Triangle

题目描述：

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).

解题思路：

逐层计算从头开始到每一层的每一个位置的路径的最小和，然后在最后一层的所有位置的最小路径和中选取最小的即可。

AC代码如下：

class Solution{public:int minimumTotal(vector<vector<int>>& triangle){int n = triangle.size();if (n == 0) return 0;vector<int> ans(n, 0);ans[0] = triangle[0][0];for (int i = 1; i < n; ++i){int tmp1 = ans[0];ans[0] = ans[0] + triangle[i][0];for (int j = 1; j < i; ++j){int tmp2 = ans[j];ans[j] = min(tmp1, tmp2) + triangle[i][j];tmp1 = tmp2;}ans[i] = tmp1 + triangle[i][i];}int minAns = ans[0];for (int i = 1; i < n; ++i) minAns = min(minAns, ans[i]);return minAns;}};