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122 lines
3.8 KiB
122 lines
3.8 KiB
"""
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:Author: James Sherratt
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:Date: 20/10/2019
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:License: MIT
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:name: heapsort.py
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Heap sorts a list-like object. Note: this has been written with code-clarity
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in mind first, efficiency second.
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"""
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from random import randint
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def get_left(i):
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"""
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Get the left element index of a heap node for an array.
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:param i: The parent index.
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:return: the left element.
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"""
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return 2 * i + 1
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def get_right(i):
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"""
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Get the right element index of a heap node for an array.
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:param i: The parent index.
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:return: the right element.
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"""
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return 2 * i + 2
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def repair_heap(vals_list, root, arr_top):
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"""
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Sifts the root element of a heap to the correct position, to
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correct a max heap. This assumes the children of the root/ node are max heaps.
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:param vals_list: list of values, which represents a heap structure.
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:param root: the index of the node we're working from/ using as a root.
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:param arr_top: the largest value of the list we're interested in.
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:return: Reference to the passed list, with the root node in the correct position.
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"""
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# This is the value to swap. We want to swap the root value down, so we swap the root first.
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swap = root
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# Get left and right nodes of root.
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left = get_left(root)
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right = get_right(root)
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while left < arr_top:
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# Check if value to swap is less than the left child.
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if vals_list[swap] < vals_list[left]:
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swap = left
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# Check if value to swap is less than the right child (if exists).
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# Note: these 2 if's could be combined using "and", but then we're relying on lazy evaluation.
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if right < arr_top:
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if vals_list[swap] < vals_list[right]:
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swap = right
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# Check if the swap is still the root. If so, there's no more children to swap and we're done.
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if swap == root:
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return vals_list
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# Else, swap.
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else:
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vals_list[root], vals_list[swap] = vals_list[swap], vals_list[root]
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# New root, left and right node for the next iteration.
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root = swap
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left = get_left(root)
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right = get_right(root)
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return vals_list
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def max_heap(vals_list):
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"""
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Convert a list of values into a max heap tree.
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:param vals_list: list of numbers.
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:return: the same list as a max heap tree.
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"""
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# Create a max heap by repairing the heap, starting from the nodes one above the leaf nodes.
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len_list = len(vals_list)
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for root in range(len_list//2, -1, -1):
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repair_heap(vals_list, root, len_list)
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return vals_list
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def max_heap_to_sorted(vals_list):
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"""
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Convert a max heap list into a sorted list.
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:param vals_list: list containing max heap.
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:return: the same list of values, sorted.
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"""
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# i is the index of the last element of the slice of the array that needs sorting.
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for top in range(len(vals_list)-1, 0, -1):
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# Swap the root value (max) with the last value of the slice.
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vals_list[0], vals_list[top] = vals_list[top], vals_list[0]
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# Sift the new root to the correct position of the remainder of the max heap.
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# Another way of doing this is to pass a slice of the vals_list up to the value top, but python passes
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# slices by copy so there's a massive performance hit.
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repair_heap(vals_list, 0, top)
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return vals_list
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def heapsort(vals_list):
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"""
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Sort a list of values using heapsort.
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:param vals_list: list of sortable values.
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:return: the same list, sorted.
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"""
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max_heap(vals_list)
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return max_heap_to_sorted(vals_list)
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if __name__ == "__main__":
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list_len = 100000
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vals_list = [randint(0, (2**16)) for i in range(list_len)]
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heap_sorted = heapsort(list(vals_list))
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py_sorted = sorted(vals_list)
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print("Did the sort work? {}".format(heap_sorted == py_sorted))
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