120. Triangle

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.
采用动态规划的思想：
采用由下到上的思想（这样最后只需要取出dp[0][0]就是答案），本层每个结点的结果根据下面一行的路基累计和而计算，要么取左边的，要么取右边的，两者取最小的即可。

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

        return triangle[0][0];
    }