Minimum Path Sum

 1 public class Solution {
 2     /**
 3      * @param grid: a list of lists of integers.
 4      * @return: An integer, minimizes the sum of all numbers along its path
 5      */
 6     public int minPathSum(int[][] grid) {
 7         if (grid == null) return 0;
 8         
 9         // initialize the first row
10         int [][] min = new int[grid.length][grid[0].length];
11         
12         min[0][0] = grid[0][0];
13         
14         for (int i = 1; i < grid[0].length; i++) {
15             min[0][i] = min[0][i - 1] + grid[0][i];
16         }
17         
18         for (int i = 1; i < grid.length; i++) {
19             min[i][0] = min[i - 1][0] + grid[i][0];
20         }
21         
22         for (int i = 1; i < grid.length; i++) {
23             for (int j = 1; j < grid[0].length; j++) {
24                 min[i][j] = (int)Math.min(min[i - 1][j], min[i][j - 1]) + grid[i][j];
25             }
26         }
27         
28         return min[grid.length - 1][grid[0].length - 1];
29     }
30 }