function levenshtein(a, b) {
  var t = [], u, i, j, m = a.length, n = b.length;
  if (!m) { return n; }
  if (!n) { return m; }
  for (j = 0; j <= n; j++) { t[j] = j; }
  for (i = 1; i <= m; i++) {
    for (u = [i], j = 1; j <= n; j++) {
      u[j] = a[i - 1] === b[j - 1] ? t[j - 1] : Math.min(t[j - 1], t[j], u[j - 1]) + 1;
    } t = u;
  } return u[n];
}

// tests
[ ['', '', 0],
  ['yo', '', 2],
  ['', 'yo', 2],
  ['yo', 'yo', 0],
  ['tier', 'tor', 2],
  ['saturday', 'sunday', 3],
  ['mist', 'dist', 1],
  ['tier', 'tor', 2],
  ['kitten', 'sitting', 3],
  ['stop', 'tops', 2],
  ['rosettacode', 'raisethysword', 8],
  ['mississippi', 'swiss miss', 8]
].forEach(function(v) {
  var a = v[0], b = v[1], t = v[2], d = levenshtein(a, b);
  if (d !== t) {
    console.log('levenstein("' + a + '","' + b + '") was ' + d + ' should be ' + t);
  }
});