LeetCode 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?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

分两种情况讨论，每次只有往下走或者往右走，那么f(m,n)=f(m-1.n)+f(m,n-1).一开始直接使用递归，超时了。应该存在数组里。

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