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* Add median() function using Quickselect * Update quick_select.py * Update quick_select.py * Update quick_select.py --------- Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
85 lines
2.4 KiB
Python
85 lines
2.4 KiB
Python
"""
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A Python implementation of the quick select algorithm, which is efficient for
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calculating the value that would appear in the index of a list if it would be
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sorted, even if it is not already sorted
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https://en.wikipedia.org/wiki/Quickselect
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"""
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import random
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def _partition(data: list, pivot) -> tuple:
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"""
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Three way partition the data into smaller, equal and greater lists,
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in relationship to the pivot
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:param data: The data to be sorted (a list)
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:param pivot: The value to partition the data on
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:return: Three list: smaller, equal and greater
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"""
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less, equal, greater = [], [], []
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for element in data:
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if element < pivot:
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less.append(element)
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elif element > pivot:
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greater.append(element)
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else:
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equal.append(element)
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return less, equal, greater
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def quick_select(items: list, index: int):
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"""
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>>> quick_select([2, 4, 5, 7, 899, 54, 32], 5)
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54
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>>> quick_select([2, 4, 5, 7, 899, 54, 32], 1)
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4
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>>> quick_select([5, 4, 3, 2], 2)
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4
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>>> quick_select([3, 5, 7, 10, 2, 12], 3)
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7
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"""
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# index = len(items) // 2 when trying to find the median
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# (value of index when items is sorted)
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# invalid input
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if index >= len(items) or index < 0:
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return None
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pivot = items[random.randint(0, len(items) - 1)]
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count = 0
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smaller, equal, larger = _partition(items, pivot)
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count = len(equal)
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m = len(smaller)
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# index is the pivot
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if m <= index < m + count:
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return pivot
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# must be in smaller
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elif m > index:
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return quick_select(smaller, index)
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# must be in larger
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else:
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return quick_select(larger, index - (m + count))
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def median(items: list):
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"""
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One common application of Quickselect is finding the median, which is
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the middle element (or average of the two middle elements) in a sorted dataset.
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It works efficiently on unsorted lists by partially sorting the data without
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fully sorting the entire list.
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>>> median([3, 2, 2, 9, 9])
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3
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>>> median([2, 2, 9, 9, 9, 3])
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6.0
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"""
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mid, rem = divmod(len(items), 2)
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if rem != 0:
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return quick_select(items=items, index=mid)
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else:
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low_mid = quick_select(items=items, index=mid - 1)
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high_mid = quick_select(items=items, index=mid)
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return (low_mid + high_mid) / 2
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