Convert Min Heap to Max Heap

Given an array representation of min Heap, convert it to max Heap.

Examples:

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}

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

Input: arr[] = {3, 4, 8, 11, 13}
Output:  arr[] = {13, 11, 8, 4, 3}

Approach: To solve the problem follow the below idea:

The idea is, simply build Max Heap without caring about the input. Start from the bottom-most and rightmost internal node of Min-Heap and heapify all internal nodes in the bottom-up way to build the Max heap.

Follow the given steps to solve the problem:

• Call the Heapify function from the rightmost internal node of Min-Heap
• Heapify all internal nodes in the bottom-up way to build max heap
• Print the Max-Heap

Algorithm: Here’s an algorithm for converting a min heap to a max heap:

1. Start at the last non-leaf node of the heap (i.e., the parent of the last leaf node). For a binary heap, this node is located at the index floor((n – 1)/2), where n is the number of nodes in the heap.
2. For each non-leaf node, perform a “heapify” operation to fix the heap property. In a min heap, this operation involves checking whether the value of the node is greater than that of its children, and if so, swapping the node with the smaller of its children. In a max heap, the operation involves checking whether the value of the node is less than that of its children, and if so, swapping the node with the larger of its children.
3. Repeat step 2 for each of the non-leaf nodes, working your way up the heap. When you reach the root of the heap, the entire heap should now be a max heap.

Below is the implementation of the above approach:

C

// C program to convert min Heap to max Heap

#include <stdio.h>

void swap(int* a, int* b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}

// 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 node and heapify all internal
    // nodes 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's code
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);

    // Function call
    convertMaxHeap(arr, N);

    printf("\nMax Heap array : ");
    printArray(arr, N);

    return 0;
}

C++

// 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 node and heapify all internal
    // nodes 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)
        cout << arr[i] << " ";
}

// Driver's code
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);

    // Function call
    convertMaxHeap(arr, N);

    printf("\nMax Heap array : ");
    printArray(arr, N);

    return 0;
}

Java

// 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 node and heapify all internal
        // nodes 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's code
    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);

        // Function call
        convertMaxHeap(arr, N);

        System.out.print("\nMax Heap array : ");
        printArray(arr, N);
    }
}

// Contributed by Pramod Kumar

Python3

# 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 = i
    if l < N and arr[l] > arr[i]:
        largest = l
    if r < N and arr[r] > arr[largest]:
        largest = r
    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 node and heapify all
    # internal nodes 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)

    # Function call
    convertMaxHeap(arr, N)

    print("Max Heap array : ")
    printArray(arr, N)

# This code is contributed by PranchalK

C#

// 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 node and
        // heapify all internal nodes
        // 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's 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);

        // Function call
        convertMaxHeap(arr, n);

        Console.Write("\nMax Heap array : ");
        printArray(arr, n);
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// A PHP program to convert min Heap to max Heap

// utility 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, $n)
{
    // Start from bottommost and rightmost
    // internal node and heapify all internal
    // nodes in bottom up way
    for ($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
?>

Javascript

<script>
// javascript program to convert min Heap to max Heap
// To heapify a subtree with root at given index
function MaxHeapify(arr , i , n)
{
    var l = 2*i + 1;
    var r = 2*i + 2;
    var 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]
        var temp = arr[i];
        arr[i] = arr[largest];
        arr[largest] = temp;
        MaxHeapify(arr, largest, n);
    }
}

// This function basically builds max heap
function convertMaxHeap(arr , n)
{
    // Start from bottommost and rightmost
    // internal node and heapify all internal
    // nodes in bottom up way
    for (i = (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)
        document.write(arr[i]+" ");
}

// driver program
// array representing Min Heap
var arr = [3, 5, 9, 6, 8, 20, 10, 12, 18, 9];
var n = arr.length;

document.write("Min Heap array : ");
printArray(arr, n);

convertMaxHeap(arr, n);

document.write("<br>Max Heap array : ");
printArray(arr, n);

// This code is contributed by 29AjayKumar
</script>

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 

Time Complexity: O(N), for details, please refer: Time Complexity of building a heap
Auxiliary Space: O(N)