Heap Sort for decreasing order using min heap
Given an array of elements, sort the array in decreasing order using min heap.
Examples:
Input : arr[] = {5, 3, 10, 1} Output : arr[] = {10, 5, 3, 1} Input : arr[] = {1, 50, 100, 25} Output : arr[] = {100, 50, 25, 1}
Prerequisite : Heap sort using min heap.
Algorithm :
- Build a min heap from the input data.
- At this point, the smallest item is stored at the root of the heap. Replace it with the last item of the heap followed by reducing the size of heap by 1. Finally, heapify the root of tree.
- Repeat above steps while size of heap is greater than 1.
Note :Heap Sort using min heap sorts in descending order where as max heap sorts in ascending order
Implementation:
C++
// C++ program for implementation of Heap Sort #include <bits/stdc++.h> using namespace std; // To heapify a subtree rooted with node i which is // an index in arr[]. n is size of heap void heapify( int arr[], int n, int i) { int smallest = i; // Initialize smallest as root int l = 2 * i + 1; // left = 2*i + 1 int r = 2 * i + 2; // right = 2*i + 2 // If left child is smaller than root if (l < n && arr[l] < arr[smallest]) smallest = l; // If right child is smaller than smallest so far if (r < n && arr[r] < arr[smallest]) smallest = r; // If smallest is not root if (smallest != i) { swap(arr[i], arr[smallest]); // Recursively heapify the affected sub-tree heapify(arr, n, smallest); } } // main function to do heap sort void heapSort( int arr[], int n) { // Build heap (rearrange array) for ( int i = n / 2 - 1; i >= 0; i--) heapify(arr, n, i); // One by one extract an element from heap for ( int i = n - 1; i >= 0; i--) { // Move current root to end swap(arr[0], arr[i]); // call min heapify on the reduced heap heapify(arr, i, 0); } } /* A utility function to print array of size n */ void printArray( int arr[], int n) { for ( int i = 0; i < n; ++i) cout << arr[i] << " " ; cout << "\n" ; } // Driver program int main() { int arr[] = { 4, 6, 3, 2, 9 }; int n = sizeof (arr) / sizeof (arr[0]); heapSort(arr, n); cout << "Sorted array is \n" ; printArray(arr, n); } |
Java
// Java program for implementation of Heap Sort import java.io.*; class GFG { // To heapify a subtree rooted with node i which is // an index in arr[]. n is size of heap static void heapify( int arr[], int n, int i) { int smallest = i; // Initialize smallest as root int l = 2 * i + 1 ; // left = 2*i + 1 int r = 2 * i + 2 ; // right = 2*i + 2 // If left child is smaller than root if (l < n && arr[l] < arr[smallest]) smallest = l; // If right child is smaller than smallest so far if (r < n && arr[r] < arr[smallest]) smallest = r; // If smallest is not root if (smallest != i) { int temp = arr[i]; arr[i] = arr[smallest]; arr[smallest] = temp; // Recursively heapify the affected sub-tree heapify(arr, n, smallest); } } // main function to do heap sort static void heapSort( int arr[], int n) { // Build heap (rearrange array) for ( int i = n / 2 - 1 ; i >= 0 ; i--) heapify(arr, n, i); // One by one extract an element from heap for ( int i = n - 1 ; i >= 0 ; i--) { // Move current root to end int temp = arr[ 0 ]; arr[ 0 ] = arr[i]; arr[i] = temp; // call min heapify on the reduced heap heapify(arr, i, 0 ); } } /* A utility function to print array of size n */ static void printArray( int arr[], int n) { 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[] = { 4 , 6 , 3 , 2 , 9 }; int n = arr.length; heapSort(arr, n); System.out.println( "Sorted array is " ); printArray(arr, n); } } // This code is contributed by vt_m. |
Python3
# Python3 program for implementation # of Heap Sort # To heapify a subtree rooted with # node i which is an index in arr[]. # n is size of heap def heapify(arr, n, i): smallest = i # Initialize smallest as root l = 2 * i + 1 # left = 2*i + 1 r = 2 * i + 2 # right = 2*i + 2 # If left child is smaller than root if l < n and arr[l] < arr[smallest]: smallest = l # If right child is smaller than # smallest so far if r < n and arr[r] < arr[smallest]: smallest = r # If smallest is not root if smallest ! = i: (arr[i], arr[smallest]) = (arr[smallest], arr[i]) # Recursively heapify the affected # sub-tree heapify(arr, n, smallest) # main function to do heap sort def heapSort(arr, n): # Build heap (rearrange array) for i in range ( int (n / 2 ) - 1 , - 1 , - 1 ): heapify(arr, n, i) # One by one extract an element # from heap for i in range (n - 1 , - 1 , - 1 ): # Move current root to end # arr[ 0 ], arr[i] = arr[i], arr[ 0 ] # call min heapify on the reduced heap heapify(arr, i, 0 ) # A utility function to print # array of size n def printArray(arr, n): for i in range (n): print (arr[i], end = " " ) print () # Driver Code if __name__ = = '__main__' : arr = [ 4 , 6 , 3 , 2 , 9 ] n = len (arr) heapSort(arr, n) print ( "Sorted array is " ) printArray(arr, n) # This code is contributed by PranchalK |
C#
// C# program for implementation of Heap Sort using System; class GFG { // To heapify a subtree rooted with // node i which is an index in arr[], // n is size of heap static void heapify( int [] arr, int n, int i) { int smallest = i; // Initialize smallest as root int l = 2 * i + 1; // left = 2*i + 1 int r = 2 * i + 2; // right = 2*i + 2 // If left child is smaller than root if (l < n && arr[l] < arr[smallest]) smallest = l; // If right child is smaller than smallest so far if (r < n && arr[r] < arr[smallest]) smallest = r; // If smallest is not root if (smallest != i) { int temp = arr[i]; arr[i] = arr[smallest]; arr[smallest] = temp; // Recursively heapify the affected sub-tree heapify(arr, n, smallest); } } // main function to do heap sort static void heapSort( int [] arr, int n) { // Build heap (rearrange array) for ( int i = n / 2 - 1; i >= 0; i--) heapify(arr, n, i); // One by one extract an element from heap for ( int i = n - 1; i >= 0; i--) { // Move current root to end int temp = arr[0]; arr[0] = arr[i]; arr[i] = temp; // call min heapify on the reduced heap heapify(arr, i, 0); } } /* A utility function to print array of size n */ static void printArray( int [] arr, int n) { for ( int i = 0; i < n; ++i) Console.Write(arr[i] + " " ); Console.WriteLine(); } // Driver program public static void Main() { int [] arr = { 4, 6, 3, 2, 9 }; int n = arr.Length; heapSort(arr, n); Console.WriteLine( "Sorted array is " ); printArray(arr, n); } } // This code is contributed by vt_m. |
Javascript
<script> // Javascript program for implementation of Heap Sort // To heapify a subtree rooted with node i which is // an index in arr[]. n is size of heap function heapify(arr, n, i) { var smallest = i; // Initialize smallest as root var l = 2 * i + 1; // left = 2*i + 1 var r = 2 * i + 2; // right = 2*i + 2 // If left child is smaller than root if (l < n && arr[l] < arr[smallest]) smallest = l; // If right child is smaller than smallest so far if (r < n && arr[r] < arr[smallest]) smallest = r; // If smallest is not root if (smallest != i) { [arr[i], arr[smallest]] = [arr[smallest], arr[i]] // Recursively heapify the affected sub-tree heapify(arr, n, smallest); } } // main function to do heap sort function heapSort(arr, n) { // Build heap (rearrange array) for ( var i = parseInt(n / 2 - 1); i >= 0; i--) heapify(arr, n, i); // One by one extract an element from heap for ( var i = n - 1; i >= 0; i--) { // Move current root to end [arr[0], arr[i]] = [arr[i], arr[0]] // call min heapify on the reduced heap heapify(arr, i, 0); } } /* A utility function to print array of size n */ function printArray(arr, n) { for ( var i = 0; i < n; ++i) document.write( arr[i] + " " ); document.write( "<br>" ); } // Driver program var arr = [4, 6, 3, 2, 9]; var n = arr.length; heapSort(arr, n); document.write( "Sorted array is <br>" ); printArray(arr, n); </script> |
Output:
Sorted array is 9 6 4 3 2
Time complexity:It takes O(logn) for heapify and O(n) for constructing a heap. Hence, the overall time complexity of heap sort using min heap or max heap is O(nlogn)
Space complexity: O(n) for call stack
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