Iterative HeapSort

Last Updated : 29 Mar, 2024

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)

kaditya139

Improve

How to check if a given array represents a Binary Heap?

Print K largest(or smallest) elements in an array

Some other type of Heap

Easy problems on Heap

Medium problems on Heap

Hard problems on Heap

Iterative HeapSort

C++

C

Java

Python3

C#

Javascript

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