64 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.
Solution:

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