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 is11(i.e.,2+3+5+1= 11).

Note:
Bonus point if you are able to do this using onlyO(n) extra space, wherenis the total number of rows in the triangle.

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle == null || triangle.size() == 0) return 0;
        int n = triangle.size();
        int[][] dp = new int[n][n];

        dp[0][0] = triangle.get(0).get(0);

        for (int i = 1; i < n; i++){
            for (int j = 0; j < triangle.get(i).size(); j++){
                Integer prev1 = null;
                Integer prev2 = null;
                if (j - 1 >= 0 && j - 1 < triangle.get(i - 1).size()) prev1 = dp[i - 1][j - 1];
                if (j >= 0 && j < triangle.get(i - 1).size()) prev2 = dp[i - 1][j];
                int prev = Integer.MAX_VALUE;
                if (prev1 != null) prev = Math.min(prev, prev1);
                if (prev2 != null) prev = Math.min(prev, prev2);

                dp[i][j] = triangle.get(i).get(j) + prev;

                //System.out.println("i: " + i + " j: " + j + " dp: " + dp[i][j]);
            }
        }

        int ans = Integer.MAX_VALUE;
        for (int j = 0; j < triangle.get(n - 1).size(); j++){
            ans = Math.min(ans, dp[n - 1][j]);
        }

        return ans;
    }
}