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 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++
// 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; } |
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 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 |
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 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 |
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 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
<?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 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 ?> |
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 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 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
The complexity of above solution might looks like O(nLogn) but it is O(n).
Space Complexity: O(n) for call stack since using recursion.
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