LeetCode 62 Unique Paths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

 1 public class Solution{
 2     public int uniquePaths(int m, int n){
 3         if(m < 0 || n < 0 ){
 4             return 0;
 5         }
 6         if(m == 0 || n == 0){
 7             return 1;
 8         }
 9         int[][] matrix = new int[m][n];
10         for(int i = 0 ; i < n; i++){
11              matrix[0][i] = 1; 
12         }
13         for(int j = 0; j < m; j++){
14             matrix[j][0] = 1;
15         }
16 
17         for(int i =1; i < m ; i++){
18             for(int j = 1; j < n; j++){
19                 matrix[i][j] = matrix[i-1][j] + matrix[i][j-1];
20             }
21         }
22         return matrix[m-1][n-1];
23     }
24 }

要到达一个点，就是要从左边或者上边到达，所以，用动态规划存到达每个点的情况。