from left-top to right-bottom

public class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        
        int dp[][] = new int[m][n];
        dp[0][0] = grid[0][0];
        for (int i=1; i<m; i++) 
            dp[i][0] = dp[i-1][0] + grid[i][0];
        for (int j=1; j<n; j++)
            dp[0][j] = dp[0][j-1] + grid[0][j];
            
        for (int i=1; i<m; i++) {
            for (int j=1; j<n; j++) {
                dp[i][j] = Math.min(dp[i-1][j], dp[i][j-1]) + grid[i][j];
            }
        }
        return dp[m-1][n-1];
    }
}