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.

由题意得，主要是自顶向下找出一条和最小的路径，然后返回最小值。这是一道很典型的动态规划的题目，首先求出状态转移：

f(i,j) = min(f[i+i][j], f[i+1][j+1]) + (i,j)

而且不需要另外的空间，因为自底向上，可以把值都保存在原来的数组里，代码如下。

Code(LeetCode运行6ms):

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];    }};

我女朋友好蠢啊，我不用跳楼了哈哈哈。