chore: import upstream snapshot with attribution

sorting/merge_sort.cpp

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+/**
+ *  \addtogroup sorting Sorting Algorithms
+ *  @{
+ *  \file
+ *  \brief [Merge Sort Algorithm
+ *  (MERGE SORT)](https://en.wikipedia.org/wiki/Merge_sort) implementation
+ *
+ *  \author [Ayaan Khan](http://github.com/ayaankhan98)
+ *
+ *  \details
+ *  Merge Sort is an efficient, general purpose, comparison
+ *  based sorting algorithm.
+ *  Merge Sort is a divide and conquer algorithm
+ *  Time  Complexity: O(n log n) 
+ *  It is  same for all best case, worst case or average case 
+ *  Merge Sort is very efficient when for the small data. 
+ *  In built-in sort function merge sort along with quick sort is used. 
+ */
+#include <iostream>
+#include <vector>
+
+/**
+ *
+ * The merge() function is used for merging two halves.
+ * The merge(arr, l, m, r) is key process that assumes that
+ * arr[l..m] and arr[m+1..r] are sorted and merges the two
+ * sorted sub-arrays into one.
+ *
+ * @param arr - array with two halves arr[l...m] and arr[m+1...r]
+ * @param l - left index or start index of first half array
+ * @param m - right index or end index of first half array
+ *
+ * (The second array starts form m+1 and goes till r)
+ *
+ * @param r - end index or right index of second half array
+ */
+void merge(int *arr, int l, int m, int r) {
+    int n1 = m - l + 1;
+    int n2 = r - m;
+
+    std::vector<int> L(n1), R(n2);
+
+    for (int i = 0; i < n1; i++) L[i] = arr[l + i];
+    for (int j = 0; j < n2; j++) R[j] = arr[m + 1 + j];
+
+    int i = 0, j = 0, k = l;
+
+    while (i < n1 && j < n2) {
+        if (L[i] <= R[j]) {
+            arr[k] = L[i];
+            i++;
+        } else {
+            arr[k] = R[j];
+            j++;
+        }
+        k++;
+    }
+
+    while (i < n1) {
+        arr[k] = L[i];
+        i++;
+        k++;
+    }
+
+    while (j < n2) {
+        arr[k] = R[j];
+        j++;
+        k++;
+    }
+}
+
+/**
+ * Merge sort is a divide and conquer algorithm, it divides the
+ * input array into two halves and calls itself for the two halves
+ * and then calls merge() to merge the two halves
+ *
+ * @param arr - array to be sorted
+ * @param l - left index or start index of array
+ * @param r - right index or end index of array
+ *
+ */
+void mergeSort(int *arr, int l, int r) {
+    if (l < r) {
+        int m = l + (r - l) / 2;
+        mergeSort(arr, l, m);
+        mergeSort(arr, m + 1, r);
+        merge(arr, l, m, r);
+    }
+}
+
+/**
+ * Utility function used to print the array after
+ * sorting
+ */
+void show(int *arr, int size) {
+    for (int i = 0; i < size; i++) std::cout << arr[i] << " ";
+    std::cout << "\n";
+}
+
+/** Main function */
+int main() {
+    int size;
+    std::cout << "Enter the number of elements: ";
+    std::cin >> size;
+
+    if (size <= 0) {
+        std::cout << "Invalid size.\n";
+        return 1;
+    }
+
+    int *arr = new int[size];
+    std::cout << "Enter the unsorted elements: ";
+    for (int i = 0; i < size; ++i) {
+        std::cin >> arr[i];
+    }
+
+    mergeSort(arr, 0, size - 1);
+    std::cout << "Sorted array: ";
+    show(arr, size);
+    delete[] arr;
+    return 0;
+}
+/** @} */