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) {
        int m = grid.size();
        int n = grid[0].size();
        vector<int> help(n,0);
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(j==0){
                    help[j] += grid[i][j];
                    continue;
                }
                if(i==0){
                    help[j] =help[j-1] + grid[i][j];
                }else{
                    help[j] = min(help[j-1],help[j])+grid[i][j];
                }
            }
        }
        return help[n-1];
    }
};