Triangle --- 至顶向下求最小值

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).

 

典型的球最短路径的问题，需要使用动态规划的思想，从上到下依次求每个点的最小距离 

 

int minimumTotal(vector<vector<int> > &triangle) {
        int nSize = triangle.size();
        if (nSize<1)
            return 0;
        vector<int> sums(nSize);
        vector<int> tmps(nSize);
    
        sums[0] = triangle[0][0];
        for (int  i = 1;  i < nSize;  i++)
        {
            vector<int> vals = triangle[i];
            int nNum = vals.size();
    
             tmps = sums;
            sums[0] = tmps[0] + vals[0];
            for (int j=1; j<i; j++)
            {
                sums[j] = tmps[j-1]>tmps[j]?tmps[j]+vals[j]:tmps[j-1]+vals[j];
            }
    
            sums[i] = tmps[i-1]+vals[i];
        }
    
        int nMin = sums[0];
        for (int i = 1; i < nSize; i++)
        {
            if (sums[i] < nMin)
                nMin = sums[i];
        }
    
        return nMin;
    }