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 heapvoid 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 sortvoid 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 programint 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 Sortimport 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 Sortusing 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 heapfunction 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 sortfunction 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 programvar 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
New Approach
- Build a min heap from the array elements.
- Create an empty result array.
- While the min heap is not empty:
a. Remove the minimum element from the heap.
b. Add the element to the beginning of the result array. - Return the result array.
C++
#include <algorithm>#include <iostream>#include <queue>#include <vector>using namespace std;vector<int> sortArrayInDescendingOrder(vector<int>& arr){ priority_queue<int, vector<int>, greater<int> > minHeap; for (int num : arr) { minHeap.push(num); } vector<int> result; while (!minHeap.empty()) { int top = minHeap.top(); minHeap.pop(); result.insert(result.begin(), top); } return result;}int main(){ vector<int> arr = { 4, 6, 3, 2, 9 }; vector<int> result = sortArrayInDescendingOrder(arr); for (int num : result) { cout << num << " "; } cout << endl; return 0;}// This code is contributed by chinmaya121221 |
Java
import java.util.*;public class Main { public static List<Integer> sortArrayInDescendingOrder(List<Integer> arr) { PriorityQueue<Integer> minHeap = new PriorityQueue<>(); for (int num : arr) { minHeap.add(num); } List<Integer> result = new ArrayList<>(); while (!minHeap.isEmpty()) { int top = minHeap.poll(); result.add(0, top); } return result; } public static void main(String[] args) { List<Integer> arr = Arrays.asList(4, 6, 3, 2, 9); List<Integer> result = sortArrayInDescendingOrder(arr); for (int num : result) { System.out.print(num + " "); } System.out.println(); }} |
Python3
import heapqdef sortArrayInDescendingOrder(arr): minHeap = [] for num in arr: heapq.heappush(minHeap, num) result = [] while minHeap: top = heapq.heappop(minHeap) result.insert(0, top) return resultif __name__ == '__main__': arr = [4, 6, 3, 2, 9] result = sortArrayInDescendingOrder(arr) for num in result: print(num, end=' ') print() |
C#
using System;using System.Collections.Generic;class Program { static List<int> SortArrayInDescendingOrder(List<int> arr) { PriorityQueue<int> minHeap = new PriorityQueue<int>(); foreach(int num in arr) { minHeap.Push(num); } List<int> result = new List<int>(); while (minHeap.Count > 0) { int top = minHeap.Top; minHeap.Pop(); result.Insert(0, top); } return result; } static void Main(string[] args) { List<int> arr = new List<int>{ 4, 6, 3, 2, 9 }; List<int> result = SortArrayInDescendingOrder(arr); foreach(int num in result) { Console.Write(num + " "); } Console.WriteLine(); }}class PriorityQueue<T> where T : IComparable<T> { private List<T> _heap; public int Count { get { return _heap.Count; } } public T Top { get { return _heap[0]; } } public PriorityQueue() { _heap = new List<T>(); } public void Push(T item) { _heap.Add(item); int i = _heap.Count - 1; while (i > 0 && _heap[(i - 1) / 2].CompareTo(_heap[i]) > 0) { Swap(i, (i - 1) / 2); i = (i - 1) / 2; } } public void Pop() { if (_heap.Count == 0) throw new InvalidOperationException( "PriorityQueue is empty"); int lastIndex = _heap.Count - 1; _heap[0] = _heap[lastIndex]; _heap.RemoveAt(lastIndex); lastIndex--; int i = 0; while (true) { int leftChild = 2 * i + 1; int rightChild = 2 * i + 2; if (leftChild > lastIndex) break; int j = leftChild; if (rightChild <= lastIndex && _heap[rightChild].CompareTo( _heap[leftChild]) < 0) { j = rightChild; } if (_heap[i].CompareTo(_heap[j]) <= 0) break; Swap(i, j); i = j; } } private void Swap(int i, int j) { T temp = _heap[i]; _heap[i] = _heap[j]; _heap[j] = temp; }}// This code is contributed by sarojmcy2e |
Javascript
// JavaScript program to sort the array in descending orderfunction sortArrayInDescendingOrder(arr) { let minHeap = new MinHeap(); // Push all elements to the min heap for (let num of arr) { minHeap.push(num); } let result = []; while (!minHeap.isEmpty()) { let top = minHeap.top(); minHeap.pop(); result.unshift( top); // Insert at the beginning of the array } return result;}class MinHeap { constructor() { this.heap = []; } push(num) { this.heap.push(num); this.bubbleUp(this.heap.length - 1); } pop() { let top = this.heap[0]; let last = this.heap.pop(); if (this.heap.length > 0) { this.heap[0] = last; this.bubbleDown(0); } return top; } top() { return this.heap[0]; } isEmpty() { return this.heap.length === 0; } bubbleUp(index) { while (index > 0) { let parent = Math.floor((index - 1) / 2); if (this.heap[parent] > this.heap[index]) { [ this.heap[parent], this.heap[index] ] = [ this.heap[index], this.heap[parent] ]; index = parent; } else { break; } } } bubbleDown(index) { while (true) { let left = 2 * index + 1; let right = 2 * index + 2; let smallest = index; if (left < this.heap.length && this.heap[left] < this.heap[smallest]) { smallest = left; } if (right < this.heap.length && this.heap[right] < this.heap[smallest]) { smallest = right; } if (smallest !== index) { [ this.heap[index], this.heap[smallest] ] = [ this.heap[smallest], this.heap[index] ]; index = smallest; } else { break; } } }}// Driver codelet arr = [ 4, 6, 3, 2, 9 ];// Function calllet result = sortArrayInDescendingOrder(arr);console.log(result.join(" ")); |
Output
9 6 4 3 2
Time Complexity: O(n log n), where n is the number of elements in the array.
Auxiliary Space: O(1), because it sort the array in place without using extra space that depends on the input size .
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