// not the fastest

module.exports = 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];
}