="line"><span class="comment"> ②当i>j时。举例，在上一轮while中交换ij元素后，进入下一轮while循环前，</span></span><br><span class="line"><span class="comment"> i == 1, j == 2，进入循环后，i++变成2，j--变成1，此时发生i > j的情况。且<2的元素<=x, >1的元素>=x。</span></span><br><span class="line"><span class="comment"> 这种情况下划分区间时，根据①的两种分法，为了保证划分的正确性:</span></span><br><span class="line"><span class="comment"> 若取数组首元素为基准值，则应采用j,即[l, j]和[j + 1, r]。</span></span><br><span class="line"><span class="comment"> 如果采用[l, i]和[i + 1, r]，右区间为[3, r]很显然缺少了下标2对应的>=x的元素，同理左区间会多一个。</span></span><br><span class="line"><span class="comment"> 若取数组尾元素为基准值，则应采用i,即[l, i - 1]和[i, r]。原理同上。</span></span><br><span class="line"><span class="comment"></span></span><br><span class="line"><span class="comment"> 总结：一整个快速排序中包含很多个小快速排序，可能出现i==j和i>j的情况。因此，为了确保两种情况下都正常运行，分类如下。</span></span><br><span class="line"><span class="comment"> ①x = t[(l + r) / 2];或者说取左端点元素为基准值的情况下，递归区间划分[l, j]和[j + 1, r]。</span></span><br><span class="line"><span class="comment"> ②x = t[(l + r + 1) / 2]；或者说取右端点元素为基准值的情况下，递归区间划分[l, i - 1]和[i, r]。</span></span><br><span class="line"><span class="comment"> */</span></span><br><span class="line"> <span class="built_in">quick_sort</span>(l,j);</span><br><span class="line"> <span class="built_in">quick_sort</span>(j + <span class="number">1</span>,r);</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>,&n);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++)</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>,&t[i]);</span><br><span class="line"></span><br><span class="line"> <span class="built_in">quick_sort</span>(<span class="number">0</span>, n - <span class="number">1</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++)</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d "</span>,t[i]);</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="归并排序"><a class="markdownIt-Anchor" href="#归并排序"></a> 归并排序</h3><ol><li>数组一分为二，递归调用归并排序。</li><li>利用双指针，合并一分为二的数组，将结果存到额外数组 tmp 中。</li><li>合并完成后，将结果数组覆盖至原数组中。</li></ol><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/16.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"><span class="type">int</span> t[N], tmp[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">merge_sort</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(l >= r) <span class="keyword">return</span>;</span><br><span class="line"> <span class="comment">//右移等同除以二</span></span><br><span class="line"> <span class="type">int</span> mid = l + r >> <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line"> <span class="comment">//从数组中间一分为二，各自归并排序</span></span><br><span class="line"> <span class="built_in">merge_sort</span>(l, mid), <span class="built_in">merge_sort</span>(mid + <span class="number">1</span>, r);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//k是结果数组的下一个放置元素的位置，ij为数组左右两部分的起始指针</span></span><br><span class="line"> <span class="type">int</span> k = <span class="number">0</span>, i = l, j = mid + <span class="number">1</span>;</span><br><span class="line"> <span class="comment">//比较ij指针值的大小，择其小存于结果中</span></span><br><span class="line"> <span class="keyword">while</span>(i <= mid && j <= r){</span><br><span class="line"> <span class="keyword">if</span>(t[i] <= t[j]) tmp[k++] = t[i++];</span><br><span class="line"> <span class="keyword">else</span> tmp[k++] = t[j++];</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//当某一部分已经全部加入结果后，另一部分的剩余元素直接加入结果</span></span><br><span class="line"> <span class="keyword">while</span>(i <= mid) tmp[k++] = t[i++];</span><br><span class="line"> <span class="keyword">while</span>(j <= r) tmp[k++] = t[j++];</span><br><span class="line"></span><br><span class="line"> <span class="comment">//用有序的结果覆盖原来无序的数组</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = l, j = <span class="number">0</span>; i <= r; i++,j++)</span><br><span class="line"> t[i] = tmp[j];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &n);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++) <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &t[i]);</span><br><span class="line"></span><br><span class="line"> <span class="built_in">merge_sort</span>(<span class="number">0</span>, n - <span class="number">1</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++) <span class="built_in">printf</span>(<span class="string">"%d "</span>, t[i]);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="归并排序的应用求解逆序对数量"><a class="markdownIt-Anchor" href="#归并排序的应用求解逆序对数量"></a> 归并排序的应用——求解逆序对数量</h4><p>对于任意给定的数字序列，举例如<strong> 4 3 2 1 </strong>，若交换相邻元素，可以减少一个逆序对而不影响这两个元素于其它元素的逆序关系。此处交换<strong> 4 , 3 </strong>会得到<strong> 3 4 2 1 </strong>，可以发现，前半部分元素与后半部分的逆序关系保持不变，前半部分内部消除了一个逆序对。</p><p>因此，我们可以考虑将数组一分为二，左右两部分分别消除内部逆序对，得到两个有序的序列，再消除序列之间的逆序对。若有两个有序序列为<strong> 2 4 6 </strong>和<strong> 1 3 5 </strong>，使用双指针分别指向两个序列开头，将序列2的小元素移到大序列的前面，比如1移到2的前面，越过了2 4 6三个元素，那么就减少了三个逆序对。多次操作，直到大序列整体有序。</p><p>很显然，上述的操作就是归并排序的一种表现。将数组不断地一分为二，当一组只有两个元素的时候，对这一组一分为二成两个序列，每个序列一个元素，使用双指针归并后，表现为逆序的两个元素交换位置。同样长度为2的毗邻序列各自有序，同样可以使用双指针进行逆序对的消除。</p><p>因此，求解逆序对的数量，我们只需要在归并排序中，保存序列2元素越过的序列1元素个数即可。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/17.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">//逆序对的数量</span></span><br><span class="line"><span class="comment">//https://www.acwing.com/problem/content/790/</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"></span><br><span class="line"><span class="type">long</span> <span class="type">long</span> t[N], tmp[N];</span><br><span class="line"></span><br><span class="line"><span class="type">long</span> <span class="type">long</span> counts = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">calculate_reverse_pair</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(l >= r) <span class="keyword">return</span>;</span><br><span class="line"> <span class="type">int</span> mid = l + r >> <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line"> <span class="built_in">calculate_reverse_pair</span>(l, mid), <span class="built_in">calculate_reverse_pair</span>(mid + <span class="number">1</span>, r);</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> k = <span class="number">0</span>, i = l, j = mid + <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(i <= mid && j <= r){</span><br><span class="line"> <span class="keyword">if</span>(t[i] <= t[j]) {</span><br><span class="line"> tmp[k++] = t[i++];</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span>{</span><br><span class="line"> tmp[k++] = t[j++];</span><br><span class="line"> <span class="comment">//将后半部分的小元素移到前半部分时，越过的前半部分元素个数即为逆序对个数</span></span><br><span class="line"> counts += (mid - i + <span class="number">1</span>);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(i <= mid) tmp[k++] = t[i++];</span><br><span class="line"> <span class="keyword">while</span>(j <= r) tmp[k++] = t[j++];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = l, j = <span class="number">0</span>; i <= r; i++, j++)</span><br><span class="line"> t[i] = tmp[j];</span><br><span class="line"></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &n);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++) <span class="built_in">scanf</span>(<span class="string">"%lld"</span>, &t[i]);</span><br><span class="line"></span><br><span class="line"> <span class="built_in">calculate_reverse_pair</span>(<span class="number">0</span>, n - <span class="number">1</span>);</span><br><span class="line"></span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%lld"</span>, counts);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="二分"><a class="markdownIt-Anchor" href="#二分"></a> 二分</h3><p>二分就是寻找一个边界，将整个数组一分为二，一边满足性质，另一边不满足。</p><h4 id="整数二分"><a class="markdownIt-Anchor" href="#整数二分"></a> 整数二分</h4><p><a href="https://www.acwing.com/problem/content/791/">AcWing—数的范围</a></p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/16.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"><span class="type">int</span> t[N];</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n, q;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d"</span>, &n, &q);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < n; i++) <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &t[i]);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(q--){</span><br><span class="line"> <span class="type">int</span> x;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &x);</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> l = <span class="number">0</span>, r = n - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(l < r){</span><br><span class="line"> <span class="type">int</span> mid = l + r >> <span class="number">1</span>;</span><br><span class="line"> <span class="comment">//查找x1位置时，x1以及其后元素都满足>=x这个性质</span></span><br><span class="line"> <span class="comment">//当mid对应元素满足性质时，x1应在mid或者mid前，更新右区间为mid</span></span><br><span class="line"> <span class="keyword">if</span>(t[mid] >= x) r = mid;</span><br><span class="line"> <span class="comment">//当mid对应元素不满足性质时，x1应在mid后，更新左区间为mid + 1.</span></span><br><span class="line"> <span class="keyword">else</span> l = mid + <span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(t[l] != x) <span class="built_in">printf</span>(<span class="string">"-1 -1\n"</span>);</span><br><span class="line"> <span class="keyword">else</span>{</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d "</span>, l);</span><br><span class="line"> <span class="type">int</span> l = <span class="number">0</span>, r = n - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span>(l < r){</span><br><span class="line"> <span class="comment">//在l == mid == r - 1时，若是t[mid]满足性质，左区间会更新为mid</span></span><br><span class="line"> <span class="comment">//为防止死循环，mid应上取整</span></span><br><span class="line"> <span class="type">int</span> mid = l + r + <span class="number">1</span> >> <span class="number">1</span>;</span><br><span class="line"> <span class="comment">//查找x_last元素位置时，x_last及其前面元素满足<=x的性质</span></span><br><span class="line"> <span class="comment">//当mid对应元素满足该性质时，x_last应在mid或者mid后，更新左区间为mid</span></span><br><span class="line"> <span class="comment">//当mid对应元素不满足时，x_last应在mid前，更新右区间为mid - 1</span></span><br><span class="line"> <span class="keyword">if</span>(t[mid] <= x) l = mid;</span><br><span class="line"> <span class="keyword">else</span> r = mid - <span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d\n"</span>, l);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="浮点数二分"><a class="markdownIt-Anchor" href="#浮点数二分"></a> 浮点数二分</h4><p><a href="https://www.acwing.com/problem/content/792/">AcWing—三次方根</a></p><p>在求解次方根的问题中，需要注意，当x处于(0,1)的区间内时，其n次方根的结果会大于x。比如0.01的平方根是0.1。因此在使用二分求解n次方根的时候，我们需要将右边界加1。</p><p>二分结束的条件设置为一定的精度，比如当结果保留6位小数的时候，我们可以设置精度为1e-8，保留7位则1e-9，以此类推。确保结果的准确性。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/16.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">double</span> x;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%lf"</span>, &x);</span><br><span class="line"></span><br><span class="line"> <span class="type">bool</span> aboveZero = <span class="literal">true</span>;</span><br><span class="line"> <span class="keyword">if</span>(x < <span class="number">0</span>) aboveZero = <span class="literal">false</span>, x = <span class="number">0</span> - x;</span><br><span class="line"></span><br><span class="line"> <span class="type">double</span> l = <span class="number">0</span>, r = x + <span class="number">1</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(r - l > <span class="number">1e-8</span>){</span><br><span class="line"> <span class="type">double</span> mid = (l + r) / <span class="number">2</span>;</span><br><span class="line"> <span class="keyword">if</span>(mid*mid*mid >= x) r = mid;</span><br><span class="line"> <span class="keyword">else</span> l = mid;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%lf"</span>, !aboveZero?-l:l);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="高精度"><a class="markdownIt-Anchor" href="#高精度"></a> 高精度</h3><h4 id="加法"><a class="markdownIt-Anchor" href="#加法"></a> 加法</h4><p>利用数组存储两个很长很长的数。数的高位存在数组的后面，地位存在数组的前面。这样一来，加法最高位进位的时候，可以方便地在数的最高位前面补上进位数。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/18.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><vector></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">add</span><span class="params">(vector<<span class="type">int</span>> &A, vector<<span class="type">int</span>> &B)</span></span>{</span><br><span class="line"> vector<<span class="type">int</span>> C;</span><br><span class="line"> <span class="type">int</span> t = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; t != <span class="number">0</span> || i < A.<span class="built_in">size</span>() || i < B.<span class="built_in">size</span>(); i++){</span><br><span class="line"> <span class="keyword">if</span>(i < A.<span class="built_in">size</span>()) t += A[i];</span><br><span class="line"> <span class="keyword">if</span>(i < B.<span class="built_in">size</span>()) t += B[i];</span><br><span class="line"> C.<span class="built_in">push_back</span>(t % <span class="number">10</span>);</span><br><span class="line"> t = t >= <span class="number">10</span> ? <span class="number">1</span> : <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> C;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> string a, b;</span><br><span class="line"> vector<<span class="type">int</span>> A, B;</span><br><span class="line"></span><br><span class="line"> cin >> a >> b;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = a.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) A.<span class="built_in">push_back</span>(a[i] - <span class="string">'0'</span>);</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = b.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) B.<span class="built_in">push_back</span>(b[i] - <span class="string">'0'</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">auto</span> C = <span class="built_in">add</span>(A, B);</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(C.<span class="built_in">size</span>() != <span class="number">0</span>){</span><br><span class="line"> cout << C.<span class="built_in">back</span>();</span><br><span class="line"> C.<span class="built_in">pop_back</span>();</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="减法正减正"><a class="markdownIt-Anchor" href="#减法正减正"></a> 减法（正减正）</h4><p>类似加法，注意借位即可。为了方便，我们可以提前判断运算数的大小，始终用大的减小的。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/18.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><vector></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="comment">//比较两个数的大小</span></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">cmp</span><span class="params">(vector<<span class="type">int</span>> &A, vector<<span class="type">int</span>> &B)</span></span>{</span><br><span class="line"> <span class="keyword">if</span>(A.<span class="built_in">size</span>() != B.<span class="built_in">size</span>()) <span class="keyword">return</span> A.<span class="built_in">size</span>() >= B.<span class="built_in">size</span>();</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = A.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--){</span><br><span class="line"> <span class="keyword">if</span>(A[i] > B[i]) <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> <span class="keyword">if</span>(A[i] < B[i]) <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">sub</span><span class="params">(vector<<span class="type">int</span>> &A, vector<<span class="type">int</span>> &B)</span></span>{</span><br><span class="line"> vector<<span class="type">int</span>> C;</span><br><span class="line"> <span class="type">int</span> t = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; t != <span class="number">0</span> || i < A.<span class="built_in">size</span>() || i < B.<span class="built_in">size</span>(); i++){</span><br><span class="line"> <span class="comment">//A位减去被借的位</span></span><br><span class="line"> <span class="keyword">if</span>(i < A.<span class="built_in">size</span>()) t = A[i] - t;</span><br><span class="line"> <span class="comment">//再减B位</span></span><br><span class="line"> <span class="keyword">if</span>(i < B.<span class="built_in">size</span>()) t -= B[i];</span><br><span class="line"> <span class="comment">//若位运算结果为负数，代表需要借位。+10取余为借位后的结果。若不需借位也无妨，+10取余为0。</span></span><br><span class="line"> C.<span class="built_in">push_back</span>((t + <span class="number">10</span>) % <span class="number">10</span>);</span><br><span class="line"> <span class="comment">//保存借位</span></span><br><span class="line"> t = t < <span class="number">0</span> ? <span class="number">1</span> : <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//去除最高位前面的0.比如运算结果为003，则去掉00，保留结果为3.</span></span><br><span class="line"> <span class="keyword">while</span>(C.<span class="built_in">size</span>() > <span class="number">1</span> && C.<span class="built_in">back</span>() == <span class="number">0</span>)</span><br><span class="line"> C.<span class="built_in">pop_back</span>();</span><br><span class="line"> <span class="keyword">return</span> C;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> string a, b;</span><br><span class="line"> vector<<span class="type">int</span>> A, B;</span><br><span class="line"></span><br><span class="line"> cin >> a >> b;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = a.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) A.<span class="built_in">push_back</span>(a[i] - <span class="string">'0'</span>);</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = b.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) B.<span class="built_in">push_back</span>(b[i] - <span class="string">'0'</span>);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//将小数-大数转换成-（大数-小数）</span></span><br><span class="line"> <span class="type">bool</span> a_greater = <span class="built_in">cmp</span>(A, B);</span><br><span class="line"> <span class="keyword">auto</span> C = a_greater ? <span class="built_in">sub</span>(A, B) : <span class="built_in">sub</span>(B, A);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//如果是小数-大数，则在结果前面添加负号</span></span><br><span class="line"> <span class="keyword">if</span>(!a_greater) <span class="built_in">printf</span>(<span class="string">"-"</span>);</span><br><span class="line"> <span class="keyword">while</span>(C.<span class="built_in">size</span>() != <span class="number">0</span>){</span><br><span class="line"> cout << C.<span class="built_in">back</span>();</span><br><span class="line"> C.<span class="built_in">pop_back</span>();</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="乘法"><a class="markdownIt-Anchor" href="#乘法"></a> 乘法</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/22.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><vector></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="comment">//乘法的实质就是123 * 4 = 100 * 4 + 20 * 4 + 3 * 4.结果的个位诞生于最低位乘以4，十位诞生于十位乘以4加上个位进的位</span></span><br><span class="line"><span class="comment">//以此类推。</span></span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">mul</span><span class="params">(vector<<span class="type">int</span>> &A, <span class="type">int</span> b)</span></span>{</span><br><span class="line"> vector<<span class="type">int</span>> C;</span><br><span class="line"> <span class="type">int</span> t = <span class="number">0</span>;</span><br><span class="line"> <span class="comment">//大数每一位乘以小数，并加上低位进的位，得到的结果最后一位，为当前位的数，结果的其余位都是进位。</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < A.<span class="built_in">size</span>(); i++){</span><br><span class="line"> t += A[i] * b;</span><br><span class="line"> C.<span class="built_in">push_back</span>(t % <span class="number">10</span>);</span><br><span class="line"> t /= <span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span>(t) C.<span class="built_in">push_back</span>(t);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(C.<span class="built_in">size</span>() > <span class="number">1</span> && C.<span class="built_in">back</span>() == <span class="number">0</span>) C.<span class="built_in">pop_back</span>();</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> C;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> string a;</span><br><span class="line"> <span class="type">int</span> b;</span><br><span class="line"> cin >> a >> b;</span><br><span class="line"></span><br><span class="line"> vector<<span class="type">int</span>> A;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = a.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) A.<span class="built_in">push_back</span>(a[i] - <span class="string">'0'</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">auto</span> C = <span class="built_in">mul</span>(A, b);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = C.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) <span class="built_in">printf</span>(<span class="string">"%d"</span>, C[i]);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="除法"><a class="markdownIt-Anchor" href="#除法"></a> 除法</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/22.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><vector></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><algorithm></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">div</span><span class="params">(vector<<span class="type">int</span>> A, <span class="type">int</span> b)</span></span>{</span><br><span class="line"> vector<<span class="type">int</span>> C;</span><br><span class="line"> <span class="type">int</span> t = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"> <span class="comment">//从大数高位开始除</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = A.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--){</span><br><span class="line"> t = t * <span class="number">10</span> + A[i];</span><br><span class="line"> <span class="comment">//能除就除</span></span><br><span class="line"> <span class="keyword">if</span>(t >= b) C.<span class="built_in">push_back</span>(t / b), t = t % b;</span><br><span class="line"> <span class="comment">//不能除，商就置零</span></span><br><span class="line"> <span class="keyword">else</span> C.<span class="built_in">push_back</span>(<span class="number">0</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//翻转数组，并去除高位0。</span></span><br><span class="line"> <span class="built_in">reverse</span>(C.<span class="built_in">begin</span>(), C.<span class="built_in">end</span>());</span><br><span class="line"> <span class="keyword">while</span>(C.<span class="built_in">size</span>() > <span class="number">1</span> && C.<span class="built_in">back</span>() == <span class="number">0</span>) C.<span class="built_in">pop_back</span>();</span><br><span class="line"> <span class="comment">//翻转回来，把最终的余数补在数组最后面</span></span><br><span class="line"> <span class="built_in">reverse</span>(C.<span class="built_in">begin</span>(), C.<span class="built_in">end</span>());</span><br><span class="line"> C.<span class="built_in">push_back</span>(t);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> C;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> string a;</span><br><span class="line"> <span class="type">int</span> b;</span><br><span class="line"> vector<<span class="type">int</span>> A;</span><br><span class="line"></span><br><span class="line"> cin >> a >> b;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = a.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; i--) A.<span class="built_in">push_back</span>(a[i] - <span class="string">'0'</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">auto</span> C = <span class="built_in">div</span>(A, b);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">0</span>; i < C.<span class="built_in">size</span>() - <span class="number">1</span>; i++) <span class="built_in">printf</span>(<span class="string">"%d"</span>, C[i]);</span><br><span class="line"></span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"\n%d"</span>, C.<span class="built_in">back</span>());</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="前缀与差分"><a class="markdownIt-Anchor" href="#前缀与差分"></a> 前缀与差分</h3><h4 id="前缀和一维"><a class="markdownIt-Anchor" href="#前缀和一维"></a> 前缀和（一维）</h4><p>对于一个普通的一维数组（从 a1 = a[1] 开始，a[0] = 0），前n项和称为前缀和。通过Sn - S(k-1)可以得到S[k,n]的部分和。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/23.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"><span class="type">int</span> a[N], s[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n, m;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d"</span>, &n, &m);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &a[i]);</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) s[i] = s[i - <span class="number">1</span>] + a[i];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(m--){</span><br><span class="line"> <span class="type">int</span> l, r;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d"</span>, &l, &r);</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d\n"</span>, s[r] - s[l - <span class="number">1</span>]);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="子矩阵的和"><a class="markdownIt-Anchor" href="#子矩阵的和"></a> 子矩阵的和</h4><p><a href="https://www.acwing.com/problem/content/798/">796. 子矩阵的和 - AcWing题库</a></p><p>要求解一个矩阵的子矩阵的元素和，只需要想象一个矩阵，切割成十字形，按需拼凑即可。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/23.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1010</span>;</span><br><span class="line"><span class="type">int</span> a[N][N], s[N][N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="comment">//n行m列，q个询问</span></span><br><span class="line"> <span class="type">int</span> n, m, q;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d%d"</span>, &n, &m, &q);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++)</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <=m; j++)</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &a[i][j]);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++)</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <= m; j++)</span><br><span class="line"> <span class="comment">/*</span></span><br><span class="line"><span class="comment"> * a11 a12 | a13</span></span><br><span class="line"><span class="comment"> * a21 a22 | a23</span></span><br><span class="line"><span class="comment"> * --------|----</span></span><br><span class="line"><span class="comment"> * a31 a32 | a33</span></span><br><span class="line"><span class="comment"> * 比如s[3][3] = s[3][2] + s[2][3] - s[2][2]（这是去除重复加的部分）+ a[3][3]</span></span><br><span class="line"><span class="comment"> * */</span></span><br><span class="line"> s[i][j] = s[i][j - <span class="number">1</span>] + s[i - <span class="number">1</span>][j] - s[i - <span class="number">1</span>][j - <span class="number">1</span>] + a[i][j];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span>(q--){</span><br><span class="line"> <span class="type">int</span> x1, y1, x2, y2;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d%d%d"</span>, &x1, &y1, &x2, &y2);</span><br><span class="line"> <span class="comment">/*</span></span><br><span class="line"><span class="comment"> * a11 a12 a13 | a14 a15</span></span><br><span class="line"><span class="comment"> * a21 a22 a23 | a24 a25</span></span><br><span class="line"><span class="comment"> * ------------|--------</span></span><br><span class="line"><span class="comment"> * a31 a32 a33 | a34 a35</span></span><br><span class="line"><span class="comment"> * a41 a42 a43 | a44 a45</span></span><br><span class="line"><span class="comment"> * s[[3][4], [4][5]] = s[4][5] - s[4][3] - s[2][5] + s[2][3]（补回多减的重叠部分）</span></span><br><span class="line"><span class="comment"> * 实际上，这里的s[[3][4], [4][5]]整体类似于上一个注释位置中的a[3][3]，都是被夹的一部分，只是包含数据个数不同的区别。</span></span><br><span class="line"><span class="comment"> * */</span></span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d\n"</span>, s[x2][y2] - s[x2][y1 - <span class="number">1</span>] - s[x1 - <span class="number">1</span>][y2] + s[x1 - <span class="number">1</span>][y1 - <span class="number">1</span>]);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="差分"><a class="markdownIt-Anchor" href="#差分"></a> 差分</h3><h4 id="一维差分"><a class="markdownIt-Anchor" href="#一维差分"></a> 一维差分</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/25.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"><span class="comment">//a数组为前缀和数组，b为差分数组</span></span><br><span class="line"><span class="type">int</span> a[N], b[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">insert</span><span class="params">(<span class="type">int</span> l, <span class="type">int</span> r, <span class="type">int</span> c)</span></span>{</span><br><span class="line"> <span class="comment">//对于前缀和数组a而言，要使[l, r]的前缀和+c</span></span><br><span class="line"> <span class="comment">//只需使差分数组b的第l位元素+c，这会让l及其以后的前缀和+c</span></span><br><span class="line"> <span class="comment">//然后第r+1位元素-c，这会让r+1及其以后的前缀和-c，即[r + 1, ?]的前缀和保持不变。</span></span><br><span class="line"> b[l] += c;</span><br><span class="line"> b[r + <span class="number">1</span>] -= c;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n, m;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d"</span>, &n, &m);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//初始时，将a和b都看作全为零的的数组，前缀和和差分都为0。</span></span><br><span class="line"> <span class="comment">//然后输入数组a。</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &a[i]);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//将输入的数组a看作待添加的元素c，即区间[i,i]上的元素都加上常数c（a[i]）。</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) <span class="built_in">insert</span>(i, i, a[i]);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//同样的执行m次insert即可。</span></span><br><span class="line"> <span class="keyword">while</span>(m--){</span><br><span class="line"> <span class="type">int</span> l, r, c;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d%d"</span>, &l, &r, &c);</span><br><span class="line"> <span class="built_in">insert</span>(l, r, c);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//计算前缀和。</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) b[i] += b[i - <span class="number">1</span>];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++) <span class="built_in">printf</span>(<span class="string">"%d "</span>, b[i]);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h4 id="二维差分"><a class="markdownIt-Anchor" href="#二维差分"></a> 二维差分</h4><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2024/1/27.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">1010</span>;</span><br><span class="line"><span class="type">int</span> a[N][N], b[N][N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">insert</span><span class="params">(<span class="type">int</span> x1, <span class="type">int</span> y1, <span class="type">int</span> x2, <span class="type">int</span> y2, <span class="type">int</span> c)</span></span>{</span><br><span class="line"> b[x1][y1] += c;</span><br><span class="line"> b[x2 + <span class="number">1</span>][y1] -= c;</span><br><span class="line"> b[x1][y2 + <span class="number">1</span>] -= c;</span><br><span class="line"> b[x2 + <span class="number">1</span>][y2 + <span class="number">1</span>] += c;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="type">int</span> n, m, q;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d%d"</span>, &n, &m, &q);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++)</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <= m; j++)</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d"</span>, &a[i][j]);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//初始化差分数组</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++)</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <= m; j++)</span><br><span class="line"> <span class="built_in">insert</span>(i, j, i, j, a[i][j]);</span><br><span class="line"></span><br><span class="line"> <span class="comment">//更新差分数组</span></span><br><span class="line"> <span class="keyword">while</span>(q--){</span><br><span class="line"> <span class="type">int</span> x1, y1, x2, y2, c;</span><br><span class="line"> <span class="built_in">scanf</span>(<span class="string">"%d%d%d%d%d"</span>, &x1, &y1, &x2, &y2, &c);</span><br><span class="line"> <span class="built_in">insert</span>(x1, y1, x2, y2, c);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//更新前缀和数组</span></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++)</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <= m; j++)</span><br><span class="line"> a[i][j] = a[i][j - <span class="number">1</span>] + a[i - <span class="number">1</span>][j] - a[i - <span class="number">1</span>][j - <span class="number">1</span>] + b[i][j];</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i = <span class="number">1</span>; i <= n; i++){</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j = <span class="number">1</span>; j <= m; j++)</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"%d "</span>, a[i][j]);</span><br><span class="line"> <span class="built_in">printf</span>(<span class="string">"\n"</span>);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h3 id="快速排序"><a class="markdownIt-Anchor" href="#快速排序"></a> 快速排序</h3>
<ol>
<li>选取基准值（分界值）x，可以是数组的第一个元素，也可以是数组的最后一个元素，中间元素亦可。</li>
<li>使用双指针</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="Algorithm" scheme="https://blog.kahvia.cn/tags/Algorithm/"/>
</entry>
<entry>
<title>数据结构——基础问题</title>
<link href="https://blog.kahvia.cn/2023/11/02/AlgorithmForGraduateTest.html"/>
<id>https://blog.kahvia.cn/2023/11/02/AlgorithmForGraduateTest.html</id>
<published>2023-11-02T14:44:06.902Z</published>
<updated>2023-11-05T14:30:49.237Z</updated>
<content type="html"><![CDATA[<h2 id="六-哈夫曼树"><a class="markdownIt-Anchor" href="#六-哈夫曼树"></a> 六、哈夫曼树</h2><h3 id="1合并果子"><a class="markdownIt-Anchor" href="#1合并果子"></a> 1.合并果子</h3><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2023/10/31.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">//https://www.acwing.com/problem/content/150/</span></span><br><span class="line"><span class="comment">//使用哈夫曼树的知识合并果子堆，计算最小花费体力</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><iostream></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><algorithm></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><queue></span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><vector></span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="comment">//定义一个优先队列，第一个参数是队列元素的类型，第二个是使用的容器类型，第三个是排序方式。</span></span><br><span class="line"> <span class="comment">//此处使用升序排序，即小的元素优先出队。</span></span><br><span class="line"> priority_queue<<span class="type">int</span>, vector<<span class="type">int</span>>, greater<<span class="type">int</span>>> stones_heap;</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> n;</span><br><span class="line"> cin>>n;</span><br><span class="line"> <span class="keyword">while</span> (n--){</span><br><span class="line"> <span class="type">int</span> stones;</span><br><span class="line"> cin>>stones;</span><br><span class="line"> stones_heap.<span class="built_in">push</span>(stones);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> strength_used = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span> (stones_heap.<span class="built_in">size</span>() > <span class="number">1</span>){</span><br><span class="line"> <span class="comment">//取出最小的两个结点（果子堆）</span></span><br><span class="line"> <span class="type">int</span> min1 = stones_heap.<span class="built_in">top</span>();</span><br><span class="line"> stones_heap.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="type">int</span> min2 = stones_heap.<span class="built_in">top</span>();</span><br><span class="line"> stones_heap.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="comment">//将这两个果子堆合并</span></span><br><span class="line"> stones_heap.<span class="built_in">push</span>(min1 + min2);</span><br><span class="line"> <span class="comment">//累计合并果子堆花费的体力</span></span><br><span class="line"> strength_used += (min1 + min2);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> cout<<strength_used;</span><br><span class="line"></span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="2荷马史诗"><a class="markdownIt-Anchor" href="#2荷马史诗"></a> 2.荷马史诗</h3><p>K叉哈夫曼树的问题类似于二叉哈夫曼树。需要注意的点是，在K叉哈夫曼树中，我们每次合并结点都会取出最小的K个结点，在我们进行最后一次合并的时候，可能存在的结点个数不足K个。</p><p>如1，2，3，4，5，6 ——> 6（1，2，3），4，5，6 ——> 6（1，2，3），15（4，5，6）.</p><p>这时候我们需要补充零结点进去充数。 6（1，2，3），15（4，5，6），0 ——> 21（6，15）.然后我们会发现，将二层的0和底部的6交换，会让K叉树的结果变好。所以，我们应在开始合并前就补充零结点，使得刚好其元素个数刚好能构建K叉哈夫曼树。</p><p>这时候我们可以分析什么时候该补充零结点。我们每次合并结点都会将K个结点合并成一个结点，减少了K-1个结点。刚开始N个元素，全部合并后仅剩1个元素，减少了N-1个结点。每次合并减少K-1个，共需减少N-1个，合并次数为（N-1）/ (K-1)。即不能整除的时候，说明需要补充零结点。</p><p>由于荷马史诗的编码要求编码树的高度最小，所以在合并结点的时候，除了选择最小的K个结点，还要在节点值相同的时候，优先选择结点展开的子树高度（深度）最小的结点。</p><p>比如，1，3，4，3 ——> 4（1，3），4，3 。根据值最小原则，可以选第一个4，也可以选第二个4，与3合并。很显然，前者合并到最后的高度为3，后者为2。所以在合并的时候，我们应尽量往矮的结点上合并。就像俄罗斯方块，合并的恰到好处才不容易到达顶端。我想大多数人都是优先平铺方块再垂直放的吧。</p><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2023/11/1.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">//https://www.acwing.com/problem/content/151/</span></span><br><span class="line"><span class="comment">//荷马史诗</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"iostream"</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"algorithm"</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"queue"</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"vector"</span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="comment">//define a pair of data. long long for word_code and int for Huffman coding node depth.</span></span><br><span class="line"><span class="keyword">typedef</span> pair<<span class="type">long</span> <span class="type">long</span>, <span class="type">int</span>> PLI;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>{</span><br><span class="line"> priority_queue<PLI, vector<PLI>, greater<>> words;</span><br><span class="line"></span><br><span class="line"> <span class="comment">//k is the system of numeration</span></span><br><span class="line"> <span class="type">long</span> <span class="type">long</span> words_num, k;</span><br><span class="line"> cin>>words_num>>k;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span> (words_num--){</span><br><span class="line"> <span class="type">long</span> <span class="type">long</span> word;</span><br><span class="line"> cin>>word;</span><br><span class="line"> words.<span class="built_in">push</span>({word, <span class="number">0</span>});</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//every loop for merge will delete k nodes and add a combined node,</span></span><br><span class="line"> <span class="comment">//so k-1 nodes decrease in each merge.</span></span><br><span class="line"> <span class="comment">//the loop will continues until there is only one node.</span></span><br><span class="line"> <span class="comment">//loop time = (words_num - 1) / (k-1).</span></span><br><span class="line"> <span class="comment">//if the time is not a integer, just add zero node until it can be a integer.</span></span><br><span class="line"> <span class="keyword">while</span> ((words.<span class="built_in">size</span>() - <span class="number">1</span>) % (k - <span class="number">1</span>) != <span class="number">0</span>)</span><br><span class="line"> words.<span class="built_in">push</span>({<span class="number">0</span>,<span class="number">0</span>});</span><br><span class="line"></span><br><span class="line"> <span class="comment">//the with power length is the new coded book length</span></span><br><span class="line"> <span class="type">long</span> <span class="type">long</span> wpl = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span> (words.<span class="built_in">size</span>() > <span class="number">1</span>){</span><br><span class="line"> <span class="type">long</span> <span class="type">long</span> combined_node_val = <span class="number">0</span>;</span><br><span class="line"> <span class="type">int</span> max_depth = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < k; ++i) {</span><br><span class="line"> <span class="comment">//get the min node</span></span><br><span class="line"> <span class="keyword">auto</span> min_node = words.<span class="built_in">top</span>();</span><br><span class="line"> <span class="comment">//merge</span></span><br><span class="line"> combined_node_val += min_node.first;</span><br><span class="line"> <span class="comment">//save the highest son-tree's depth</span></span><br><span class="line"> max_depth = <span class="built_in">max</span>(max_depth, min_node.second);</span><br><span class="line"> <span class="comment">//delete the node</span></span><br><span class="line"> words.<span class="built_in">pop</span>();</span><br><span class="line"> }</span><br><span class="line"> <span class="comment">//add the combined node.</span></span><br><span class="line"> words.<span class="built_in">push</span>({combined_node_val,max_depth + <span class="number">1</span>});</span><br><span class="line"> <span class="comment">//the new combined node value is a part of the WPL.</span></span><br><span class="line"> wpl += combined_node_val;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> cout<<wpl<<endl<<words.<span class="built_in">top</span>().second;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h2 id="七-拓扑排序有向图问题"><a class="markdownIt-Anchor" href="#七-拓扑排序有向图问题"></a> 七、拓扑排序（有向图问题）</h2><h3 id="1基于广搜广度优先遍历的拓扑排序实现方法"><a class="markdownIt-Anchor" href="#1基于广搜广度优先遍历的拓扑排序实现方法"></a> 1.基于广搜（广度优先遍历）的拓扑排序实现方法</h3><p>广度优先遍历（BFS），实际上就是一层一层地遍历。</p><ol><li>将第一个顶点入队</li><li>队列出队，将出队的顶点连接的顶点进行入队，我简称为出队展开。</li><li>重复步骤2直到队列为空</li></ol><ul><li>注意，需要开一个数组保存顶点是否被遍历过。顶点入队的时候，就该标记为被遍历过了，防止重复入队（比如出现回环的时候，A<—>B，A出队会B会入队，B出队A会入队，会出现死循环）。</li></ul><p>拓扑排序实现方式</p><pre><code>1. 入队的标准改为：入度为0的顶点才能入队。2. 当顶点入队的时候，将该顶点可以通往顶点的入度减1（即在图中隐藏该入队的顶点，代表该工程任务结束）3. 简单来说，就是在BFS出队展开时，只让入度为0的顶点入队（即只有前置任务全部完成，才能将新的任务加入执行清单）。</code></pre><ul><li>需要开一个数组维护每个顶点的入度。</li><li>因为只有入度为0的才能入队，重边，或者回环，都会导致度不为0无法入队，所以不需要BFS那个判断是否被遍历过的数组。</li></ul><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">// Created by Kahiva on 2023/11/5.</span></span><br><span class="line"><span class="comment">//</span></span><br><span class="line"><span class="comment">//https://www.acwing.com/problem/content/850/</span></span><br><span class="line"><span class="comment">//拓扑排序(采用广度遍历实现)</span></span><br><span class="line"></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"iostream"</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"algorithm"</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">"queue"</span></span></span><br><span class="line"></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="comment">//n个顶点m条边</span></span><br><span class="line"><span class="type">int</span> n, m;</span><br><span class="line"><span class="comment">//定义一个常量N，即最大可能用到的顶点数。定义入度数组和模拟队列的数组时可以用到。</span></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">100010</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">Node</span> {</span><br><span class="line"> <span class="type">int</span> nodeId;</span><br><span class="line"> Node* next;</span><br><span class="line"> <span class="built_in">Node</span>(<span class="type">int</span> id):<span class="built_in">nodeId</span>(id), <span class="built_in">next</span>(<span class="literal">NULL</span>){};</span><br><span class="line">}*link[N];</span><br><span class="line"></span><br><span class="line"><span class="comment">//保存各顶点的入度</span></span><br><span class="line"><span class="type">int</span> inDegree[N];</span><br><span class="line"><span class="comment">//采用数组模拟队列，出队移动头索引，入队移动尾索引。这样可以在模拟队列的同时，保留原队列中的元素。</span></span><br><span class="line"><span class="type">int</span> checkQueue[N];</span><br><span class="line"></span><br><span class="line"><span class="comment">//将某个点和另一个点的边加入邻接表表示的图中。</span></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">addLink</span><span class="params">(<span class="type">int</span> fromNodeId, <span class="type">int</span> toNodeId)</span></span>{</span><br><span class="line"> Node* node = <span class="keyword">new</span> <span class="built_in">Node</span>(toNodeId);</span><br><span class="line"> node->next = link[fromNodeId];</span><br><span class="line"> link[fromNodeId] = node;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">topSort</span><span class="params">()</span></span>{</span><br><span class="line"> <span class="comment">//head指向队头，rear指向队列最后一个元素</span></span><br><span class="line"> <span class="type">int</span> head = <span class="number">0</span>, rear = <span class="number">-1</span>;</span><br><span class="line"> <span class="comment">//因为顶点编号从1开始，所以入度数组从索引1开始遍历</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i) {</span><br><span class="line"> <span class="comment">//遍历顶点，如果顶点入度为0，就入队</span></span><br><span class="line"> <span class="keyword">if</span> (!inDegree[i]){</span><br><span class="line"> checkQueue[++rear] = i;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span> (head <= rear){</span><br><span class="line"> <span class="comment">//取出队头元素</span></span><br><span class="line"> <span class="keyword">auto</span> top = checkQueue[head++];</span><br><span class="line"> <span class="comment">//遍历它的邻边，将邻边那头对应点的入度减一</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="keyword">auto</span> p = link[top]; p ; p = p->next){</span><br><span class="line"> inDegree[p->nodeId]--;</span><br><span class="line"> <span class="comment">//如果没有了前置结点，代表可以入队(即被遍历，或者说该工程任务可以执行了)</span></span><br><span class="line"> <span class="keyword">if</span> (inDegree[p->nodeId] == <span class="number">0</span>){</span><br><span class="line"> checkQueue[++rear] = p->nodeId;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//如果队列中的元素个数刚好等于顶点个数，就代表拓扑排序成立，即不存在闭环。</span></span><br><span class="line"> <span class="comment">//因为如果有闭环，闭环上结点的入度始终不为0，无法入队。</span></span><br><span class="line"> <span class="keyword">return</span> n == rear + <span class="number">1</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span> </span>{</span><br><span class="line"></span><br><span class="line"> cin>>n>>m;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span> (m--){</span><br><span class="line"> <span class="type">int</span> from, to;</span><br><span class="line"> cin>>from>>to;</span><br><span class="line"> <span class="built_in">addLink</span>(from, to);</span><br><span class="line"> inDegree[to]++;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="comment">//如果拓扑排序无效，则输出-1</span></span><br><span class="line"> <span class="keyword">if</span> (!<span class="built_in">topSort</span>())</span><br><span class="line"> cout<<<span class="string">"-1"</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> cout<<checkQueue[i]<<<span class="string">' '</span>;</span><br><span class="line"></span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line">}</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h2 id="六-哈夫曼树"><a class="markdownIt-Anchor" href="#六-哈夫曼树"></a> 六、哈夫曼树</h2>
<h3 id="1合并果子"><a class="markdownIt-Anchor" href="#1合并果子"></a> </summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="Algorithm" scheme="https://blog.kahvia.cn/tags/Algorithm/"/>
</entry>
<entry>
<title>Clion中Cmake的设置问题</title>
<link href="https://blog.kahvia.cn/2023/10/15/Clion-cmake.html"/>
<id>https://blog.kahvia.cn/2023/10/15/Clion-cmake.html</id>
<published>2023-10-15T08:58:30.017Z</published>
<updated>2023-10-15T09:14:10.042Z</updated>
<content type="html"><![CDATA[<h3 id="1设置可执行程序输出目录"><a class="markdownIt-Anchor" href="#1设置可执行程序输出目录"></a> 1.设置可执行程序输出目录</h3><figure class="highlight cmake"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">set</span>(CMAKE_RUNTIME_OUTPUT_DIRECTORY <span class="string">"${CMAKE_CURRENT_SOURCE_DIR}/bin"</span>)</span><br></pre></td></tr></table></figure><h3 id="2将cpp文件添加为生成可执行文件的源文件"><a class="markdownIt-Anchor" href="#2将cpp文件添加为生成可执行文件的源文件"></a> 2.将cpp文件添加为“生成可执行文件”的源文件</h3><figure class="highlight cmake"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">add_executable</span>(AcWing3375 Acwing/graduate/AcWing3375.cpp)</span><br></pre></td></tr></table></figure><h3 id="完整的cmake设置"><a class="markdownIt-Anchor" href="#完整的cmake设置"></a> 完整的cmake设置</h3><figure class="highlight cmake"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">cmake_minimum_required</span>(VERSION <span class="number">3.24</span>)</span><br><span class="line"><span class="comment">#指定cmake工程名</span></span><br><span class="line"><span class="keyword">project</span>(algorithm)</span><br><span class="line"></span><br><span class="line"><span class="comment">#c++版本</span></span><br><span class="line"><span class="keyword">set</span>(CMAKE_CXX_STANDARD <span class="number">14</span>)</span><br><span class="line"><span class="comment"># 指定可执行程序输出目录</span></span><br><span class="line"><span class="keyword">set</span>(CMAKE_RUNTIME_OUTPUT_DIRECTORY <span class="string">"${CMAKE_CURRENT_SOURCE_DIR}/bin"</span>)</span><br><span class="line"><span class="keyword">add_executable</span>(AcWing3375 Acwing/graduate/AcWing3375.cpp)</span><br></pre></td></tr></table></figure><h3 id="附普通的gitignore文件"><a class="markdownIt-Anchor" href="#附普通的gitignore文件"></a> 附：普通的gitignore文件</h3><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">/.idea/</span><br><span class="line">/cmake-build-debug/</span><br><span class="line">/bin/</span><br></pre></td></tr></table></figure>]]></content>
<summary type="html"><h3 id="1设置可执行程序输出目录"><a class="markdownIt-Anchor" href="#1设置可执行程序输出目录"></a> 1.设置可执行程序输出目录</h3>
<figure class="highlight cmake"><table><tr><</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="clion cmake" scheme="https://blog.kahvia.cn/tags/clion-cmake/"/>
</entry>
<entry>
<title>Vue3使用Echarts</title>
<link href="https://blog.kahvia.cn/2023/07/19/vue3-echarts.html"/>
<id>https://blog.kahvia.cn/2023/07/19/vue3-echarts.html</id>
<published>2023-07-19T01:30:49.148Z</published>
<updated>2023-07-19T11:13:09.375Z</updated>
<content type="html"><![CDATA[<h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3><p>响应式布局，是为五个不同的屏幕尺寸制定不同的显示比例。这是网页收缩导致网页布局变乱的究极解决方案。</p>]]></content>
<summary type="html"><h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3>
<p>响应式布局，是为五个不同的屏幕尺寸制定不同的显示比例。这是网页收缩导致网页布局变乱的究极解决方案。</p>
</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="echarts vue3" scheme="https://blog.kahvia.cn/tags/echarts-vue3/"/>
</entry>
<entry>
<title>响应式布局</title>
<link href="https://blog.kahvia.cn/2023/07/04/ResponsiveDesign.html"/>
<id>https://blog.kahvia.cn/2023/07/04/ResponsiveDesign.html</id>
<published>2023-07-04T11:58:41.653Z</published>
<updated>2023-07-04T13:58:56.460Z</updated>
<content type="html"><![CDATA[<h3 id="响应式布局"><a class="markdownIt-Anchor" href="#响应式布局"></a> 响应式布局</h3><p>响应式布局，是为五个不同的屏幕尺寸制定不同的显示比例。这是网页收缩导致网页布局变乱的究极解决方案。</p>]]></content>
<summary type="html"><h3 id="响应式布局"><a class="markdownIt-Anchor" href="#响应式布局"></a> 响应式布局</h3>
<p>响应式布局，是为五个不同的屏幕尺寸制定不同的显示比例。这是网页收缩导致网页布局变乱的究极解决方案。</p>
</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="html element" scheme="https://blog.kahvia.cn/tags/html-element/"/>
</entry>
<entry>
<title>Nodejs-包</title>
<link href="https://blog.kahvia.cn/2023/06/28/NodeJsPackage.html"/>
<id>https://blog.kahvia.cn/2023/06/28/NodeJsPackage.html</id>
<published>2023-06-28T06:31:43.686Z</published>
<updated>2023-06-29T07:59:06.907Z</updated>
<content type="html"><![CDATA[<h3 id="包的类型"><a class="markdownIt-Anchor" href="#包的类型"></a> 包的类型</h3><ul><li>项目包：用于编写项目和和业务逻辑</li><li>软件包：封装工具和方法进行使用<ul><li>本地软件包：当前项目内使用，封装<strong>属性和方法</strong>，存在于 node_modules中。</li><li>全局软件包：本机所有项目使用，封装<strong>命令和工具</strong>，存在于系统设置的位置。</li></ul></li></ul><h3 id="软件包的结构"><a class="markdownIt-Anchor" href="#软件包的结构"></a> 软件包的结构</h3><p>如下图所示。整个util包由三部分组成，libs、index.js、package.json。</p><ul><li>libs中，存放工具包的源代码 js 文件。</li><li>index.js文件作为入口文件，通过这个文件统一暴露对外工具方法等。</li><li>package.json文件，描述包的一些信息。</li></ul><p><img src="https://pics.kahvia.cn/img/image-20230628145428487.png" alt="包的结构图" /></p><h3 id="libs示例"><a class="markdownIt-Anchor" href="#libs示例"></a> libs示例</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//printHello.js</span></span><br><span class="line"><span class="keyword">function</span> <span class="title function_">printHello</span>(<span class="params"></span>) {</span><br><span class="line"> <span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"Hello,Adong. It's your first tools package."</span>)</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> words = <span class="string">"How old are you?"</span></span><br><span class="line"></span><br><span class="line"><span class="variable language_">module</span>.<span class="property">exports</span> = {</span><br><span class="line"> printHello,</span><br><span class="line"> words</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="indexjs示例"><a class="markdownIt-Anchor" href="#indexjs示例"></a> index.js示例</h3><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//下面这用法叫做解析重构</span></span><br><span class="line"><span class="keyword">let</span> { printHello, words } = <span class="built_in">require</span>(<span class="string">"./libs/printHello"</span>)</span><br><span class="line"></span><br><span class="line"><span class="keyword">let</span> resHeaderUtil = <span class="built_in">require</span>(<span class="string">"./libs/resHeaderUtil-commonjs"</span>)</span><br><span class="line"></span><br><span class="line"><span class="comment">//对libs中的工具，统一作模块暴露</span></span><br><span class="line"><span class="variable language_">module</span>.<span class="property">exports</span> = {</span><br><span class="line"> printHello,</span><br><span class="line"> words,</span><br><span class="line"> resHeaderUtil</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h3 id="packagejson示例"><a class="markdownIt-Anchor" href="#packagejson示例"></a> package.json示例</h3><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"name"</span><span class="punctuation">:</span> <span class="string">"kahvia_tools"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"author"</span><span class="punctuation">:</span> <span class="string">"Kahvia"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"description"</span><span class="punctuation">:</span> <span class="string">"包含了设置http请求的响应头的工具和输出你好的工具函数"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"main"</span><span class="punctuation">:</span> <span class="string">"index.js"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"version"</span><span class="punctuation">:</span> <span class="string">"1.0.0"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"license"</span><span class="punctuation">:</span> <span class="string">"MIT"</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>其中，main表示工具包的入口文件，version代表版本，license表示许可证。</p><h3 id="软件包的使用"><a class="markdownIt-Anchor" href="#软件包的使用"></a> 软件包的使用</h3><p>在使用软件包时，路径只需要到软件包的根目录即可。无需指定更详细的路径。它会自动寻找index.js，若无则查找package.json中的main入口。</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">let</span> kahvia_utils = <span class="built_in">require</span>(<span class="string">"./util"</span>)</span><br><span class="line"></span><br><span class="line">kahvia_utils.<span class="title function_">printHello</span>()</span><br></pre></td></tr></table></figure><p>结果如下所示。</p><p><img src="https://pics.kahvia.cn/img/image-20230628150604791.png" alt="工具包使用结果" /></p><h3 id="npm"><a class="markdownIt-Anchor" href="#npm"></a> NPM</h3><p>npm是nodejs的包管理器。</p><p>若项目中没有package.json，可以通过以下命令执行初始化。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm init -y</span><br></pre></td></tr></table></figure><p>若我们需要安装某个软件包，则通过以下命令执行安装，软件包会存放在node_modules目录下，软件包的版本则会保存在package-lock.json文件中，用作固化版本。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i package-name</span><br></pre></td></tr></table></figure><p>我们使用下载的软件包时，可以<strong>直接通过包名引入</strong>，而不用通过路径。</p><p>当我们协同开发时，git不会同步我们的node_modules文件夹。可能别人使用了某个包，但是我们自己没有使用，所以本地没有这个包。我们可以通过以下命令，根据package.json文件，安装本地缺少的包。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i</span><br></pre></td></tr></table></figure><h3 id="常用的软件包"><a class="markdownIt-Anchor" href="#常用的软件包"></a> 常用的软件包</h3><h4 id="nodemon"><a class="markdownIt-Anchor" href="#nodemon"></a> nodemon</h4><p>一个全局软件包，需要全局安装。通过这个nodemon启动 js 文件，可以检测代码更改，自动重启程序。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i nodemon -g</span><br></pre></td></tr></table></figure><h4 id="webpack"><a class="markdownIt-Anchor" href="#webpack"></a> webpack</h4><p>一个常用的打包工具，安装在项目的dev环境中。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i webpack webpack-cli --save-dev</span><br></pre></td></tr></table></figure><p>在项目的package.json中添加自定义脚本命令。其中，build是自定义的名称，什么都可以，其后面的值即webpack才是真正执行的命令。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="attr">"scripts"</span><span class="punctuation">:</span><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"build"</span><span class="punctuation">:</span><span class="string">"webpack"</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>将要打包的文件放在根目录的src目录中，通过npm run build，实现项目打包。不过这里的打包只能实现<strong>部分</strong> js 文件的打包，至于为什么是<strong>部分</strong>，因为打包那种nodejs写的后端项目，会报很多错误，而我暂时还不太懂问题出在哪里。目前打包给前端页面引用的js文件是没有问题的。</p><p>通过配置项目根目录的webpack.config.js文件，可以配置打包的参数，比如入口、出口、插件等。其中，entry是入口，output是出口，path是输出路径，filename是打包后的文件名。</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span></span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h5 id="htmlwebpackplugin根据自动生成目标页面并连接打包压缩的js文件"><a class="markdownIt-Anchor" href="#htmlwebpackplugin根据自动生成目标页面并连接打包压缩的js文件"></a> HtmlWebpackPlugin（根据自动生成目标页面并连接打包压缩的JS文件）</h5><p>webpack通过上述方式打包的话，只能打包普通的静态js文件。也就是说，打包完成后，我们需要手动为页面引入打包后的js文件，这无疑的麻烦的。通过HtmlWebpackPlugin，我们可以将页面一起打包，自动为页面引入打包好的js文件，一起输出到目标目录。</p><blockquote><p>详细的使用可以参考<a href="https://www.webpackjs.com/plugins/html-webpack-plugin/#basic-usage">官方文档</a></p></blockquote><p>通过如下命令安装插件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm install --save-dev html-webpack-plugin</span><br></pre></td></tr></table></figure><p>在webpack配置文件中，配置如下。其中，template作为模板，即以此模板在目标目录生成一份以filename为文件名的html文件，同时为其引入打包好的js文件。output中的clean属性可以清除上一次打包的东西。</p><figure class="highlight javascript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./public/index.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'test.html'</span></span><br><span class="line"> })</span><br><span class="line"> ]</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h5 id="css-loaderstyle-loader加载器把css打包到js文件中"><a class="markdownIt-Anchor" href="#css-loaderstyle-loader加载器把css打包到js文件中"></a> css-loader,style-loader（加载器，把css打包到js文件中）</h5><blockquote><p><a href="https://www.webpackjs.com/loaders/css-loader/">这两个加载器的官方文档</a></p></blockquote><ul><li>css-loader：解析css代码。</li><li>style-loader：把解析后的css代码插入到DOM。最后css代码在打包后的js文件中，通过函数的方式保存。</li></ul><p>按照下方命令安装加载器。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm install --save-dev css-loader style-loader</span><br></pre></td></tr></table></figure><p>在webpack配置文件中配置加载器。下方的module部分。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./Login/login.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'login.html'</span></span><br><span class="line"> })</span><br><span class="line"> ],</span><br><span class="line"> <span class="attr">module</span>: {</span><br><span class="line"> <span class="attr">rules</span>: [</span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.css$/i</span>,</span><br><span class="line"> <span class="attr">use</span>: [<span class="string">"style-loader"</span>, <span class="string">"css-loader"</span>],</span><br><span class="line"> },</span><br><span class="line"> ],</span><br><span class="line"> },</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>use数组中的元素顺序是有影响的。loader是从右到左应用的。在这种情况下，首先应用css-loader，然后应用style-loader。即先解析css引用，再绑定DOM元素。</p><p>配置好加载器以后，就可以把使用到的css文件引用到入口js文件中了。比如我这里的打包入口是hello.js文件，那我在文件内容开头import即可。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//hello.js</span></span><br><span class="line"><span class="keyword">import</span> <span class="string">'../Login/login.css'</span></span><br><span class="line"></span><br><span class="line"><span class="comment">//测试打包</span></span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"hello, kahvia !"</span>)</span><br><span class="line"><span class="comment">//二次输出</span></span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"what's up ?"</span>)</span><br></pre></td></tr></table></figure><p>以上都完成后，即可打包。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm run build</span><br></pre></td></tr></table></figure><h5 id="mini-css-extract-plugin提取css文件"><a class="markdownIt-Anchor" href="#mini-css-extract-plugin提取css文件"></a> mini-css-extract-plugin(提取css文件)</h5><blockquote><p><a href="https://www.webpackjs.com/plugins/mini-css-extract-plugin/">MiniCssExtractPlugin | webpack 中文文档</a></p></blockquote><p>我们在上面通过style-loader，是将css打包进js文件，这会导致js文件比平常更大。所以官方更推荐的一个做法是将css提取出来，而不是打包进js文件。通过<strong>mini-css-extract-plugin</strong>这个插件，配合css-loader我们可以做到提取css文件。</p><p>值得注意的是，mini-css-extract-plugin<strong>不能</strong>和style-loader一起使用，因为既要单独提取，又要打包进js文件，这不是相互矛盾了吗？</p><p>顺带一提，单独提取的css文件，是不会被压缩的。</p><p>通过以下命令安装插件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm install --save-dev mini-css-extract-plugin</span><br></pre></td></tr></table></figure><p>再在webpack配置文件中引入该插件，为其配置plugin选项，并在rules-use中添加插件内置的loader。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"><span class="comment">//引入css提取插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">MiniCssExtractPlugin</span> <span class="keyword">from</span> <span class="string">'mini-css-extract-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./Login/login.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'login.html'</span></span><br><span class="line"> }),</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">MiniCssExtractPlugin</span>()</span><br><span class="line"> ],</span><br><span class="line"> <span class="attr">module</span>: {</span><br><span class="line"> <span class="attr">rules</span>: [</span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.css$/i</span>,</span><br><span class="line"> <span class="attr">use</span>: [<span class="title class_">MiniCssExtractPlugin</span>.<span class="property">loader</span>, <span class="string">"css-loader"</span>],</span><br><span class="line"> },</span><br><span class="line"> ],</span><br><span class="line"> },</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h5 id="cssminimizerwebpackplugin压缩提取的css文件"><a class="markdownIt-Anchor" href="#cssminimizerwebpackplugin压缩提取的css文件"></a> CssMinimizerWebpackPlugin（压缩提取的css文件）</h5><p>通过上述的mini-css-extract-plugin插件，只能做到提取，但是会发现提取出来的css文件并没有做到压缩。而CssMinimizerWebpackPlugin就是为了压缩而使用的。</p><p>通过命令安装插件。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm install css-minimizer-webpack-plugin --save-dev</span><br></pre></td></tr></table></figure><p>在webpack配置文件中引入并配置。其中optimization-minimizer是配置项。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"><span class="comment">//引入css提取插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">MiniCssExtractPlugin</span> <span class="keyword">from</span> <span class="string">'mini-css-extract-plugin'</span></span><br><span class="line"><span class="comment">//引入css压缩插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">CssMinimizerPlugin</span> <span class="keyword">from</span> <span class="string">'css-minimizer-webpack-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./Login/login.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'login.html'</span></span><br><span class="line"> }),</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">MiniCssExtractPlugin</span>(),</span><br><span class="line"> ],</span><br><span class="line"> <span class="attr">module</span>: {</span><br><span class="line"> <span class="attr">rules</span>: [</span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.css$/i</span>,</span><br><span class="line"> <span class="attr">use</span>: [<span class="title class_">MiniCssExtractPlugin</span>.<span class="property">loader</span>, <span class="string">"css-loader"</span>],</span><br><span class="line"> },</span><br><span class="line"> ],</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//优化</span></span><br><span class="line"> <span class="attr">optimization</span>: {</span><br><span class="line"> <span class="comment">//minimize 减小</span></span><br><span class="line"> <span class="attr">minimizer</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">CssMinimizerPlugin</span>()</span><br><span class="line"> ]</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><h5 id="打包图片"><a class="markdownIt-Anchor" href="#打包图片"></a> 打包图片</h5><p>在上述操作中，我们可以打包html，css，js了，但是图片该如何处理呢？如果项目中的图片，采用网络地址url访问，那么我们打包后自然可以正常使用。但如果采用的是本地的图片呢？我们就需要把图片也一起打包了。</p><blockquote><p><a href="https://www.webpackjs.com/guides/asset-modules/">资源模块 | webpack 中文文档</a></p></blockquote><p>在webpack5中，我们无需使用外置loader，配置如下所示，在rule中配置图片打包。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"><span class="comment">//引入css提取插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">MiniCssExtractPlugin</span> <span class="keyword">from</span> <span class="string">'mini-css-extract-plugin'</span></span><br><span class="line"><span class="comment">//引入css压缩插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">CssMinimizerPlugin</span> <span class="keyword">from</span> <span class="string">'css-minimizer-webpack-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./Login/login.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'login.html'</span></span><br><span class="line"> }),</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">MiniCssExtractPlugin</span>(),</span><br><span class="line"> ],</span><br><span class="line"> <span class="attr">module</span>: {</span><br><span class="line"> <span class="attr">rules</span>: [</span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.css$/i</span>,</span><br><span class="line"> <span class="attr">use</span>: [<span class="title class_">MiniCssExtractPlugin</span>.<span class="property">loader</span>, <span class="string">"css-loader"</span>],</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//配置图片打包</span></span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.(png|jpg|gif)$/i</span>,</span><br><span class="line"> <span class="attr">type</span>: <span class="string">'asset'</span></span><br><span class="line"> },</span><br><span class="line"> ],</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//优化</span></span><br><span class="line"> <span class="attr">optimization</span>: {</span><br><span class="line"> <span class="comment">//minimize 减小</span></span><br><span class="line"> <span class="attr">minimizer</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">CssMinimizerPlugin</span>()</span><br><span class="line"> ]</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>在asset类型下，大于8kb的图片会直接作拷贝处理，小于8kb的会转为base64，通过uri的方式替换项目中的src引用。</p><p>类似于css打包，我们将要打包的图片也引入入口JS文件即可。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//hello.js</span></span><br><span class="line"><span class="keyword">import</span> <span class="string">'../Login/login.css'</span></span><br><span class="line"><span class="comment">//导入需要打包的本地图片</span></span><br><span class="line"><span class="keyword">import</span> <span class="string">'../Login/ganda.jpg'</span></span><br><span class="line"></span><br><span class="line"><span class="comment">//测试打包</span></span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"hello, kahvia !"</span>)</span><br><span class="line"><span class="comment">//二次输出</span></span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">"what's up ?"</span>)</span><br></pre></td></tr></table></figure><p>正常打包即可。</p><h5 id="搭建热更新开发环境"><a class="markdownIt-Anchor" href="#搭建热更新开发环境"></a> 搭建热更新开发环境</h5><p>下载webpack-dev-server。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm i webpack-dev-server --save-dev</span><br></pre></td></tr></table></figure><p>在webpack配置文件中，设置模式（mode）为开发模式（development）,并在package.json中配置自定义命令，即scripts中的选项，“dev”: “webpack serve --open”。</p><p>设置开发模式。</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> path <span class="keyword">from</span> <span class="string">'path'</span></span><br><span class="line"><span class="keyword">import</span> { getRecentDir } <span class="keyword">from</span> <span class="string">'./utils/recentPath.js'</span></span><br><span class="line"><span class="comment">//引入插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">HtmlWebpackPlugin</span> <span class="keyword">from</span> <span class="string">'html-webpack-plugin'</span></span><br><span class="line"><span class="comment">//引入css提取插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">MiniCssExtractPlugin</span> <span class="keyword">from</span> <span class="string">'mini-css-extract-plugin'</span></span><br><span class="line"><span class="comment">//引入css压缩插件</span></span><br><span class="line"><span class="keyword">import</span> <span class="title class_">CssMinimizerPlugin</span> <span class="keyword">from</span> <span class="string">'css-minimizer-webpack-plugin'</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">export</span> <span class="keyword">default</span> {</span><br><span class="line"> <span class="comment">//设置热更新开发模式</span></span><br><span class="line"> <span class="attr">mode</span>: <span class="string">"development"</span>,</span><br><span class="line"> <span class="comment">//设置入口</span></span><br><span class="line"> <span class="attr">entry</span>: <span class="string">'./src/hello.js'</span>,</span><br><span class="line"> <span class="comment">//出口</span></span><br><span class="line"> <span class="attr">output</span>: {</span><br><span class="line"> <span class="attr">path</span>: path.<span class="title function_">resolve</span>(<span class="title function_">getRecentDir</span>(<span class="keyword">import</span>.<span class="property">meta</span>.<span class="property">url</span>), <span class="string">'dist'</span>),</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'testPack.js'</span>,</span><br><span class="line"> <span class="attr">clean</span>: <span class="literal">true</span></span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//插件</span></span><br><span class="line"> <span class="attr">plugins</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">MiniCssExtractPlugin</span>({</span><br><span class="line"> <span class="comment">// filename: "login.css"</span></span><br><span class="line"> }),</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">HtmlWebpackPlugin</span>({</span><br><span class="line"> <span class="attr">template</span>: <span class="string">'./Login/login.html'</span>,</span><br><span class="line"> <span class="attr">filename</span>: <span class="string">'login.html'</span></span><br><span class="line"> }),</span><br><span class="line"> ],</span><br><span class="line"> <span class="attr">module</span>: {</span><br><span class="line"> <span class="attr">rules</span>: [</span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.css$/i</span>,</span><br><span class="line"> <span class="attr">use</span>: [<span class="title class_">MiniCssExtractPlugin</span>.<span class="property">loader</span>, <span class="string">"css-loader"</span>],</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//配置图片打包</span></span><br><span class="line"> {</span><br><span class="line"> <span class="attr">test</span>: <span class="regexp">/\.(png|jpg|gif)$/i</span>,</span><br><span class="line"> <span class="attr">type</span>: <span class="string">'asset'</span></span><br><span class="line"> },</span><br><span class="line"> ],</span><br><span class="line"> },</span><br><span class="line"> <span class="comment">//优化</span></span><br><span class="line"> <span class="attr">optimization</span>: {</span><br><span class="line"> <span class="comment">//minimize 减小</span></span><br><span class="line"> <span class="attr">minimizer</span>: [</span><br><span class="line"> <span class="keyword">new</span> <span class="title class_">CssMinimizerPlugin</span>()</span><br><span class="line"> ]</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure><p>在package.json中，如下所示。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"type"</span><span class="punctuation">:</span> <span class="string">"module"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"devDependencies"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"css-loader"</span><span class="punctuation">:</span> <span class="string">"^6.8.1"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"css-minimizer-webpack-plugin"</span><span class="punctuation">:</span> <span class="string">"^5.0.1"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"html-webpack-plugin"</span><span class="punctuation">:</span> <span class="string">"^5.5.3"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"mini-css-extract-plugin"</span><span class="punctuation">:</span> <span class="string">"^2.7.6"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"style-loader"</span><span class="punctuation">:</span> <span class="string">"^3.3.3"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack"</span><span class="punctuation">:</span> <span class="string">"^5.88.0"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack-cli"</span><span class="punctuation">:</span> <span class="string">"^5.1.4"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack-dev-server"</span><span class="punctuation">:</span> <span class="string">"^4.15.1"</span></span><br><span class="line"> <span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"scripts"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"build"</span><span class="punctuation">:</span> <span class="string">"webpack"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"dev"</span><span class="punctuation">:</span> <span class="string">"webpack serve --open"</span></span><br><span class="line"> <span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>通过自定义命令启动。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">npm run dev</span><br></pre></td></tr></table></figure><p>这种情况下，会自动创建一个8080端口的服务，服务器的根目录为项目的public目录和webpack配置文件中的出口目录。默认打开的是public目录下的index网页，而我们要查看的网页在出口目录，那么我们可以为public目录的index网页添加重定向，自动跳转到我们要查看的网页。</p><figure class="highlight html"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"><!-- public目录下的index.html --></span></span><br><span class="line"><span class="meta"><!DOCTYPE <span class="keyword">html</span>></span></span><br><span class="line"><span class="tag"><<span class="name">html</span> <span class="attr">lang</span>=<span class="string">"en"</span>></span></span><br><span class="line"></span><br><span class="line"><span class="tag"><<span class="name">head</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">meta</span> <span class="attr">charset</span>=<span class="string">"UTF-8"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">meta</span> <span class="attr">http-equiv</span>=<span class="string">"X-UA-Compatible"</span> <span class="attr">content</span>=<span class="string">"IE=edge"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">meta</span> <span class="attr">name</span>=<span class="string">"viewport"</span> <span class="attr">content</span>=<span class="string">"width=device-width, initial-scale=1.0"</span>></span></span><br><span class="line"> <span class="tag"><<span class="name">title</span>></span>Document<span class="tag"></<span class="name">title</span>></span></span><br><span class="line"><span class="tag"></<span class="name">head</span>></span></span><br><span class="line"></span><br><span class="line"><span class="tag"><<span class="name">body</span>></span></span><br><span class="line"><span class="tag"></<span class="name">body</span>></span></span><br><span class="line"></span><br><span class="line"><span class="tag"><<span class="name">script</span>></span><span class="language-javascript"></span></span><br><span class="line"><span class="language-javascript"> location.<span class="property">href</span> = <span class="string">"/login.html"</span></span></span><br><span class="line"><span class="language-javascript"></span><span class="tag"></<span class="name">script</span>></span></span><br><span class="line"></span><br><span class="line"><span class="tag"></<span class="name">html</span>></span></span><br></pre></td></tr></table></figure><h5 id="生产模式"><a class="markdownIt-Anchor" href="#生产模式"></a> 生产模式</h5><p>上面使用到了开发模式，配合webpack-dev-server可以热更新。与之相对的，还有生产模式（production），即打包模式。</p><p>我们开发模式用的更多，所以mode设置为development，那打包的时候怎么办呢？再去修改mode吗？这很显然不方便。所以我们可以通过自定义命令指定模式。命令的优先级＞配置文件。</p><p>在package.json文件中，我们这样设置，在build和dev后面加上–mode=[mode]即可。</p><figure class="highlight json"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"type"</span><span class="punctuation">:</span> <span class="string">"module"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"devDependencies"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"css-loader"</span><span class="punctuation">:</span> <span class="string">"^6.8.1"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"css-minimizer-webpack-plugin"</span><span class="punctuation">:</span> <span class="string">"^5.0.1"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"html-webpack-plugin"</span><span class="punctuation">:</span> <span class="string">"^5.5.3"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"mini-css-extract-plugin"</span><span class="punctuation">:</span> <span class="string">"^2.7.6"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"style-loader"</span><span class="punctuation">:</span> <span class="string">"^3.3.3"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack"</span><span class="punctuation">:</span> <span class="string">"^5.88.0"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack-cli"</span><span class="punctuation">:</span> <span class="string">"^5.1.4"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"webpack-dev-server"</span><span class="punctuation">:</span> <span class="string">"^4.15.1"</span></span><br><span class="line"> <span class="punctuation">}</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"scripts"</span><span class="punctuation">:</span> <span class="punctuation">{</span></span><br><span class="line"> <span class="attr">"build"</span><span class="punctuation">:</span> <span class="string">"webpack --mode=production"</span><span class="punctuation">,</span></span><br><span class="line"> <span class="attr">"dev"</span><span class="punctuation">:</span> <span class="string">"webpack serve --open --mode=development"</span></span><br><span class="line"> <span class="punctuation">}</span></span><br><span class="line"><span class="punctuation">}</span></span><br></pre></td></tr></table></figure><p>这样一来，开发的时候就使用热更新开发模式，打包的时候就使用生产模式，两不误。</p>]]></content>
<summary type="html"><h3 id="包的类型"><a class="markdownIt-Anchor" href="#包的类型"></a> 包的类型</h3>
<ul>
<li>项目包：用于编写项目和和业务逻辑</li>
<li>软件包：封装工具和方法进行使用
<ul>
<li>本地软件包：当前项</summary>
<category term="知识" scheme="https://blog.kahvia.cn/categories/%E7%9F%A5%E8%AF%86/"/>
<category term="node.js" scheme="https://blog.kahvia.cn/tags/node-js/"/>
</entry>
</feed>