Overview

Heap sort is a comparison-based sorting algorithm that uses a binary heap data structure. It divides the input into a sorted and an unsorted region and iteratively shrinks the unsorted region by extracting the largest element from the heap and moving it to the sorted region.

Program Structure

The following C program implements the heap sort algorithm. It consists of the following main parts:

• Heapify Function: This function maintains the heap property. It assumes the binary tree rooted at index i is a heap, but the subtree rooted at index i might not be.
• Heap Sort Function: This function builds a heap from the input data and then repeatedly extracts the maximum element to produce a sorted array.
• Main Function: This function handles input and output, calling the heap sort function and displaying the sorted array.

Heap Sort Program

#include 

// Function to heapify a subtree rooted with node i which is 
// an index in arr[]. n is the size of the heap
void heapify(int arr[], int n, int i) {
    int largest = i; // Initialize largest as root
    int left = 2 * i + 1; // left = 2*i + 1
    int right = 2 * i + 2; // right = 2*i + 2

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

    // If right child is larger than largest so far
    if (right < n && arr[right] > arr[largest])
        largest = right;

    // If largest is not root
    if (largest != i) {
        int temp = arr[i];
        arr[i] = arr[largest];
        arr[largest] = temp;

        // Recursively heapify the affected subtree
        heapify(arr, n, largest);
    }
}

// Main function to do heap sort
void heapSort(int arr[], int n) {
    // Build heap (rearrange array)
    for (int i = n / 2 - 1; i >= 0; i--)
        heapify(arr, n, i);

    // One by one extract an element from heap
    for (int i = n - 1; i >= 0; i--) {
        // Move current root to end
        int temp = arr[0];
        arr[0] = arr[i];
        arr[i] = temp;

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

// Function to print an array
void printArray(int arr[], int size) {
    for (int i = 0; i < size; i++)
        printf("%d ", arr[i]);
    printf("\\n");
}

// Driver program
int main() {
    int arr[] = {12, 11, 13, 5, 6, 7};
    int n = sizeof(arr) / sizeof(arr[0]);

    heapSort(arr, n);

    printf("Sorted array is: \\n");
    printArray(arr, n);
    return 0;
}

How to Compile and Run

To compile and run the program, follow these steps:

1. Save the code in a file named heapsort.c.
2. Open a terminal and navigate to the directory where the file is saved.
3. Compile the program using the command: gcc heapsort.c -o heapsort
4. Run the program with the command: ./heapsort

Output

Upon running the program, you should see the following output:

Sorted array is:
5 6 7 11 12 13 

Conclusion

The heap sort algorithm is efficient with a time complexity of O(n log n) and can be implemented in-place. This makes it a useful sorting technique in scenarios where memory usage is a concern.