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Levenshtein distance between two given strings implemented in JavaScript and usable as a Node.js module

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levenshtein.js
JavaScript
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/*
Copyright (c) 2011 Andrei Mackenzie
 
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
 
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
 
// Compute the edit distance between the two given strings
exports.getEditDistance = function(a, b){
if(a.length == 0) return b.length;
if(b.length == 0) return a.length;
 
var matrix = [];
 
// increment along the first column of each row
var i;
for(i = 0; i <= b.length; i++){
matrix[i] = [i];
}
 
// increment each column in the first row
var j;
for(j = 0; j <= a.length; j++){
matrix[0][j] = j;
}
 
// Fill in the rest of the matrix
for(i = 1; i <= b.length; i++){
for(j = 1; j <= a.length; j++){
if(b.charAt(i-1) == a.charAt(j-1)){
matrix[i][j] = matrix[i-1][j-1];
} else {
matrix[i][j] = Math.min(matrix[i-1][j-1] + 1, // substitution
Math.min(matrix[i][j-1] + 1, // insertion
matrix[i-1][j] + 1)); // deletion
}
}
}
 
return matrix[b.length][a.length];
};

A faster implementation

function levenshteinDistance (s, t) {
    if (!s.length) return t.length;
    if (!t.length) return s.length;

    return Math.min(
        levenshteinDistance(s.substr(1), t) + 1,
        levenshteinDistance(t.substr(1), s) + 1,
        levenshteinDistance(s.substr(1), t.substr(1)) + (s[0] !== t[0] ? 1 : 0)
    ) + 1;
}

A faster implementation

function levenshteinDistance (s, t) {
    if (!s.length) return t.length;
    if (!t.length) return s.length;

    return Math.min(
        levenshteinDistance(s.substr(1), t) + 1,
        levenshteinDistance(t.substr(1), s) + 1,
        levenshteinDistance(s.substr(1), t.substr(1)) + (s[0] !== t[0] ? 1 : 0)
    ) + 1;
}

@mohsen1

Your implementation is not faster: http://jsperf.com/levenshtein-distance-2

Someone asked me to be explicit about how this code is licensed, so I added an MIT license header.

Thanks for the implementation. Does wonders, exactly what I needed for my NodeJS script.

Sorry if this is dumb question, but what exactly is the use case?

@dotnetCarpenter I've used this as part of a simple suggestion system. It works by calculating edit distances between some input string and all known acceptable inputs. If the edit distance of any is within an acceptable range, the system can offer a suggestion - e.g. input 'JvaaScript' - "Did you mean 'JavaScript'?"

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