Triangle *****DP

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, where _n _is the total number of rows in the triangle.

• [x] #### adjacent element coordinate, line i, jth element is adjacent to level i+1, jth and (j+1)th element
• [x] #### the number of levels are equal to the total number in the last level
• [x] #### since it has the restriction of choosing the adjacent element in each level, so it means you could not just add up all the minimum numbers in each level
• [x] #### at first the res is [0,0,0,0,0] you use int[] res = new int[triangle.size() + 1] to initialize in case pointer out of boundary

public int minimumTotal(List<List<Integer>> triangle) {
        int[] res = new int[triangle.size() + 1];
        for (int i = triangle.size() - 1; i >= 0; i--) {
            for (int j = 0; j < triangle.get(i).size(); j++) {
                res[j] =    Math.min(res[j], res[j + 1])      + triangle.get(i).get(j);
            }
        }
        return res[0];
}

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).
     i : j
     i + 1 : j, j + 1
     res = [4, 1, 8, 3, 0]
     res = [7, 6, 10]
     res = [9, 10]
     res = [2]
     time : O(n^2)
     space : O(n)