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* Added Median of Medians Algorithm * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update median_of_medians.py as per requested changes * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
108 lines
2.7 KiB
Python
108 lines
2.7 KiB
Python
"""
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A Python implementation of the Median of Medians algorithm
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to select pivots for quick_select, which is efficient for
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calculating the value that would appear in the index of a
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list if it would be sorted, even if it is not already
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sorted. Search in time complexity O(n) at any rank
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deterministically
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https://en.wikipedia.org/wiki/Median_of_medians
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"""
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def median_of_five(arr: list) -> int:
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"""
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Return the median of the input list
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:param arr: Array to find median of
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:return: median of arr
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>>> median_of_five([2, 4, 5, 7, 899])
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5
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>>> median_of_five([5, 7, 899, 54, 32])
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32
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>>> median_of_five([5, 4, 3, 2])
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4
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>>> median_of_five([3, 5, 7, 10, 2])
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5
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"""
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arr = sorted(arr)
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return arr[len(arr) // 2]
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def median_of_medians(arr: list) -> int:
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"""
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Return a pivot to partition data on by calculating
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Median of medians of input data
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:param arr: The data to be checked (a list)
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:return: median of medians of input array
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>>> median_of_medians([2, 4, 5, 7, 899, 54, 32])
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54
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>>> median_of_medians([5, 7, 899, 54, 32])
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32
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>>> median_of_medians([5, 4, 3, 2])
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4
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>>> median_of_medians([3, 5, 7, 10, 2, 12])
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12
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"""
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if len(arr) <= 5:
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return median_of_five(arr)
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medians = []
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i = 0
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while i < len(arr):
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if (i + 4) <= len(arr):
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medians.append(median_of_five(arr[i:].copy()))
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else:
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medians.append(median_of_five(arr[i : i + 5].copy()))
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i += 5
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return median_of_medians(medians)
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def quick_select(arr: list, target: int) -> int:
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"""
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Two way partition the data into smaller and greater lists,
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in relationship to the pivot
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:param arr: The data to be searched (a list)
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:param target: The rank to be searched
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:return: element at rank target
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>>> quick_select([2, 4, 5, 7, 899, 54, 32], 5)
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32
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>>> quick_select([2, 4, 5, 7, 899, 54, 32], 1)
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2
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>>> quick_select([5, 4, 3, 2], 2)
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3
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>>> quick_select([3, 5, 7, 10, 2, 12], 3)
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5
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"""
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# Invalid Input
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if target > len(arr):
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return -1
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# x is the estimated pivot by median of medians algorithm
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x = median_of_medians(arr)
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left = []
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right = []
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check = False
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for i in range(len(arr)):
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if arr[i] < x:
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left.append(arr[i])
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elif arr[i] > x:
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right.append(arr[i])
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elif arr[i] == x and not check:
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check = True
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else:
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right.append(arr[i])
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rank_x = len(left) + 1
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if rank_x == target:
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answer = x
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elif rank_x > target:
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answer = quick_select(left, target)
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elif rank_x < target:
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answer = quick_select(right, target - rank_x)
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return answer
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print(median_of_five([5, 4, 3, 2]))
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