Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        if(grid.size()==0 || grid[0].size()==0) return 0;
        int min[grid[0].size()];
        min[0]=grid[0][0];
        for(int i=1;i<grid[0].size();i++)
            min[i]=min[i-1]+grid[0][i];
        for(int i=1;i<grid.size();i++)
        {
            min[0]=min[0]+grid[i][0];
            for(int j=1;j<grid[0].size();j++)
            {
                int sum1=min[j]+grid[i][j];
                int sum2=min[j-1]+grid[i][j];
                min[j]=sum1;
                if(sum1>sum2) min[j]=sum2;
            }
        }
        return min[grid[0].size()-1];
    }
};