min path for number triangle

minpath.java

public static int minPathBetter(List<int[]> input){
  int levels = input.size();
  int[] dp = new int[levels];
  //we start at the bottom
  //here the min path sum is the numbers at the bottom
  dp = input.get(levels-1);
  //now we go up
  for(int l=levels-2; l>=0; l--){
   for(int pos = 0; pos<=l; pos++){
    dp[pos] = Math.min(dp[pos], dp[pos+1]) + input.get(l)[pos];
   }
  }
  return dp[0];
}