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:
- Import the Python STL library “heapq“.
- Convert the input list into a heap using the “heapify” function from heapq.
- Create an empty list “result” to store the sorted elements.
- Iterate over the heap and extract the minimum element using “heappop” function from heapq and append it to the “result” list.
- 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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