42 lines
1.5 KiB
Python
42 lines
1.5 KiB
Python
# The Levenshtein distance (Edit distance) Problem
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# Informally, the Levenshtein distance between two words is
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# the minimum number of single-character edits (insertions, deletions or substitutions)
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# required to change one word into the other.
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# For example, the Levenshtein distance between kitten and sitting is 3.
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# The minimal edit script that transforms the former into the latter is:
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# kitten —> sitten (substitution of s for k)
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# sitten —> sittin (substitution of i for e)
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# sittin —> sitting (insertion of g at the end)
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def levenshtein_distance(word_1, chars_1, word_2, chars_2):
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# base case if the strings are empty
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if chars_1 == 0:
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return chars_2
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if chars_2 == 0:
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return chars_1
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# if last characters of the string match, the cost of
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# operations is 0, i.e. no changes are made
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if word_1[chars_1 - 1] == word_2[chars_2 - 1]:
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cost = 0
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else:
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cost = 1
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# calculating the numbers of operations recursively
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deletion = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2) + 1
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insertion = levenshtein_distance(word_1, chars_1, word_2, chars_2 - 1) + 1
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substitution = levenshtein_distance(word_1, chars_1 - 1, word_2, chars_2 - 1) + cost
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return min(deletion, insertion, substitution)
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# driving script
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if __name__ == '__main__':
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word_1 = 'plain'
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word_2 = 'plane'
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print('The Levenshtein distance is:')
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print(levenshtein_distance(word_1, len(word_1), word_2, len(word_2)))
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