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.

public class Solution {
    public int minPathSum(int[][] grid) {
        int len1 = grid.length;
        if(len1 == 0) return 0;
        int len2 = grid[0].length;
        if(len2 == 0) return 0;
        
        int f[] = new int[len2];
        for(int i = 0; i<len1; i++){
            f[0] += grid[i][0];
            for(int j = 1; j<len2; j++){
                if(i == 0){
                    f[j] = f[j-1] + grid[0][j];
                }else{
                    f[j] = Math.min(f[j-1], f[j]) + grid[i][j];
                }
            }
        }
        return f[len2-1];
    }
}