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81 lines
2.3 KiB
Python
81 lines
2.3 KiB
Python
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"""
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Python implementation of the MSD radix sort algorithm.
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It used the binary representation of the integers to sort
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them.
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https://en.wikipedia.org/wiki/Radix_sort
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"""
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from typing import List
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def msd_radix_sort(list_of_ints: List[int]) -> List[int]:
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"""
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Implementation of the MSD radix sort algorithm. Only works
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with positive integers
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:param list_of_ints: A list of integers
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:return: Returns the sorted list
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>>> msd_radix_sort([40, 12, 1, 100, 4])
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[1, 4, 12, 40, 100]
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>>> msd_radix_sort([])
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[]
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>>> msd_radix_sort([123, 345, 123, 80])
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[80, 123, 123, 345]
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>>> msd_radix_sort([1209, 834598, 1, 540402, 45])
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[1, 45, 1209, 540402, 834598]
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>>> msd_radix_sort([-1, 34, 45])
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Traceback (most recent call last):
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...
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ValueError: All numbers must be positive
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"""
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if not list_of_ints:
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return []
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if min(list_of_ints) < 0:
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raise ValueError("All numbers must be positive")
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most_bits = max(len(bin(x)[2:]) for x in list_of_ints)
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return _msd_radix_sort(list_of_ints, most_bits)
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def _msd_radix_sort(list_of_ints: List[int], bit_position: int) -> List[int]:
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"""
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Sort the given list based on the bit at bit_position. Numbers with a
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0 at that position will be at the start of the list, numbers with a
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1 at the end.
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:param list_of_ints: A list of integers
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:param bit_position: the position of the bit that gets compared
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:return: Returns a partially sorted list
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>>> _msd_radix_sort([45, 2, 32], 1)
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[2, 32, 45]
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>>> _msd_radix_sort([10, 4, 12], 2)
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[4, 12, 10]
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"""
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if bit_position == 0 or len(list_of_ints) in [0, 1]:
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return list_of_ints
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zeros = list()
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ones = list()
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# Split numbers based on bit at bit_position from the right
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for number in list_of_ints:
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if (number >> (bit_position - 1)) & 1:
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# number has a one at bit bit_position
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ones.append(number)
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else:
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# number has a zero at bit bit_position
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zeros.append(number)
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# recursively split both lists further
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zeros = _msd_radix_sort(zeros, bit_position - 1)
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ones = _msd_radix_sort(ones, bit_position - 1)
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# recombine lists
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res = zeros
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res.extend(ones)
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return res
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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