Example: Heap Sort using Recursion in C++

// Heap Sort using Recursion
#include <iostream>
#include <vector> // Using vector for dynamic array behavior, can also use raw arrays

// Function to heapify a subtree rooted with node i
// n is size of heap
void heapify(std::vector<int>& arr, int n, int i) {
    // Step 1: Initialize largest as root
    int largest = i;
    int left = 2 * i + 1; // Left child
    int right = 2 * i + 2; // Right child

    // Step 2: If left child is larger than root
    if (left < n && arr[left] > arr[largest]) {
        largest = left;
    }

    // Step 3: If right child is larger than current largest
    if (right < n && arr[right] > arr[largest]) {
        largest = right;
    }

    // Step 4: If largest is not root
    if (largest != i) {
        std::swap(arr[i], arr[largest]);

        // Step 5: Recursively heapify the affected sub-tree
        heapify(arr, n, largest);
    }
}

// Main function to perform heap sort
void heapSort(std::vector<int>& arr, int n) {
    // Step 1: Build max heap (rearrange array)
    // Start from the last non-leaf node and heapify downwards
    for (int i = n / 2 - 1; i >= 0; i--) {
        heapify(arr, n, i);
    }

    // Step 2: Extract elements one by one from heap
    for (int i = n - 1; i > 0; i--) {
        // Move current root to end
        std::swap(arr[0], arr[i]);

        // Call heapify on the reduced heap
        heapify(arr, i, 0);
    }
}

// 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: Define an array to be sorted
    std::vector<int> arr = {12, 11, 13, 5, 6, 7};
    int n = arr.size();

    std::cout << "Original array: ";
    printArray(arr);

    // Step 2: Perform heap sort
    heapSort(arr, n);

    std::cout << "Sorted array: ";
    printArray(arr);

    // Step 3: Test with another array
    std::vector<int> arr2 = {4, 10, 3, 5, 1};
    n = arr2.size();

    std::cout << "Original array 2: ";
    printArray(arr2);

    heapSort(arr2, n);

    std::cout << "Sorted array 2: ";
    printArray(arr2);

    return 0;
}