Week 11.3

🚀 Week 11 - Day 3: DSA Session 1

📌 Topic: Recursion - Factorials, GCD, and Finding Factors

Today, we explored recursion in depth and learned how to solve problems like factorial computation, GCD (Greatest Common Divisor), and finding factors of a number using recursion. 🔥

---

🔢 Finding the GCD (Greatest Common Divisor) Using Recursion

The GCD (HCF - Highest Common Factor) of two numbers is the largest number that divides both numbers completely.

Approach 1: Iterative Recursive Method

• Start from the minimum of two numbers and check divisibility.
• Decrease the divisor (c) until the GCD is found.

let a = 20;
let b = 32;
let c = a < b ? a : b;

console.log(findGCD(a, b, c));

function findGCD(a, b, c) {
    if (c == 1) return c;
    if (a % c == 0 && b % c == 0) return c;
    return findGCD(a, b, c - 1);
}

⏳ Time Complexity: O(min(a, b))

---

Approach 2: Using Euclidean Algorithm (Optimized)

🔹 The Euclidean algorithm reduces the problem by subtracting the smaller number from the larger one.
🔹 This is much faster than iterating from min(a, b) downwards.

console.log(GCD(20, 32));

function GCD(a, b) {
    if (a == b) return a; 
    if (a > b) return GCD(a - b, b);
    else return GCD(a, b - a);
}

🔹 Time Complexity: O(log(min(a, b)))
✔ Most efficient way to find GCD using recursion! ✅

---

🔄 Printing Numbers Using Recursion

This function prints numbers from n to 1 recursively. 📉

let n = 5;
temp(n);

function temp(n) {
    if (n == 0) return;
    console.log(n);
    temp(--n);
}

✔ This function decrements n until 0 is reached.

---

🧩 Finding Factors of a Number Using Recursion

🔹 A factor of n is any number that divides n completely.
🔹 We recursively check divisibility starting from 1.

Method 1: Checking from 1 to n/2

let n = 50;
factor(n, 1);

function factor(n, i) {
    if (n % i == 0) console.log(i); // Print factor
    if (i > Math.floor(n / 2)) {
        console.log(n); // Print n itself as a factor
        return;
    }
    factor(n, i + 1);
}

✔ Time Complexity: O(n/2)

---

Method 2: Optimized Factorization (Using sqrt(n))

Instead of checking all numbers up to n/2, we only go up to sqrt(n), which is more efficient.

function printFactors(n) {
    let result = [];
    for (let i = 1; i <= Math.sqrt(n); i++) {
        if (n % i === 0) {
            if (i === n / i) {
                result.push(i);
            } else {
                result.push(i);
                result.push(n / i);
            }
        }
    }
    result.sort((a, b) => a - b);
    console.log(result.join(", "));
}

printFactors(50);

✔ Time Complexity: O(√n) (Much Faster!)

---

🔑 Key Takeaways

✅ Recursion is a powerful concept that helps break problems into smaller instances of the same problem.
✅ GCD can be optimized using the Euclidean algorithm.
✅ Factorization can be optimized by checking only up to sqrt(n) instead of n/2.

🔥 Keep practicing recursion, and you'll master it in no time! 🚀💡

🚀 Week 11 - Day 3: Backend Session 2

🛠️ Building a User Management System with Express & MongoDB

Today, we built a User Management System using Express, MongoDB (Mongoose), and EJS! 🎉

---

📌 Steps We Followed

🔹 Step 1: Initialize the Project

We started by setting up our Node.js project:

npm init -y
npm i ejs mongoose express

This installs:

• EJS for templating 🖼️
• Mongoose for database interaction 🛢️
• Express for handling routes 🚀

---

🔹 Step 2: Create a Simple User Form 📝

Our form collects:
✔ Username
✔ Email
✔ Bio
✔ Profile Image (URL)

📍 Route to Render the Form:

app.get("/create", (req, res) => {
    res.render("createUser");  // Renders EJS form
});

📍 EJS Form (views/createUser.ejs):

<form action="/create" method="POST">
    <input type="text" name="username" placeholder="Enter Username" required />
    <input type="email" name="email" placeholder="Enter Email" required />
    <textarea name="bio" placeholder="Enter Bio"></textarea>
    <input type="text" name="profileImage" placeholder="Enter Profile Image URL" />
    <button type="submit">Create User</button>
</form>

---

🔹 Step 3: Store User Data in MongoDB

We post the form data to /create and store it in our MongoDB database.

📍 Mongoose User Schema (models/user.model.js):

const mongoose = require("mongoose");

const userSchema = new mongoose.Schema({
    username: String,
    email: String,
    bio: String,
    profileImage: String
});

const User = mongoose.model("User", userSchema);
module.exports = User;

📍 Handling Form Submission in Express (routes/userRoutes.js)

const User = require("../models/user.model");

app.post("/create", async (req, res) => {
    try {
        const { username, email, bio, profileImage } = req.body;
        await User.create({ username, email, bio, profileImage });
        res.redirect("/users");  // Redirect to users list after creation
    } catch (error) {
        res.status(500).send("Error creating user");
    }
});

---

🔹 Step 4: Display All Users

We now fetch all users and display them as cards! 📜

📍 Fetching Users (routes/userRoutes.js)

app.get("/users", async (req, res) => {
    const users = await User.find();  
    res.render("users", { users });  
});

📍 EJS Template to Show Users (views/users.ejs)

<% users.forEach(user => { %>
    <div class="card">
        <img src="<%= user.profileImage %>" alt="Profile" />
        <h2><%= user.username %></h2>
        <a href="/userDetails/<%= user._id %>">View Profile</a>
    </div>
<% }); %>

---

🔹 Step 5: Show User Details

When clicking a user card, it redirects to userDetails/:user_id 📌

📍 Route for User Details (routes/userRoutes.js)

app.get("/userDetails/:user_id", async (req, res) => {
    const user = await User.findById(req.params.user_id);
    res.render("userDetails", { user });
});

📍 EJS Template for User Details (views/userDetails.ejs)

<div class="profile">
    <img src="<%= user.profileImage %>" alt="Profile" />
    <h2><%= user.username %></h2>
    <p>Email: <%= user.email %></p>
    <p>Bio: <%= user.bio %></p>
</div>

---

🎯 Features Implemented Today

✅ Form to Create Users
✅ Store Users in MongoDB
✅ Display Users as Cards
✅ Click on User Card to View Full Profile

🚀 Awesome Work! Keep Learning! 💡🔥