feature: big number add and minus

04-algrithm/08-bigNumber/__tests__/index.spec.js

@@ -0,0 +1,49 @@
+const { bigAdd, bigMin } = require("../20230826大数加减");
+
+describe("大数加减", () => {
+  describe("加法", () => {
+    it("普通加法", () => {
+      expect(bigAdd("1", "1")).toEqual("2");
+      expect(bigAdd("9", "1")).toEqual("10");
+      expect(bigAdd("10", "1")).toEqual("11");
+      expect(bigAdd("19999", "1")).toEqual("20000");
+      expect(bigAdd("99999", "1")).toEqual("100000");
+      expect(bigAdd("100", "1")).toEqual("101");
+      expect(bigAdd("1", "199")).toEqual("200");
+    });
+  });
+  describe("减法", () => {
+    it("正减正", () => {
+      expect(bigMin("1", "1")).toEqual("0");
+      expect(bigMin("0", "1")).toEqual("-1");
+      expect(bigMin("10", "1")).toEqual("9");
+      expect(bigMin("19", "1")).toEqual("18");
+      expect(bigMin("100", "1")).toEqual("99");
+      expect(bigMin("1", "100")).toEqual("-99");
+    });
+    it("正减负", () => {
+      expect(bigMin("1", "-1")).toEqual("2");
+      expect(bigMin("0", "-1")).toEqual("1");
+      expect(bigMin("10", "-1")).toEqual("11");
+      expect(bigMin("19", "-1")).toEqual("20");
+      expect(bigMin("100", "-1")).toEqual("101");
+      expect(bigMin("1", "-100")).toEqual("101");
+    });
+    it("负减正", () => {
+      expect(bigMin("-1", "1")).toEqual("-2");
+      expect(bigMin("-2", "1")).toEqual("-3");
+      expect(bigMin("-10", "1")).toEqual("-11");
+      expect(bigMin("-19", "1")).toEqual("-20");
+      expect(bigMin("-100", "1")).toEqual("-101");
+      expect(bigMin("-1", "100")).toEqual("-101");
+    });
+    it("负减负", () => {
+      expect(bigMin("-1", "-1")).toEqual("0");
+      expect(bigMin("-2", "-1")).toEqual("-1");
+      expect(bigMin("-10", "-1")).toEqual("-9");
+      expect(bigMin("-19", "-1")).toEqual("-18");
+      expect(bigMin("-100", "-1")).toEqual("-99");
+      expect(bigMin("-1", "-100")).toEqual("99");
+    });
+  });
+});

04-algrithm/08-bigNumber/index.js

@@ -0,0 +1,197 @@
+function minus(a1, a2) {
+  let carry = 0;
+  let i = a1.length - 1;
+  let j = a2.length - 1;
+  let arr = [];
+  while (a1[i]) {
+    let x = Number(a1[i]);
+    let y = 0;
+    if (a2[j]) {
+      y = Number(a2[j]);
+    }
+    let temp;
+    if (x - y + carry < 0) {
+      temp = x + 10;
+    } else {
+      temp = x;
+    }
+    let res = temp - y + carry;
+    if (x - y + carry < 0) {
+      carry = -1;
+    } else {
+      carry = 0;
+    }
+    arr.unshift(res);
+    i--;
+    j--;
+  }
+  while (arr[0] === 0 && arr.length > 1) {
+    arr.shift();
+  }
+  return arr.join("");
+}
+
+/**
+ *
+ * @param {string} a1
+ * @param {string} a2
+ * @returns {number}
+ */
+// 正负数，比较大数大小
+function compare(a1, a2) {
+  if (a1.startsWith("-") && !a2.startsWith("-")) {
+    return -1;
+  } else if (!a1.startsWith("-") && a2.startsWith("-")) {
+    return 1;
+  } else if (a1.startsWith("-") && a2.startsWith("-")) {
+    return compareNegative(a1, a2);
+  } else if (!a1.startsWith("-") && !a2.startsWith("-")) {
+    return comparePositive(a1, a2);
+  }
+  return 0;
+}
+
+function compareNegative(a1, a2) {
+  // 谁位数多谁小
+  if (a1.length > a2.length) {
+    return -1;
+  } else if (a1.length < a2.length) {
+    return 1;
+  } else {
+    let i = 0;
+    while (a1[i] && a2[i]) {
+      /// 123 789
+      if (a1[i] > a2[i]) {
+        return -1;
+      } else if (a1[i] < a2[i]) {
+        return 1;
+      } else {
+        i++;
+      }
+    }
+  }
+  return 0;
+}
+
+function comparePositive(a1, a2) {
+  if (a1.length > a2.length) {
+    return 1;
+  } else if (a1.length < a2.length) {
+    return -1;
+  } else {
+    let i = 0;
+    while (a1[i] && a2[i]) {
+      if (a1[i] > a2[i]) {
+        return 1;
+      } else if (a1[i] < a2[i]) {
+        return -1;
+      } else {
+        i++;
+      }
+    }
+  }
+  return 0;
+}
+
+/**
+ * 大数加法
+ * @param {number} a1 加数 1
+ * @param {number} a2 加数 2
+ * @returns {number} 加法结果
+ */
+function bigAdd(a1, a2) {
+  let carry = 0;
+  let i = a1.length - 1;
+  let j = a2.length - 1;
+  let arr = [];
+  while (a1[i] || a2[j]) {
+    let x = 0;
+    if (a1[i]) {
+      x = Number(a1[i]);
+    }
+    let y = 0;
+    if (a2[j]) {
+      y = Number(a2[j]);
+    }
+    let res = (x + y + carry) % 10;
+    arr.unshift(res);
+    carry = Math.floor((x + y + carry) / 10);
+    i--;
+    j--;
+  }
+  if (carry) {
+    arr.unshift(carry);
+  }
+  return arr.join("");
+}
+
+/**
+ * 大数减法，包含正负数
+ * @param {number} a1 被减数
+ * @param {number} a2 减数
+ * @returns {number} 减法结果
+ */
+function bigMin(a1, a2) {
+  // 负数减负数（去掉符号，大减小）（如果 a2 > a1，正号；如果 a1 > a2，负号）
+  // 正数减负数（去掉符号，加起来）（正号）
+  // 正数减正数（去掉符号，大减小）（如果 a2 > a1，负号；如果 a1 > a2，正号）
+  // 负数减正数（去掉符号，加起来）（负号）
+  let s = "";
+
+  if (
+    // 小减大，负数
+    (a1[0] === "-" && a2[0] === "-") ||
+    // 小减大，负数
+    (!a1[0] === "-" && !a2[0] === "-")
+  ) {
+    if (compare(a1, a2) < 0) {
+      // -123 - -12
+      s = "-";
+    }
+  } else if (a1[0] === "-" && a2[0] !== "-") {
+    // -123 - 789
+    s = "-";
+  }
+
+  let res = "";
+  if (
+    // 正 - 负
+    (a1[0] !== "-" && a2[0] === "-") ||
+    // 负 - 正
+    (a1[0] === "-" && a2[0] !== "-")
+  ) {
+    if (a1[0].startsWith("-")) {
+      a1 = a1.slice(1);
+    }
+    if (a2[0].startsWith("-")) {
+      a2 = a2.slice(1);
+    }
+    res = bigAdd(a1, a2);
+  } else if (
+    // 正 - 正
+    (a1[0] !== "-" && a2[0] !== "-") ||
+    // 负 - 负
+    (a1[0] === "-" && a2[0] === "-")
+  ) {
+    if (a1[0].startsWith("-")) {
+      a1 = a1.slice(1);
+    }
+    if (a2[0].startsWith("-")) {
+      a2 = a2.slice(1);
+    }
+    if (compare(a1, a2) > 0) {
+      res = minus(a1, a2);
+    } else {
+      a1 = a2;
+      a2 = a1;
+      res = minus(a1, a2);
+    }
+  }
+
+  return `${s}${res}`;
+}
+
+module.exports = {
+  bigAdd,
+  bigMin,
+};