leetcode------Triangle

标题：	Triangle
通过率：	27.1%
难度：	中等

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.

动态规划题目，自底向上，最小和一定是每行的最小值，那么从下面开始向上合并，公式就是 res[i][j]=res[i+1][j]+res[i+1][j+1]

公式解释从最后一行开始，每次挑选j 和j+1的较小值加上上一行的j 赋值给j，依次类推

public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if(triangle.size()==1)return triangle.get(0).get(0);
        int [] res=new int[triangle.size()];
        for(int i=0;i<triangle.size();i++){
            res[i]=triangle.get(triangle.size()-1).get(i);
        }
        for(int i=triangle.size()-2;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];
    }
}