From 075fe39f5a7e2e1334f6be59bbb7d09319f54ff9 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 24 Apr 2018 06:41:16 +0300
Subject: [PATCH] Add Levenshtein.

---
 README.md                                     |  2 +-
 .../string/levenshtein-distance/README.md     | 45 +++++++++++++++++++
 2 files changed, 46 insertions(+), 1 deletion(-)
 create mode 100644 src/algorithms/string/levenshtein-distance/README.md

diff --git a/README.md b/README.md
index 7f68441e..bcd85d3c 100644
--- a/README.md
+++ b/README.md
@@ -39,7 +39,7 @@
   * [Least Common Multiple (LCM)](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/least-common-multiple)
   * [Fisher–Yates Shuffle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/fisher-yates) - random permutation of a finite sequence
 * **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
   * Huffman
   * Knuth Morris Pratt
diff --git a/src/algorithms/string/levenshtein-distance/README.md b/src/algorithms/string/levenshtein-distance/README.md
new file mode 100644
index 00000000..4085c533
--- /dev/null
+++ b/src/algorithms/string/levenshtein-distance/README.md
@@ -0,0 +1,45 @@
+# 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)