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# Python Program for Heap Sort

Pre-requisite: What is Heap Sort?

Heapsort is a comparison-based sorting technique based on a Binary Heap data structure. It is similar to 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.

## Python

 `#!/usr/bin/python` `# -*- coding: utf-8 -*-` `# Python program for implementation of heap Sort`   `# To heapify subtree rooted at index i.` `# n is size of heap`     `def` `heapify(arr, n, i):` `    ``largest ``=` `i  ``# Initialize largest as root` `    ``l ``=` `2` `*` `i ``+` `1`  `# left = 2*i + 1` `    ``r ``=` `2` `*` `i ``+` `2`  `# right = 2*i + 2`   ` ``# See if left child of root exists and is` ` ``# greater than root`   `    ``if` `l < n ``and` `arr[i] < arr[l]:` `        ``largest ``=` `l`   ` ``# See if right child of root exists and is` ` ``# greater than root`   `    ``if` `r < n ``and` `arr[largest] < arr[r]:` `        ``largest ``=` `r`   ` ``# Change root, if needed`   `    ``if` `largest !``=` `i:` `        ``(arr[i], arr[largest]) ``=` `(arr[largest], arr[i])  ``# swap`   `  ``# Heapify the root.`   `        ``heapify(arr, n, largest)`     `# The main function to sort an array of given size`   `def` `heapSort(arr):` `    ``n ``=` `len``(arr)`   ` ``# Build a maxheap.` ` ``# Since last parent will be at ((n//2)-1) we can start at that location.`   `    ``for` `i ``in` `range``(n ``/``/` `2` `-` `1``, ``-``1``, ``-``1``):` `        ``heapify(arr, n, i)`   ` ``# One by one extract elements`   `    ``for` `i ``in` `range``(n ``-` `1``, ``0``, ``-``1``):` `        ``(arr[i], arr[``0``]) ``=` `(arr[``0``], arr[i])  ``# swap` `        ``heapify(arr, i, ``0``)`     `# Driver code to test above`   `arr ``=` `[``12``, ``11``, ``13``, ``5``, ``6``, ``7``, ]` `heapSort(arr)` `n ``=` `len``(arr)` `print``(``'Sorted array is'``)` `for` `i ``in` `range``(n):` `    ``print``(arr[i])`   `# This code is contributed by Mohit Kumra`

Output

```Sorted array is
5
6
7
11
12
13```

Time Complexity: O(n*log(n))

• The time complexity of heapify is O(log(n)).
• Time complexity of createAndBuildHeap() is O(n).
• And, hence the overall time complexity of Heap Sort is O(n*log(n)).

Auxiliary Space: O(log(n))

### Approach Name: Heap Sort using Python STL

Steps:

1. Import the Python STL library “heapq“.
2. Convert the input list into a heap using the “heapify” function from heapq.
3. Create an empty list “result” to store the sorted elements.
4. Iterate over the heap and extract the minimum element using “heappop” function from heapq and append it to the “result” list.
5. Return the “result” list as the sorted output.

## Python3

 `import` `heapq`   `# Function to perform the sorting using` `# heaop sort` `def` `heap_sort(arr):` `    ``heapq.heapify(arr)` `    ``result ``=` `[]` `    ``while` `arr:` `        ``result.append(heapq.heappop(arr))` `    ``return` `result` `  `  `# Driver Code` `arr ``=` `[``60``, ``20``, ``40``, ``70``, ``30``, ``10``]` `print``(``"Input Array: "``, arr)` `print``(``"Sorted Array: "``, heap_sort(arr))`

Output

```Input Array:  [60, 20, 40, 70, 30, 10]
Sorted Array:  [10, 20, 30, 40, 60, 70]```

Time Complexity: O(n log n), where “n” is the size of the input list.

Auxiliary Space: O(1).

Please refer complete article on Heap Sort for more details!

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