min path sum for number triangle

gistfile1.java

public static int minPath(List<int[]> input){
  int levels = input.size();
  int[][] dp = new int[levels][levels];

  //we start at the bottom
  //here the min path sum is the numbers at the bottom
  dp[levels-1] = input.get(levels-1);

  //now we go up
  for(int l=levels-2; l>=0; l--){
   for(int pos = 0; pos<=l; pos++){
    dp[l][pos] = Math.min(dp[l+1][pos], dp[l+1][pos+1]) + input.get(l)[pos];
   }
  }
  return dp[0][0];
}