# Iterative HeapSort

HeapSort is a comparison based sorting technique where we first build Max Heap and then swaps the root element with last element (size times) and maintains the heap property each time to finally make it sorted.

Examples:

```Input :  10 20 15 17 9 21
Output : 9 10 15 17 20 21

Input:  12 11 13 5 6 7 15 5 19
Output: 5 5 6 7 11 12 13 15 19 ```

In first Example, first we have to build Max Heap.
So, we will start from 20 as child and check for its parent. Here 10 is smaller, so we will swap these two.
Now, 20 10 15 17 9 21
Now, child 17 is greater than its parent 10. So, both will be swapped and order will be
20 17 15 10 9 21
Now, child 21 is greater than parent 15. So, both will be swapped.
20 17 21 10 9 15
Now, again 21 is bigger than parent 20. So,
21 17 20 10 9 15
This is Max Heap.

Now, we have to apply sorting. Here, we have to swap first element with last one and we have to maintain Max Heap property.
So, after first swapping : 15 17 20 10 9 21
It clearly violates Max Heap property. So, we have to maintain it. So, order will be
20 17 15 10 9 21
17 10 15 9 20 21
15 10 9 17 20 21
10 9 15 17 20 21
9 10 15 17 20 21
Here, underlined part is sorted part.

## C++

 `// C++ program for implementation  ` `// of Iterative Heap Sort ` `#include ` `using` `namespace` `std; ` ` `  `// function build Max Heap where value  ` `// of each child is always smaller ` `// than value of their parent ` `void` `buildMaxHeap(``int` `arr[], ``int` `n)  ` `{  ` `    ``for` `(``int` `i = 1; i < n; i++)  ` `    ``{ ` `        ``// if child is bigger than parent ` `        ``if` `(arr[i] > arr[(i - 1) / 2])  ` `        ``{ ` `            ``int` `j = i; ` `     `  `            ``// swap child and parent until ` `            ``// parent is smaller ` `            ``while` `(arr[j] > arr[(j - 1) / 2])  ` `            ``{ ` `                ``swap(arr[j], arr[(j - 1) / 2]); ` `                ``j = (j - 1) / 2; ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `void` `heapSort(``int` `arr[], ``int` `n)  ` `{ ` `    ``buildMaxHeap(arr, n); ` ` `  `    ``for` `(``int` `i = n - 1; i > 0; i--) ` `    ``{ ` `        ``// swap value of first indexed  ` `        ``// with last indexed  ` `        ``swap(arr[0], arr[i]); ` `     `  `        ``// maintaining heap property ` `        ``// after each swapping ` `        ``int` `j = 0, index; ` `         `  `        ``do` `        ``{ ` `            ``index = (2 * j + 1); ` `             `  `            ``// if left child is smaller than  ` `            ``// right child point index variable  ` `            ``// to right child ` `            ``if` `(arr[index] < arr[index + 1] && ` `                                ``index < (i - 1)) ` `                ``index++; ` `         `  `            ``// if parent is smaller than child  ` `            ``// then swapping parent with child  ` `            ``// having higher value ` `            ``if` `(arr[j] < arr[index] && index < i) ` `                ``swap(arr[j], arr[index]); ` `         `  `            ``j = index; ` `         `  `        ``} ``while` `(index < i); ` `    ``} ` `} ` ` `  `// Driver Code to test above ` `int` `main()  ` `{ ` `    ``int` `arr[] = {10, 20, 15, 17, 9, 21}; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `     `  `    ``printf``(``"Given array: "``); ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``printf``(``"%d "``, arr[i]); ` `         `  `    ``printf``(````" "````);  ` ` `  `    ``heapSort(arr, n); ` ` `  `    ``// print array after sorting ` `    ``printf``(``"Sorted array: "``); ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``printf``(``"%d "``, arr[i]); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of Iterative Heap Sort  ` `public` `class` `HeapSort { ` ` `  `  ``// function build Max Heap where value ` `  ``// of each child is always smaller ` `  ``// than value of their parent ` `  ``static` `void` `buildMaxHeap(``int` `arr[], ``int` `n) ` `  ``{ ` `    ``for` `(``int` `i = ``1``; i < n; i++) ` `    ``{ ` `      ``// if child is bigger than parent ` `      ``if` `(arr[i] > arr[(i - ``1``) / ``2``]) ` `      ``{ ` `        ``int` `j = i; ` ` `  `        ``// swap child and parent until ` `        ``// parent is smaller ` `        ``while` `(arr[j] > arr[(j - ``1``) / ``2``]) ` `        ``{ ` `          ``swap(arr, j, (j - ``1``) / ``2``); ` `          ``j = (j - ``1``) / ``2``; ` `        ``} ` `      ``} ` `    ``} ` `  ``} ` ` `  `  ``static` `void` `heapSort(``int` `arr[], ``int` `n) ` `  ``{ ` `    ``buildMaxHeap(arr, n); ` ` `  `    ``for` `(``int` `i = n - ``1``; i > ``0``; i--) ` `    ``{ ` `      ``// swap value of first indexed ` `      ``// with last indexed ` `      ``swap(arr, ``0``, i); ` ` `  `      ``// maintaining heap property ` `      ``// after each swapping ` `      ``int` `j = ``0``, index; ` ` `  `      ``do` `      ``{ ` `        ``index = (``2` `* j + ``1``); ` ` `  `        ``// if left child is smaller than ` `        ``// right child point index variable ` `        ``// to right child ` `        ``if` `(index < (i - ``1``) && arr[index] < arr[index + ``1``]) ` `          ``index++; ` ` `  `        ``// if parent is smaller than child ` `        ``// then swapping parent with child ` `        ``// having higher value ` `        ``if` `(index < i && arr[j] < arr[index]) ` `          ``swap(arr, j, index); ` ` `  `        ``j = index; ` ` `  `      ``} ``while` `(index < i); ` `    ``} ` `  ``} ` ` `  `  ``public` `static` `void` `swap(``int``[] a, ``int` `i, ``int` `j) { ` `    ``int` `temp = a[i]; ` `    ``a[i]=a[j]; ` `    ``a[j] = temp; ` `  ``} ` ` `  `  ``/* 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++) ` `      ``System.out.print(arr[i] + ``" "``); ` `    ``System.out.println(); ` `  ``} ` ` `  `  ``// Driver program ` `  ``public` `static` `void` `main(String args[]) ` `  ``{ ` `    ``int` `arr[] = {``10``, ``20``, ``15``, ``17``, ``9``, ``21``}; ` `    ``int` `n = arr.length; ` ` `  `    ``System.out.print(``"Given array: "``); ` `    ``printArray(arr); ` ` `  `    ``heapSort(arr, n); ` ` `  `    ``System.out.print(``"Sorted array: "``); ` `    ``printArray(arr); ` `  ``} ` `} `

## Python3

 `# Python3 program for implementation  ` `# of Iterative Heap Sort  ` ` `  `# function build Max Heap where value  ` `# of each child is always smaller  ` `# than value of their parent  ` `def` `buildMaxHeap(arr, n):  ` ` `  `    ``for` `i ``in` `range``(n): ` `         `  `        ``# if child is bigger than parent  ` `        ``if` `arr[i] > arr[``int``((i ``-` `1``) ``/` `2``)]: ` `            ``j ``=` `i  ` `     `  `            ``# swap child and parent until  ` `            ``# parent is smaller  ` `            ``while` `arr[j] > arr[``int``((j ``-` `1``) ``/` `2``)]: ` `                ``(arr[j],  ` `                 ``arr[``int``((j ``-` `1``) ``/` `2``)]) ``=` `(arr[``int``((j ``-` `1``) ``/` `2``)],  ` `                                           ``arr[j]) ` `                ``j ``=` `int``((j ``-` `1``) ``/` `2``) ` ` `  `def` `heapSort(arr, n):  ` ` `  `    ``buildMaxHeap(arr, n)  ` ` `  `    ``for` `i ``in` `range``(n ``-` `1``, ``0``, ``-``1``): ` `         `  `        ``# swap value of first indexed  ` `        ``# with last indexed  ` `        ``arr[``0``], arr[i] ``=` `arr[i], arr[``0``] ` `     `  `        ``# maintaining heap property  ` `        ``# after each swapping  ` `        ``j, index ``=` `0``, ``0` `         `  `        ``while` `True``: ` `            ``index ``=` `2` `*` `j ``+` `1` `             `  `            ``# if left child is smaller than  ` `            ``# right child point index variable  ` `            ``# to right child  ` `            ``if` `(index < (i ``-` `1``) ``and`  `                ``arr[index] < arr[index ``+` `1``]):  ` `                ``index ``+``=` `1` `         `  `            ``# if parent is smaller than child  ` `            ``# then swapping parent with child  ` `            ``# having higher value  ` `            ``if` `index < i ``and` `arr[j] < arr[index]:  ` `                ``arr[j], arr[index] ``=` `arr[index], arr[j]  ` `         `  `            ``j ``=` `index  ` `            ``if` `index >``=` `i: ` `                ``break` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``10``, ``20``, ``15``, ``17``, ``9``, ``21``]  ` `    ``n ``=` `len``(arr)  ` `     `  `    ``print``(``"Given array: "``) ` `    ``for` `i ``in` `range``(n): ` `        ``print``(arr[i], end ``=` `" "``)  ` `         `  `    ``print``()  ` ` `  `    ``heapSort(arr, n)  ` ` `  `    ``# print array after sorting  ` `    ``print``(``"Sorted array: "``) ` `    ``for` `i ``in` `range``(n): ` `        ``print``(arr[i], end ``=` `" "``) ` ` `  `# This code is contributed by PranchalK `

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Output :

```Given array: 10 20 15 17 9 21

Sorted array: 9 10 15 17 20 21 ```

Here, both function buildMaxHeap and heapSort runs in O(nlogn) time. So, overall time complexity is O(nlogn)

## tags:

Heap Sorting Sorting Heap