Iterative HeapSort

HeapSort is a comparison-based sorting technique where we first build Max Heap and then swap the root element with the last element (size times) and maintains the heap property each time to finally make it sorted. 

Examples:

Input :  10 20 15 17 9 21
Output : 9 10 15 17 20 21 

Input:  12 11 13 5 6 7 15 5 19
Output: 5 5 6 7 11 12 13 15 19 

In first Example, first we have to build Max Heap. 

So, we will start from 20 as child and check for its parent. Here 10 is smaller, so we will swap these two. 

Now, 20 10 15 17 9 21 

Now, child 17 is greater than its parent 10. So, both will be swapped and order will be 20 17 15 10 9 21 

Now, child 21 is greater than parent 15. So, both will be swapped. 

20 17 21 10 9 15 

Now, again 21 is bigger than parent 20. So, 21 17 20 10 9 15

This is Max Heap. 

Now, we have to apply sorting. Here, we have to swap first element with last one and we have to maintain Max Heap property. So, after first swapping : 15 17 20 10 9 21 It clearly violates Max Heap property. 

So, we have to maintain it. So, order will be 

20 17 15 10 9 21

17 10 15 9 20 21

15 10 9 17 20 21

10 9 15 17 20 21

9 10 15 17 20 21

Here, underlined part is sorted part.

Implementation:

C++

// C++ program for implementation
// of Iterative Heap Sort
#include <bits/stdc++.h>
using namespace std;

// function build Max Heap where value
// of each child is always smaller
// than value of their parent
void buildMaxHeap(int arr[], int n)
{
    for (int i = 1; i < n; i++)
    {
        // if child is bigger than parent
        if (arr[i] > arr[(i - 1) / 2])
        {
            int j = i;

            // swap child and parent until
            // parent is smaller
            while (arr[j] > arr[(j - 1) / 2])
            {
                swap(arr[j], arr[(j - 1) / 2]);
                j = (j - 1) / 2;
            }
        }
    }
}

void heapSort(int arr[], int n)
{
    buildMaxHeap(arr, n);

    for (int i = n - 1; i > 0; i--)
    {
        // swap value of first indexed
        // with last indexed
        swap(arr[0], arr[i]);

        // maintaining heap property
        // after each swapping
        int j = 0, index;

        do
        {
            index = (2 * j + 1);

            // if left child is smaller than
            // right child point index variable
            // to right child
            if (arr[index] < arr[index + 1] &&
                                index < (i - 1))
                index++;

            // if parent is smaller than child
            // then swapping parent with child
            // having higher value
            if (arr[j] < arr[index] && index < i)
                swap(arr[j], arr[index]);

            j = index;

        } while (index < i);
    }
}

// Driver Code to test above
int main()
{
    int arr[] = {10, 20, 15, 17, 9, 21};
    int n = sizeof(arr) / sizeof(arr[0]);

    printf("Given array: ");
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);

    printf("\n\n");

    heapSort(arr, n);

    // print array after sorting
    printf("Sorted array: ");
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);

    return 0;
}

C

// C program for implementation
// of Iterative Heap Sort
#include <stdio.h>

// function build Max Heap where value
// of each child is always smaller
// than value of their parent
void buildMaxHeap(int arr[], int n)
{
    for (int i = 1; i < n; i++)
    {
        // if child is bigger than parent
        if (arr[i] > arr[(i - 1) / 2])
        {
            int j = i;

            // swap child and parent until
            // parent is smaller
            while (arr[j] > arr[(j - 1) / 2])
            {
                int temp=arr[j];
                arr[j]=arr[(j-1)/2];
                arr[(j-1)/2]=temp;
                j = (j - 1) / 2;
            }
        }
    }
}

void heapSort(int arr[], int n)
{
    buildMaxHeap(arr, n);

    for (int i = n - 1; i > 0; i--)
    {
        // swap value of first indexed
        // with last indexed
        int temp=arr[0];
        arr[0]=arr[i];
        arr[i]=temp;

        // maintaining heap property
        // after each swapping
        int j = 0, index;

        do
        {
            index = (2 * j + 1);

            // if left child is smaller than
            // right child point index variable
            // to right child
            if (arr[index] < arr[index + 1] &&
                                index < (i - 1))
                index++;

            // if parent is smaller than child
            // then swapping parent with child
            // having higher value
            if (arr[j] < arr[index] && index < i)
            {
                int tem1=arr[j];
                arr[j]=arr[index];
                arr[index]=tem1;
            }

            j = index;

        } while (index < i);
    }
}

// Driver Code to test above
int main()
{
    int arr[] = {10, 20, 15, 17, 9, 21};
    int n = sizeof(arr) / sizeof(arr[0]);

    printf("Given array: ");
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);

    printf("\n\n");

    heapSort(arr, n);

    // print array after sorting
    printf("Sorted array: ");
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);

    return 0;
}

Java

// Java implementation of Iterative Heap Sort
public class HeapSort {

  // function build Max Heap where value
  // of each child is always smaller
  // than value of their parent
  static void buildMaxHeap(int arr[], int n)
  {
    for (int i = 1; i < n; i++)
    {
      // if child is bigger than parent
      if (arr[i] > arr[(i - 1) / 2])
      {
        int j = i;

        // swap child and parent until
        // parent is smaller
        while (arr[j] > arr[(j - 1) / 2])
        {
          swap(arr, j, (j - 1) / 2);
          j = (j - 1) / 2;
        }
      }
    }
  }

  static void heapSort(int arr[], int n)
  {
    buildMaxHeap(arr, n);

    for (int i = n - 1; i > 0; i--)
    {
      // swap value of first indexed
      // with last indexed
      swap(arr, 0, i);

      // maintaining heap property
      // after each swapping
      int j = 0, index;

      do
      {
        index = (2 * j + 1);

        // if left child is smaller than
        // right child point index variable
        // to right child
        if (index < (i - 1) && arr[index] < arr[index + 1])
          index++;

        // if parent is smaller than child
        // then swapping parent with child
        // having higher value
        if (index < i && arr[j] < arr[index])
          swap(arr, j, index);

        j = index;

      } while (index < i);
    }
  }

  public static void swap(int[] a, int i, int j) {
    int temp = a[i];
    a[i]=a[j];
    a[j] = temp;
  }

  /* A utility function to print array of size n */
  static void printArray(int arr[])
  {
    int n = arr.length;
    for (int i = 0; i < n; i++)
      System.out.print(arr[i] + " ");
    System.out.println();
  }

  // Driver program
  public static void main(String args[])
  {
    int arr[] = {10, 20, 15, 17, 9, 21};
    int n = arr.length;

    System.out.print("Given array: ");
    printArray(arr);

    heapSort(arr, n);

    System.out.print("Sorted array: ");
    printArray(arr);
  }
}

Python3

# Python3 program for implementation
# of Iterative Heap Sort

# function build Max Heap where value
# of each child is always smaller
# than value of their parent
def buildMaxHeap(arr, n):

    for i in range(n):

        # if child is bigger than parent
        if arr[i] > arr[int((i - 1) / 2)]:
            j = i

            # swap child and parent until
            # parent is smaller
            while arr[j] > arr[int((j - 1) / 2)]:
                (arr[j],
                 arr[int((j - 1) / 2)]) = (arr[int((j - 1) / 2)],
                                           arr[j])
                j = int((j - 1) / 2)

def heapSort(arr, n):

    buildMaxHeap(arr, n)

    for i in range(n - 1, 0, -1):

        # swap value of first indexed
        # with last indexed
        arr[0], arr[i] = arr[i], arr[0]

        # maintaining heap property
        # after each swapping
        j, index = 0, 0

        while True:
            index = 2 * j + 1

            # if left child is smaller than
            # right child point index variable
            # to right child
            if (index < (i - 1) and
                arr[index] < arr[index + 1]):
                index += 1

            # if parent is smaller than child
            # then swapping parent with child
            # having higher value
            if index < i and arr[j] < arr[index]:
                arr[j], arr[index] = arr[index], arr[j]

            j = index
            if index >= i:
                break

# Driver Code
if __name__ == '__main__':
    arr = [10, 20, 15, 17, 9, 21]
    n = len(arr)

    print("Given array: ")
    for i in range(n):
        print(arr[i], end = " ")

    print()

    heapSort(arr, n)

    # print array after sorting
    print("Sorted array: ")
    for i in range(n):
        print(arr[i], end = " ")

# This code is contributed by PranchalK

C#

// C# implementation of Iterative Heap Sort
using System;

class HeapSort
{

// function build Max Heap where value
// of each child is always smaller
// than value of their parent
static void buildMaxHeap(int []arr, int n)
{
    for (int i = 1; i < n; i++)
    {
        // if child is bigger than parent
        if (arr[i] > arr[(i - 1) / 2])
        {
            int j = i;

            // swap child and parent until
            // parent is smaller
            while (arr[j] > arr[(j - 1) / 2])
            {
                swap(arr, j, (j - 1) / 2);
                j = (j - 1) / 2;
            }
        }
    }
}

static void heapSort(int []arr, int n)
{
    buildMaxHeap(arr, n);

    for (int i = n - 1; i > 0; i--)
    {

        // swap value of first indexed
        // with last indexed
        swap(arr, 0, i);

        // maintaining heap property
        // after each swapping
        int j = 0, index;

        do
        {
            index = (2 * j + 1);

            // if left child is smaller than
            // right child point index variable
            // to right child
            if (index < (i - 1) && arr[index] <
                                   arr[index + 1])
            index++;

            // if parent is smaller than child
            // then swapping parent with child
            // having higher value
            if (index < i && arr[j] < arr[index])
                swap(arr, j, index);

            j = index;

        } while (index < i);
    }
}

public static void swap(int[] a, int i, int j)
{
    int temp = a[i];
    a[i] = a[j];
    a[j] = temp;
}

/* A utility function to print array of size n */
static void printArray(int []arr)
{
    int n = arr.Length;
    for (int i = 0; i < n; i++)
    Console.Write(arr[i] + " ");
    Console.WriteLine();
}

// Driver Code
public static void Main(String []args)
{
    int []arr = {10, 20, 15, 17, 9, 21};
    int n = arr.Length;

    Console.Write("Given array: ");
    printArray(arr);

    heapSort(arr, n);

    Console.Write("Sorted array: ");
    printArray(arr);
}
}

// This code is contributed by Princi Singh

Javascript

<script>
// javascript program for implementation
// of Iterative Heap Sort

function swap(arr, i, j) {
    let temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

// function build Max Heap where value
// of each child is always smaller
// than value of their parent
function buildMaxHeap(arr, n) {
    for(let i=1;i<n;i++)
    {
        // if child is bigger than parent
        if (arr[i] > arr[(i - 1) / 2])
        {
            let j = i;

            // swap child and parent until
            // parent is smaller
            while (arr[j] > arr[(j - 1) / 2])
            {
                swap(arr,j,(j-1)/2);
                j = (j - 1) / 2;
            }
        }
    }
}


function heapSort(arr, n) {

    buildMaxHeap(arr,n);

    for (let i = n - 1; i > 0; i--)
    {
        // swap value of first indexed
        // with last indexed
        swap(arr,0,i);

        // maintaining heap property
        // after each swapping
        let j = 0, index;

        do
        {
            index = (2 * j + 1);

            // if left child is smaller than
            // right child point index variable
            // to right child
            if (arr[index] < arr[index + 1] && index < (i - 1))
            index++;

            // if parent is smaller than child
            // then swapping parent with child
            // having higher value
            if (arr[j] < arr[index] && index < i)
                swap(arr, j, index);

            j = index;

        } while (index < i);
    }
}

// Driver Code to test above
let arr = [10, 20, 15, 17, 9, 21];

let n = arr.length;

document.write("Given array : ");
for (let i = 0; i < n; ++i)
        document.write(arr[i]+" ");

document.write("<br>");

heapSort(arr,n);

// print array after sorting
document.write("Sorted array : ");
for (let i = 0; i < n; ++i)
        document.write(arr[i]+" ");

// This code is contributed by aditya942003patil

</script>

Output

Given array: 10 20 15 17 9 21 

Sorted array: 9 10 15 17 20 21 

Time Complexity: O(n log n), Here, both function buildMaxHeap and heapSort runs in O(nlogn) time.
Auxiliary Space: O(1)