Triangle（动态规划）

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 only O(n) extra space, where n is the total number of rows in the triangle.

 

 

　　给定一个数字三角形，找到从顶部到底部的最小路径和。每一步可以移动到下面一行的相邻数字上。

 

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int n=triangle.size();
        vector<int>dp(triangle.back());
        for(int i=n-2;i>=0;i--){
            for(int j=0;j<=i;j++){
                dp[j]=min(dp[j+1],dp[j])+triangle[i][j];
            }
        }
        return dp[0];
    }
};