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.

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