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.

动态规划，填格子。空间不是问题。

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        vector<vector<int> >path (triangle);
        for(int i = 1 ; i < triangle.size();i++)
        {
            for(int j = 0 ; j <=i ; j ++)
            {
                if(j <= i-1 && j > 0)  path[i][j] = min(path[i-1][j-1],path[i-1][j])+triangle[i][j];
                else if(j > i-1 && j!=0) path[i][j] = path[i-1][j-1]+triangle[i][j];
                else path[i][j]= path[i-1][j] +triangle[i][j];
            }
        }
        int min = path[triangle.size()-1][0];
        for(int i = 1 ; i < triangle.size();i++)
        {
            if(path[triangle.size()-1][i] < min)min = path[triangle.size()-1][i];
        }
        return min;
    }
};