动态规划----Triangle

问题描述：

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.

动态规划描述：

设状态为（i，j），表示从位置（i，j）出发，路径的最小和，则状态转移方程为：

源代码

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