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61 lines
2.1 KiB
61 lines
2.1 KiB
7 years ago
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## QuickSelect -- Linear-time k-th order statistic
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## (i.e. select the k-th smallest element in an unsorted array)
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## https://en.wikipedia.org/wiki/Quickselect
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def partition(array, start, end, pivot):
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"""Partitions by a pivot value, which might not necessarily be in the array.
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This variant is useful when you want to bound your recursion depth by the
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range of the input values, and not the length of the array."""
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pivot_index = start
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for i in range(start, end):
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if array[i] <= pivot:
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array[i], array[pivot_index] = array[pivot_index], array[i]
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pivot_index += 1
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return pivot_index
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import random
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def partition_first(array, start, end):
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"""Selects the first element as pivot. Returns the index where the pivot went to.
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In this variant, we can guarantee that the pivot will be in its final sorted position.
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We need this guarantee for QuickSelect."""
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if start + 1 == end:
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return start
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pivot = array[start]
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pivot_index = start + 1
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for i in range(start + 1, end):
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if array[i] <= pivot:
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array[i], array[pivot_index] = array[pivot_index], array[i]
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pivot_index += 1
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# Move pivot to front
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array[start], array[pivot_index - 1] = array[pivot_index - 1], array[start]
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return pivot_index - 1
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def quick_select(array, k):
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"""NOTE: k-th smallest element counts from 0!"""
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left = 0
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right = len(array)
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while True:
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random_index = random.sample(range(left, right), 1)[0]
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array[left], array[random_index] = array[random_index], array[left]
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pivot_index = partition_first(array, left, right)
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if k == pivot_index:
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return array[pivot_index]
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if k < pivot_index:
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right = pivot_index
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else:
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left = pivot_index + 1
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print(quick_select([0], 0) == 0)
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print(quick_select([0, 1, 2, 3, 4], 2) == 2)
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print(quick_select([4, 3, 2, 1, 0], 2) == 2)
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print(quick_select([1, 3, 4, 2, 0], 2) == 2)
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# Large test case, for randomized tests
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lst = list(range(1000))
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for _ in range(10):
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k = random.randint(0, 999)
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random.shuffle(lst)
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print(quick_select(lst, k) == k)
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