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];
}