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"""
Heap Sort
---------
Uses the max heap data structure implemented in a list.
Time Complexity: O(n log n)
Space Complexity: O(1) Auxiliary
Stable: Yes
Psuedo Code: CLRS. Introduction to Algorithms. 3rd ed.
"""
def max_heapify(seq, i, n):
"""
The function of max_heapify is to let the value at seq[i] "float down" in
the max-heap so that the subtree rooted at index i becomes a max-heap.
:param seq: A list of integers
:param i: An integer that is an index in to the list that represents the
root of a subtree that max heapify is called on.
:param n: length of the list
"""
l = 2 * i + 1
r = 2 * i + 2
if l <= n and seq[l] > seq[i]:
largest = l
else:
largest = i
if r <= n and seq[r] > seq[largest]:
largest = r
if largest != i:
seq[i], seq[largest] = seq[largest], seq[i]
max_heapify(seq, largest, n)
def build_heap(seq):
"""
Continously calls max_heapify on the list for each subtree.
:param seq: A list of integers
"""
n = len(seq) - 1
for i in range(n//2, -1, -1):
max_heapify(seq, i, n)
def sort(seq):
"""
Takes a list of integers and sorts them in ascending order. This sorted
list is then returned.
:param seq: A list of integers
:rtype: A list of sorted integers
"""
build_heap(seq)
heap_size = len(seq) - 1
for x in range(heap_size, 0, -1):
seq[0], seq[x] = seq[x], seq[0]
heap_size = heap_size - 1
max_heapify(seq, 0, heap_size)
return seq
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