Convert min Heap to max Heap

Given array representation of min Heap, convert it to max Heap in O(n) time.
Example :

Input: arr[] = [3 5 9 6 8 20 10 12 18 9]
         3
      /     \
     5       9
   /   \    /  \
  6     8  20   10
 /  \   /
12   18 9 


Output: arr[] = [20 18 10 12 9 9 3 5 6 8] OR 
       [any Max Heap formed from input elements]

         20
       /    \
     18      10
   /    \    /  \
  12     9  9    3
 /  \   /
5    6 8 

The problem might look complex at first look. But our final goal is to only build the max heap. The idea is very simple – we simply build Max Heap without caring about the input. We start from bottom-most and rightmost internal mode of min Heap and heapify all internal modes in bottom up way to build the Max heap.

Below is its implementation



C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// A C++ program to convert min Heap to max Heap
#include<bits/stdc++.h>
using namespace std;
  
// to heapify a subtree with root at given index
void MaxHeapify(int arr[], int i, int n)
{
    int l = 2*i + 1;
    int r = 2*i + 2;
    int largest = i;
    if (l < n && arr[l] > arr[i])
        largest = l;
    if (r < n && arr[r] > arr[largest])
        largest = r;
    if (largest != i)
    {
        swap(arr[i], arr[largest]);
        MaxHeapify(arr, largest, n);
    }
}
  
// This function basically builds max heap
void convertMaxHeap(int arr[], int n)
{
    // Start from bottommost and rightmost
    // internal mode and heapify all internal
    // modes in bottom up way
    for (int i = (n-2)/2; i >= 0; --i)
        MaxHeapify(arr, i, n);
}
  
// A utility function to print a given array
// of given size
void printArray(int* arr, int size)
{
    for (int i = 0; i < size; ++i)
        printf("%d ", arr[i]);
}
  
// Driver program to test above functions
int main()
{
    // array representing Min Heap
    int arr[] = {3, 5, 9, 6, 8, 20, 10, 12, 18, 9};
    int n = sizeof(arr)/sizeof(arr[0]);
  
    printf("Min Heap array : ");
    printArray(arr, n);
  
    convertMaxHeap(arr, n);
  
    printf("\nMax Heap array : ");
    printArray(arr, n);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to convert min Heap to max Heap
  
class GFG 
{
    // To heapify a subtree with root at given index
    static void MaxHeapify(int arr[], int i, int n)
    {
        int l = 2*i + 1;
        int r = 2*i + 2;
        int largest = i;
        if (l < n && arr[l] > arr[i])
            largest = l;
        if (r < n && arr[r] > arr[largest])
            largest = r;
        if (largest != i)
        {
            // swap arr[i] and arr[largest]
            int temp = arr[i];
            arr[i] = arr[largest];
            arr[largest] = temp;
            MaxHeapify(arr, largest, n);
        }
    }
   
    // This function basically builds max heap
    static void convertMaxHeap(int arr[], int n)
    {
        // Start from bottommost and rightmost
        // internal mode and heapify all internal
        // modes in bottom up way
        for (int i = (n-2)/2; i >= 0; --i)
            MaxHeapify(arr, i, n);
    }
   
    // A utility function to print a given array
    // of given size
    static void printArray(int arr[], int size)
    {
        for (int i = 0; i < size; ++i)
            System.out.print(arr[i]+" ");
    }
      
    // driver program
    public static void main (String[] args) 
    {
        // array representing Min Heap
        int arr[] = {3, 5, 9, 6, 8, 20, 10, 12, 18, 9};
        int n = arr.length;
   
        System.out.print("Min Heap array : ");
        printArray(arr, n);
   
        convertMaxHeap(arr, n);
   
        System.out.print("\nMax Heap array : ");
        printArray(arr, n);
    }
}
  
// Contributed by Pramod Kumar

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# A Python3 program to convert min Heap
# to max Heap 
  
# to heapify a subtree with root 
# at given index 
def MaxHeapify(arr, i, n):
    l = 2 * i + 1
    r = 2 * i + 2
    largest =
    if l < n and arr[l] > arr[i]: 
        largest = l
    if r < n and arr[r] > arr[largest]: 
        largest =
    if largest != i:
        arr[i], arr[largest] = arr[largest], arr[i] 
        MaxHeapify(arr, largest, n)
  
# This function basically builds max heap 
def convertMaxHeap(arr, n):
      
    # Start from bottommost and rightmost 
    # internal mode and heapify all 
    # internal modes in bottom up way 
    for i in range(int((n - 2) / 2), -1, -1):
        MaxHeapify(arr, i, n)
  
# A utility function to print a 
# given array of given size 
def printArray(arr, size):
    for i in range(size):
        print(arr[i], end = " ")
    print()
  
# Driver Code
if __name__ == '__main__':
      
    # array representing Min Heap 
    arr = [3, 5, 9, 6, 8, 20, 10, 12, 18, 9
    n = len(arr)
  
    print("Min Heap array : "
    printArray(arr, n) 
  
    convertMaxHeap(arr, n) 
  
    print("Max Heap array : "
    printArray(arr, n)
  
# This code is contributed by PranchalK

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to convert 
// min Heap to max Heap
using System;
  
class GFG 
{
    // To heapify a subtree with 
    // root at given index
    static void MaxHeapify(int []arr, 
                           int i, int n)
    {
        int l = 2 * i + 1;
        int r = 2 * i + 2;
        int largest = i;
        if (l < n && arr[l] > arr[i])
            largest = l;
        if (r < n && arr[r] > arr[largest])
            largest = r;
        if (largest != i)
        {
            // swap arr[i] and arr[largest]
            int temp = arr[i];
            arr[i] = arr[largest];
            arr[largest] = temp;
            MaxHeapify(arr, largest, n);
        }
    }
  
    // This function basically
    // builds max heap
    static void convertMaxHeap(int []arr, 
                               int n)
    {
        // Start from bottommost and 
        // rightmost internal mode and 
        // heapify all internal modes 
        // in bottom up way
        for (int i = (n - 2) / 2; i >= 0; --i)
            MaxHeapify(arr, i, n);
    }
  
    // A utility function to print 
    // a given array of given size
    static void printArray(int []arr, 
                           int size)
    {
        for (int i = 0; i < size; ++i)
            Console.Write(arr[i]+" ");
    }
      
    // Driver Code
    public static void Main () 
    {
        // array representing Min Heap
        int []arr = {3, 5, 9, 6, 8, 
                     20, 10, 12, 18, 9};
        int n = arr.Length;
  
        Console.Write("Min Heap array : ");
        printArray(arr, n);
  
        convertMaxHeap(arr, n);
  
        Console.Write("\nMax Heap array : ");
        printArray(arr, n);
    }
}
  
// This code is contributed by nitin mittal.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// A PHP program to convert min Heap to max Heap
  
// utlity swap function
function swap(&$a,&$b)
{
    $tmp=$a;
    $a=$b;
    $b=$tmp;
}
  
// to heapify a subtree with root at given index
function MaxHeapify(&$arr, $i, $n)
{
    $l = 2*$i + 1;
    $r = 2*$i + 2;
    $largest = $i;
    if ($l < $n && $arr[$l] > $arr[$i])
        $largest = $l;
    if ($r < $n && $arr[$r] > $arr[$largest])
        $largest = $r;
    if ($largest != $i)
    {
        swap($arr[$i], $arr[$largest]);
        MaxHeapify($arr, $largest, $n);
    }
}
  
// This function basically builds max heap
function convertMaxHeap(&$arr, $n)
{
    // Start from bottommost and rightmost
    // internal mode and heapify all internal
    // modes in bottom up way
    for ($i = (int)(($n-2)/2); $i >= 0; --$i)
        MaxHeapify($arr, $i, $n);
}
  
// A utility function to print a given array
// of given size
function printArray($arr, $size)
{
    for ($i = 0; $i <$size; ++$i)
        print($arr[$i]." ");
}
  
    // Driver code
  
    // array representing Min Heap
    $arr = array(3, 5, 9, 6, 8, 20, 10, 12, 18, 9);
    $n = count($arr);
  
    print("Min Heap array : ");
    printArray($arr, $n);
  
    convertMaxHeap($arr, $n);
  
    print("\nMax Heap array : ");
    printArray($arr, $n);
  
  
// This code is contributed by mits
?>

chevron_right



Output :

Min Heap array : 3 5 9 6 8 20 10 12 18 9 
Max Heap array : 20 18 10 12 9 9 3 5 6 8 

The complexity of above solution might looks like O(nLogn) but it is O(n). Refer this G-Fact for more details.

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above



My Personal Notes arrow_drop_up



Article Tags :
Practice Tags :


3


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.