Convert min Heap to max Heap - GeeksforGeeks

20 Oct, 2021
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 the bottom-most and rightmost internal mode of min Heap and heapify all internal modes in the bottom-up way to build the Max heap.Below is its implementation 
C++
Java
Python3
C#
PHP
Javascript
// 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 indexvoid 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 heapvoid 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 sizevoid printArray(int* arr, int size){    for (int i = 0; i < size; ++i)        printf("%d ", arr[i]);} // Driver program to test above functionsint 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;}
// 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
# A Python3 program to convert min Heap# to max Heap # to heapify a subtree with root# at given indexdef 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 heapdef 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 sizedef printArray(arr, size):    for i in range(size):        print(arr[i], end = " ")    print() # Driver Codeif __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
// C# program to convert// min Heap to max Heapusing 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.
<?php// A PHP program to convert min Heap to max Heap // utility swap functionfunction swap(&$a,&$b){    $tmp=$a;    $a=$b;    $b=$tmp;} // to heapify a subtree with root at given indexfunction 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, $n);    }} // This function basically builds max heapfunction convertMaxHeap(&$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, $n);} // A utility function to print a given array// of given sizefunction printArray($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?>
<script>// javascript program to convert min Heap to max Heap   // To heapify a subtree with root at given indexfunction 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 heapfunction convertMaxHeap(arr , n){    // Start from bottommost and rightmost    // internal mode and heapify all internal    // modes 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 sizefunction printArray(arr , size){    for (i = 0; i < size; ++i)        document.write(arr[i]+" ");} // driver program// array representing Min Heapvar 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 
The complexity of above solution might looks like O(nLogn) but it is O(n). Refer to 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 review-team@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 
nitin mittal
PranchalKatiyar
Mithun Kumar
29AjayKumar
gabaa406
tanmay_thaker
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