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50 lines
1.4 KiB
Python
50 lines
1.4 KiB
Python
"""
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Author : Alexander Pantyukhin
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Date : October 14, 2022
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This is an implementation of the up-bottom approach to find edit distance.
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The implementation was tested on Leetcode: https://leetcode.com/problems/edit-distance/
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Levinstein distance
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Dynamic Programming: up -> down.
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"""
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import functools
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def min_distance_up_bottom(word1: str, word2: str) -> int:
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"""
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>>> min_distance_up_bottom("intention", "execution")
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5
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>>> min_distance_up_bottom("intention", "")
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9
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>>> min_distance_up_bottom("", "")
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0
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>>> min_distance_up_bottom("zooicoarchaeologist", "zoologist")
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10
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"""
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len_word1 = len(word1)
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len_word2 = len(word2)
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@functools.cache
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def min_distance(index1: int, index2: int) -> int:
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# if first word index overflows - delete all from the second word
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if index1 >= len_word1:
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return len_word2 - index2
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# if second word index overflows - delete all from the first word
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if index2 >= len_word2:
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return len_word1 - index1
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diff = int(word1[index1] != word2[index2]) # current letters not identical
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return min(
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1 + min_distance(index1 + 1, index2),
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1 + min_distance(index1, index2 + 1),
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diff + min_distance(index1 + 1, index2 + 1),
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)
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return min_distance(0, 0)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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