Example: Merge Sort using Recursion in C++

// Merge Sort using Recursion
#include <iostream>
#include <vector>
#include <algorithm> // For std::min (optional, could use ternary operator)

// Function to merge two sorted subarrays
// arr[left...mid] and arr[mid+1...right]
void merge(std::vector<int>& arr, int left, int mid, int right) {
    // Step 1: Calculate sizes of the two subarrays to be merged
    int n1 = mid - left + 1;
    int n2 = right - mid;

    // Step 2: Create temporary arrays for the left and right subarrays
    std::vector<int> L(n1);
    std::vector<int> R(n2);

    // Step 3: Copy data to temporary arrays L[] and R[]
    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];

    // Step 4: Merge the temporary arrays back into arr[left...right]
    int i = 0; // Initial index of first subarray
    int j = 0; // Initial index of second subarray
    int k = left; // Initial index of merged subarray

    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    // Step 5: Copy the remaining elements of L[], if any
    while (i < n1) {
        arr[k] = L[i];
        i++;
        k++;
    }

    // Step 6: Copy the remaining elements of R[], if any
    while (j < n2) {
        arr[k] = R[j];
        j++;
        k++;
    }
}

// Main function that sorts arr[left...right] using merge()
void mergeSort(std::vector<int>& arr, int left, int right) {
    // Step 1: Base case for recursion - if left >= right, the subarray has 0 or 1 element, which is already sorted
    if (left < right) {
        // Step 2: Find the middle point to divide the array into two halves
        int mid = left + (right - left) / 2; // Avoids potential overflow for large left/right

        // Step 3: Recursively sort the first half
        mergeSort(arr, left, mid);
        // Step 4: Recursively sort the second half
        mergeSort(arr, mid + 1, right);

        // Step 5: Merge the sorted halves
        merge(arr, left, mid, right);
    }
}

// Utility function to print an array
void printArray(const std::vector<int>& arr) {
    for (int x : arr) {
        std::cout << x << " ";
    }
    std::cout << std::endl;
}

int main() {
    // Step 1: Initialize an unsorted array
    std::vector<int> arr = {38, 27, 43, 3, 9, 82, 10};
    int arr_size = arr.size();

    // Step 2: Print the original array
    std::cout << "Original array: ";
    printArray(arr);

    // Step 3: Call mergeSort to sort the array
    mergeSort(arr, 0, arr_size - 1);

    // Step 4: Print the sorted array
    std::cout << "Sorted array:   ";
    printArray(arr);

    return 0;
}