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# Javascript Implementation Of Damerau-Levenshtein Distance

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```From Wikipedia: Damerauâ€“Levenshtein distance is a "distance" (string metric) between two strings, i.e., finite sequence of symbols, given by counting the minimum number of operations needed to transform one string into the other, where an operation is defined as an insertion, deletion, or substitution of a single character, or a transposition of two characters.
```
//based on: http://en.wikibooks.org/wiki/Algorithm_implementation/Strings/Levenshtein_distance
//and:  http://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance
function levenshtein( a, b )
{
var i;
var j;
var cost;
var d = new Array();

if ( a.length == 0 )
{
return b.length;
}

if ( b.length == 0 )
{
return a.length;
}

for ( i = 0; i <= a.length; i++ )
{
d[ i ] = new Array();
d[ i ][ 0 ] = i;
}

for ( j = 0; j <= b.length; j++ )
{
d[ 0 ][ j ] = j;
}

for ( i = 1; i <= a.length; i++ )
{
for ( j = 1; j <= b.length; j++ )
{
if ( a.charAt( i - 1 ) == b.charAt( j - 1 ) )
{
cost = 0;
}
else
{
cost = 1;
}

d[ i ][ j ] = Math.min( d[ i - 1 ][ j ] + 1, d[ i ][ j - 1 ] + 1, d[ i - 1 ][ j - 1 ] + cost );

if(
i > 1 &&
j > 1 &&
a.charAt(i - 1) == b.charAt(j-2) &&
a.charAt(i-2) == b.charAt(j-1)
){
d[i][j] = Math.min(
d[i][j],
d[i - 2][j - 2] + cost
)

}
}
}

return d[ a.length ][ b.length ];
}

``````
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