add: Implement Merge Sort algorithm with utility functions and example usage

Author: Karanjot786

CPP/algorithms/sorting/merge_sort.cpp

@@ -0,0 +1,128 @@
+/**
+ * Merge Sort Algorithm
+ *
+ * A divide-and-conquer algorithm that divides the input array into two halves,
+ * recursively sorts them, and then merges the sorted halves.
+ *
+ * Time Complexity: O(n log n) in all cases
+ * Space Complexity: O(n) for temporary array
+ *
+ * Author: Karanjot Singh
+ * Date: September 2025
+ */
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+/**
+ * Merges two sorted subarrays into one sorted array
+ *
+ * @param arr The main array containing both subarrays
+ * @param left Starting index of first subarray
+ * @param mid Ending index of first subarray
+ * @param right Ending index of second subarray
+ */
+void merge(vector<int>& arr, int left, int mid, int right) {
+    // Calculate sizes of two subarrays
+    int n1 = mid - left + 1;
+    int n2 = right - mid;
+
+    // Create temporary arrays
+    vector<int> leftArr(n1);
+    vector<int> rightArr(n2);
+
+    // Copy data to temporary arrays
+    for (int i = 0; i < n1; i++)
+        leftArr[i] = arr[left + i];
+    for (int j = 0; j < n2; j++)
+        rightArr[j] = arr[mid + 1 + j];
+
+    // Merge the temporary arrays back into arr[left..right]
+    int i = 0, j = 0, k = left;
+
+    while (i < n1 && j < n2) {
+        if (leftArr[i] <= rightArr[j]) {
+            arr[k] = leftArr[i];
+            i++;
+        } else {
+            arr[k] = rightArr[j];
+            j++;
+        }
+        k++;
+    }
+
+    // Copy remaining elements of leftArr[], if any
+    while (i < n1) {
+        arr[k] = leftArr[i];
+        i++;
+        k++;
+    }
+
+    // Copy remaining elements of rightArr[], if any
+    while (j < n2) {
+        arr[k] = rightArr[j];
+        j++;
+        k++;
+    }
+}
+
+/**
+ * Main merge sort function that recursively divides and sorts the array
+ *
+ * @param arr The array to be sorted
+ * @param left Starting index
+ * @param right Ending index
+ */
+void mergeSort(vector<int>& arr, int left, int right) {
+    if (left < right) {
+        // Find the middle point
+        int mid = left + (right - left) / 2;
+
+        // Sort first and second halves
+        mergeSort(arr, left, mid);
+        mergeSort(arr, mid + 1, right);
+
+        // Merge the sorted halves
+        merge(arr, left, mid, right);
+    }
+}
+
+/**
+ * Utility function to print an array
+ */
+void printArray(const vector<int>& arr) {
+    for (int num : arr)
+        cout << num << " ";
+    cout << endl;
+}
+
+/**
+ * Main function demonstrating merge sort usage
+ */
+int main() {
+    vector<int> arr = {64, 34, 25, 12, 22, 11, 90};
+
+    cout << "Original array: ";
+    printArray(arr);
+
+    mergeSort(arr, 0, arr.size() - 1);
+
+    cout << "Sorted array: ";
+    printArray(arr);
+
+    return 0;
+}
+
+/*
+Example Output:
+Original array: 64 34 25 12 22 11 90
+Sorted array: 11 12 22 25 34 64 90
+
+Test Cases:
+1. Empty array: [] -> []
+2. Single element: [5] -> [5]
+3. Already sorted: [1,2,3,4,5] -> [1,2,3,4,5]
+4. Reverse sorted: [5,4,3,2,1] -> [1,2,3,4,5]
+5. Duplicates: [3,1,3,2,1] -> [1,1,2,3,3]
+*/