Update mergesort.md

lessons/mergesort.md

@@ -5,3 +5,69 @@ order: "8E"
 section: "Recursion"
 description: "learn Recursion from scratch"
 ---
+# Merge Sort
+
+## 1. Introduction
+Merge Sort is a **Divide & Conquer** sorting algorithm.  
+The main idea: split the array into two halves, sort each half recursively, and then **merge** the two sorted halves into one sorted array.  
+It is stable, always runs in **O(n log n)** time, but requires **O(n)** extra space.
+
+---
+
+## 2. Understanding the Merge Sort
+1. If the array has length 0 or 1 → already sorted.  
+2. Split the array into two halves.  
+3. Sort each half using Merge Sort (recursive calls).  
+4. Merge the two halves into a single sorted array.  
+
+---
+
+## 3. Implementation + Illustration
+Example walkthrough with array `[5, 2, 4, 6, 1, 3]`:
+
+Step 1: Split → [5, 2, 4] | [6, 1, 3]  
+Step 2: Split → [5] [2,4] | [6] [1,3]  
+Step 3: Split → [5] [2] [4] | [6] [1] [3]  
+Step 4: Merge → [2,4,5] | [1,3,6]  
+Step 5: Merge → [1,2,3,4,5,6]
+
+---
+
+## 4. Code for Merge Sort (Java)
+
+```java
+public class MergeSort {
+    public static void sort(int[] arr) {
+        if (arr.length <= 1) return;
+        mergeSort(arr, 0, arr.length - 1);
+    }
+
+    private static void mergeSort(int[] arr, int left, int right) {
+        if (left >= right) return;
+        int mid = left + (right - left) / 2;
+        mergeSort(arr, left, mid);
+        mergeSort(arr, mid + 1, right);
+        merge(arr, left, mid, right);
+    }
+
+    private static void merge(int[] arr, int left, int mid, int right) {
+        int[] temp = new int[right - left + 1];
+        int i = left, j = mid + 1, k = 0;
+
+        while (i <= mid && j <= right) {
+            if (arr[i] <= arr[j]) temp[k++] = arr[i++];
+            else temp[k++] = arr[j++];
+        }
+        while (i <= mid) temp[k++] = arr[i++];
+        while (j <= right) temp[k++] = arr[j++];
+
+        for (i = left; i <= right; i++) arr[i] = temp[i - left];
+    }
+
+    public static void main(String[] args) {
+        int[] arr = {5, 2, 4, 6, 1, 3};
+        sort(arr);
+        for (int x : arr) System.out.print(x + " ");
+        // Output: 1 2 3 4 5 6
+    }
+}