Add Levenshtein.

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Oleksii Trekhleb 2018-04-24 06:41:16 +03:00
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* [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple) * [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple)
* [FisherYates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence * [FisherYates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
* **String** * **String**
* Minimum Edit distance (Levenshtein Distance) * [Levenshtein Distance](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences
* Hamming * Hamming
* Huffman * Huffman
* Knuth Morris Pratt * Knuth Morris Pratt

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# Levenshtein Distance
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.
## Definition
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
![Levenshtein](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0a48ecfc9852c042382fdc33c19e11a16948e85)
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`.
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.
## Example
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:
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).
## References
- [Wikipedia](https://en.wikipedia.org/wiki/Levenshtein_distance)