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).

思路：经典的动态规划题目。自底向上遍历给定的数组，依次算出每点到底部的最短路径，当遍历到第一层时即得到结果。

代码：

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

Triangle