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.

类似一个滚动数组，做DP

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