javascript: calculation Levenshtein distance using dynamic programming

levenshtein-distance.js

function minimum(a,b,c) {
	var min = a;

	if (b<min) {
		min = b;
	}

	if (c<min) {
		min = c;
	}

	return min;
}

function levenshtein_distance(string1, string2) {
	length1 = string1.length;
	length2 = string2.length;

	if (length1 == 0) {
		return length2;
	}
	if (length2 == 0) {
		return length1;
	}

	var d = [];
	for(var i=0; i<=length1; i++) {
		d[i] = [];
	}

	for(var i=0; i<=length1; i++) {
		d[i][0] = i;
	}
	for(var j=0; j<=length2; j++) {
		d[0][j] = j;
	}

	for(var i=1; i<=length1; i++) {
		s_i = string1.charAt(i-1);
		for(var j=1; j<=length2; j++) {
			t_j = string2.charAt(j-1);
			if (s_i == t_j) {
				cost = 0;
			}else{
				cost = 1;
			}
			d[i][j] = minimum(d[i-1][j]+1, d[i][j-1]+1, d[i-1][j-1]+cost);
		}
	}

	for(var i=1; i<=length1; i++) {
		dG[i] = [];
		for(var j=1; j<=length2; j++) {
			dG[i][j] = d[i][j];
		}
	}

	return d[length1][length2];
}