Add Merge Sort algorithm in Java with recursive implementation

Author: Farheen Shabbir Shaikh

Sorting/MergeSort.java

@@ -0,0 +1,69 @@
+/**
+ * MergeSort.java
+ * This program implements the Merge Sort algorithm using recursion.
+ * Time Complexity: O(n log n)
+ */
+
+public class MergeSort {
+
+    // Method to recursively divide and sort the array
+    public static void mergeSort(int[] arr, int left, int right) {
+        if (left < right) {
+            int mid = (left + right) / 2;
+
+            // Recursively sort the left half
+            mergeSort(arr, left, mid);
+
+            // Recursively sort the right half
+            mergeSort(arr, mid + 1, right);
+
+            // Merge the two sorted halves
+            merge(arr, left, mid, right);
+        }
+    }
+
+    // Method to merge two sorted halves
+    public static void merge(int[] arr, int left, int mid, int right) {
+        // Sizes of subarrays
+        int n1 = mid - left + 1;
+        int n2 = right - mid;
+
+        // Temp arrays
+        int[] L = new int[n1];
+        int[] R = new int[n2];
+
+        // Copy data to temp arrays
+        for (int i = 0; i < n1; ++i)
+            L[i] = arr[left + i];
+        for (int j = 0; j < n2; ++j)
+            R[j] = arr[mid + 1 + j];
+
+        // Merge temp arrays back into arr
+        int i = 0, j = 0, k = left;
+        while (i < n1 && j < n2) {
+            if (L[i] <= R[j]) {
+                arr[k++] = L[i++];
+            } else {
+                arr[k++] = R[j++];
+            }
+        }
+
+        // Copy remaining elements of L[]
+        while (i < n1)
+            arr[k++] = L[i++];
+
+        // Copy remaining elements of R[]
+        while (j < n2)
+            arr[k++] = R[j++];
+    }
+
+    public static void main(String[] args) {
+        int[] arr = {38, 27, 43, 3, 9, 82, 10};
+        mergeSort(arr, 0, arr.length - 1);
+
+        System.out.println("Sorted array:");
+        for (int value : arr) {
+            System.out.print(value + " ");
+        }
+    }
+}