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.

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

 public class Solution {
     /**
      * @param grid: a list of lists of integers.
      * @return: An integer, minimizes the sum of all numbers along its path
      */
     public int minPathSum(int[][] grid) {
         if (grid == null) return ;

         // initialize the first row
         int [][] min = new int[grid.length][grid[].length];

         min[][] = grid[][];

         for (int i = ; i < grid[].length; i++) {
             min[][i] = min[][i - ] + grid[][i];
         }

         for (int i = ; i < grid.length; i++) {
             min[i][] = min[i - ][] + grid[i][];
         }

         for (int i = ; i < grid.length; i++) {
             for (int j = ; j < grid[].length; j++) {
                 min[i][j] = (int)Math.min(min[i - ][j], min[i][j - ]) + grid[i][j];
             }
         }

         return min[grid.length - ][grid[].length - ];
     }
 }