120. 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.

给定一个三角形，找出从顶到底的最小路径和，每一步可以从上一行移动到下一行相邻的数字 

思路：由底向上依次获取到第i层的最小值。最终顶层节点值就是最小路径和

    public int minimumTotal(List<List<Integer>> triangle) {
        if(triangle.size() == 0) return -1;
        if(triangle.size() == 1) return triangle.get(0).get(0);
        for(int i=triangle.size()-2;i>=0;i--){
            for(int j=0;j<=i;j++){
               int minValue =  Math.min(triangle.get(i+1).get(j),triangle.get(i+1).get(j+1)) + triangle.get(i).get(j);
               triangle.get(i).set(j,minValue);
            }
        }
        return triangle.get(0).get(0);     
    }