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.

分析

找出一个三角形从顶到底最短路径。很简单的动态规划问题，从上到下，依次计算到当前行左边路线和右边路线哪个是最短距离。不过需要两端的点只有一条路，需要另处理。
当然也可以从下到上，更方面了。

int minimumTotal(int** triangle, int triangleRowSize, int *triangleColSizes) {
    int ans=0;
    for(int i=1;i<triangleRowSize;i++)
    {
        triangle[i][0]=triangle[i-1][0]+triangle[i][0];
        for(int j=1;j<triangleColSizes[i]-1;j++)
        {
            int left=triangle[i-1][j-1]+triangle[i][j];
            int right=triangle[i-1][j]+triangle[i][j];
            if(left<right)
                triangle[i][j]=left;
            else
                triangle[i][j]=right;
        }
        triangle[i][ triangleColSizes[i]-1 ]=triangle[i-1][ triangleColSizes[i]-2 ]+triangle[i][ triangleColSizes[i]-1 ];
    }
    ans=triangle[triangleRowSize-1][0];
    for(int j=1;j<triangleColSizes[triangleRowSize-1];j++)
        if(triangle[triangleRowSize-1][j]<ans)
            ans=triangle[triangleRowSize-1][j];
    
    return ans;
}