# Luis Andrés López Mañán
# Program written by hand as a draft on 09/19/2022
# Credit goes to GeeksForGeeks
# Link: https://www.geeksforgeeks.org/python-program-for-heap-sort/
# Last access on 09/19/2022
# Program wrriten and edited on 10/10/2022

# This function heapifies a subtree rooted at an index
# i. Also, n is the size of a heap and arr is array.

def heapify (arr, n, i):
		# largest is root for now
		largest = i
		
		# left child of root
		left = 2 * i + 1
		
		# right child of root
		right = 2 * i + 2
		
		# Checks if root has a left child and is greater
		# than root
		if l < n and arr[i] < arr[l] :
			largest = l
			
		# Checks if root has a right child and is greater
		# than root
		if r < n and arr[largest] < arr[r]:
			largest = r
			
		# If necessary, this changes root by swapping va-
		# lues
		arr[i], arr[largest] = arr[largest], arr[i]
		
		# This heapifies the root repeatedly
		heapify(arr, n, largest)
		
# This function sorts an array of a given size n
def heapSort(arr, n):
		# A max heap is built and last parent will be at
		# position number h1, i.e., half the given size of
		# and array. Therefore, that will be the starting
		# location.
		h1 = n // 2 - 1
		for i in range(h1, -1, -1):
			heapify(arr, n, i)
			
		# This extracts elements one by one.
		for i in range(n - 1, 0, -1):
			# Swaps, then heapifies
			arr[i], arr[0] = arr[0], arr[i]
			heapify(arr, i, 0)