leetcode_120. Triangle

题目：

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).
动态规划问题。从下到上，每个数的最短路径都是到下面两个数的最短路径+这个数。即min（minm[i], minm[i+1]）+triangle[row][i];
从下到上，第一层得到的就是到第2层的最短路的最小值加第一层的数。

代码如下：

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