Heapsort is an examination constructed arranging method situated in based Binary Heap data structure. It is like determination sort where we first locate the most significant component and place the most extreme component toward the end. We rehash a similar procedure for the remaining array element.
What is Binary Heap?
Let us first define a Complete Binary Tree. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible (Source Wikipedia)
A Binary Heap is a Complete Binary Tree where items are stored in a special order such that value in a parent node is greater (or smaller) than the values in its two children nodes. The former is called as max heap and the latter is called min heap. The heap can be represented by binary tree or array.
using System;
public class HeapSort
{
public void sort(int[] arr)
{
int n = arr.Length;
// 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 max heapify on the reduced heap
heapify(arr, i, 0);
}
}
// 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 largest = i; // Initialize largest as root
int l = 2 * i + 1; // left = 2*i + 1
int r = 2 * i + 2; // right = 2*i + 2
// If left child is larger than root
if (l < n && arr[l] > arr[largest])
largest = l;
// If right child is larger than largest so far
if (r < n && arr[r] > arr[largest])
largest = r;
// If largest is not root
if (largest != i)
{
int swap = arr[i];
arr[i] = arr[largest];
arr[largest] = swap;
// Recursively heapify the affected subtree
heapify(arr, n, largest);
}
}
/* A utility function to print array of size n */
static void printArray(int[] arr)
{
int n = arr.Length;
for (int i = 0; i < n; ++i)
Console.Write(arr[i] + " ");
Console.Read();
}
// Driver program
public static void Main()
{
int[] arr = { 12, 11, 13, 5, 6, 7 };
int n = arr.Length;
HeapSort ob = new HeapSort();
ob.sort(arr);
Console.WriteLine("Sorted array is");
printArray(arr);
}
}

Complexity Analysis of Heap Sort
Worst Case Time Complexity: O(n*log n)
Best Case Time Complexity: O(n*log n)
Average Time Complexity: O(n*log n)
Space Complexity : O(1)
 Heap sort is not a Stable sort, and requires a constant space for sorting a list.
 Heap Sort is very fast and is widely used for sorting.
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