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Find k largest elements in an array
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Iterative HeapSort

Last Updated : 29 Mar, 2024
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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)


Next Article
Find k largest elements in an array

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Article Tags :
  • Algorithms
  • Sorting
  • Heap
  • DSA
Practice Tags :
  • Algorithms
  • Heap
  • Sorting

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