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# Levenshtein Distance | ||
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The Levenshtein distance is a string metric for measuring the | ||
difference between two sequences. Informally, the Levenshtein | ||
distance between two words is the minimum number of | ||
single-character edits (insertions, deletions or substitutions) | ||
required to change one word into the other. | ||
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## Definition | ||
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Mathematically, the Levenshtein distance between two strings | ||
`a` and `b` (of length `|a|` and `|b|` respectively) is given by | ||
![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/4cf357d8f2135035207088d2c7b890fb4b64e410) | ||
where | ||
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![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0a48ecfc9852c042382fdc33c19e11a16948e85) | ||
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where | ||
![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/52512ede08444b13838c570ba4a3fc71d54dbce9) | ||
is the indicator function equal to `0` when | ||
![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/231fda9ee578f0328c5ca28088d01928bb0aaaec) | ||
and equal to 1 otherwise, and | ||
![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdc0315678caad28648aafedb6ebafb16bd1655c) | ||
is the distance between the first `i` characters of `a` and the first | ||
`j` characters of `b`. | ||
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Note that the first element in the minimum corresponds to | ||
deletion (from `a` to `b`), the second to insertion and | ||
the third to match or mismatch, depending on whether the | ||
respective symbols are the same. | ||
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## Example | ||
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For example, the Levenshtein distance between `kitten` and | ||
`sitting` is `3`, since the following three edits change one | ||
into the other, and there is no way to do it with fewer than | ||
three edits: | ||
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1. **k**itten → **s**itten (substitution of "s" for "k") | ||
2. sitt**e**n → sitt**i**n (substitution of "i" for "e") | ||
3. sittin → sittin**g** (insertion of "g" at the end). | ||
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## References | ||
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- [Wikipedia](https://en.wikipedia.org/wiki/Levenshtein_distance) |