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

1     public int minimumTotal(List
     
      
       > triangle) { 2         if(triangle.size() == 0) return -1; 3         if(triangle.size() == 1) return triangle.get(0).get(0); 4         for(int i=triangle.size()-2;i>=0;i--){ 5             for(int j=0;j<=i;j++){ 6                int minValue =  Math.min(triangle.get(i+1).get(j),triangle.get(i+1).get(j+1)) + triangle.get(i).get(j); 7                triangle.get(i).set(j,minValue); 8             } 9         }10         return triangle.get(0).get(0);     11     }