Leetcode: Triangle

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:

Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

Dynamic programming: solve this problem from bottom up. 

public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle == null || triangle.size() == 0) {
            return Integer.MAX_VALUE;
        }
        
        int n = triangle.size();
        int[][] sum = new int[n][n];
        for (int i = 0; i < n; i++) {
            sum[n - 1][i] = triangle.get(n - 1).get(i);
        }
        
        for (int i = n - 2; i >= 0; i--) {
            for (int j = 0; j <= i; j++) {
                sum[i][j] = triangle.get(i).get(j) + Math.min(sum[i + 1][j], sum[i + 1][j + 1]);
            }
        }
        
        return sum[0][0];
    }
}