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.

经典的DP问题。bottom up.通过重用sum数组,使得空间达到O(n).

sum[i][j] = min(sum[i-1][j-1],sum[i-1][j]) + triangle[i][j];

j = 0/ j = i特殊情况。

    int minimumTotal(vector<vector<int> > &triangle) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        if(triangle.empty())
            return 0;
        int rows = triangle.size();
        vector<int> sum(rows);
        sum[0] = triangle[0][0];
        int prev,temp;
        for(int i=1;i<rows;i++)
        {
            prev = sum[0];
            sum[0]+=triangle[i][0];
            for(int j=1;j<i;j++)
            {
               temp = sum[j];
               sum[j] = (prev>temp?(temp+triangle[i][j]):(prev+triangle[i][j]));
               prev = temp;
            }
            sum[i] = prev + triangle[i][i];
        }
        int minSum = sum[0];
        for(int i=1;i<rows;i++)
        {
            if(sum[i]<minSum)
                minSum = sum[i];
        }
        return minSum;
        
    }