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# C++ Program for Heap Sort

Heap sort is a comparison-based sorting technique based on the Binary Heap data structure. It is similar to the selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for the remaining element.

Recommended Practice

Implementation:

## CPP

 `// C++ program for implementation of Heap Sort``#include ``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` `largest = i; ``// Initialize largest as root Since we are using 0 based indexing``    ``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) {``        ``swap(arr[i], arr[largest]);` `        ``// Recursively heapify the affected sub-tree``        ``heapify(arr, n, largest);``    ``}``}` `// 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, arr[i]);` `        ``// call max 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[] = { 60 ,20 ,40 ,70, 30, 10};``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``  ``//heapify algorithm``  ``// the loop must go reverse you will get after analyzing manually``  ``// (i=n/2 -1) because other nodes/ ele's are leaf nodes``  ``// (i=n/2 -1) for 0 based indexing``  ``// (i=n/2)  for 1 based indexing``     ``for``(``int` `i=n/2 -1;i>=0;i--){``       ``heapify(arr,n,i);``   ``}``  ` `  ``cout << ``"After heapifying array is \n"``;``    ``printArray(arr, n);``  ` `  ` `    ``heapSort(arr, n);` `    ``cout << ``"Sorted array is \n"``;``    ``printArray(arr, n);``    ` `  ``return` `0;``}``//code by Prajwal Chougale`

Output

```After heapifying array is
70 60 40 20 30 10
Sorted array is
10 20 30 40 60 70 ```

Time complexity : O(N*logN)
Auxiliary space: O(1)

### Approach Name: Heap Sort (Using STL)

Steps:

1. Convert the input array to a vector.
2. Convert the vector into a Max Heap using the make_heap function of the STL.
3. Sort the Max Heap using the sort_heap function of the STL.

## C++

 `#include ``#include ``#include ``using` `namespace` `std;` `void` `heapSort(``int` `arr[], ``int` `n)``{``    ``// Convert array to vector``    ``vector<``int``> v(arr, arr + n);` `    ``// Convert vector to Max Heap``    ``make_heap(v.begin(), v.end());` `    ``// Sort Max Heap``    ``sort_heap(v.begin(), v.end());` `    ``// Copy sorted vector back to array``    ``copy(v.begin(), v.end(), arr);``}` `int` `main()``{``    ``int` `arr[] = { 60, 20, 40, 70, 30, 10 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``heapSort(arr, n);` `    ``cout << ``"Sorted array is \n"``;``    ``for` `(``int` `i = 0; i < n; ++i)``        ``cout << arr[i] << ``" "``;``    ``cout << endl;``}`

Output

```Sorted array is
10 20 30 40 60 70 ```

Time Complexity: O(n*log(n)) in all cases.
Auxiliary Space: O(1) in-place sorting algorithm.

Please refer complete article on Heap Sort for more details!

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