leetcode------Unique Paths

标题：	Unique Paths
通过率：	32.6%
难度：	中等

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.

第（i,j）步的上一步只可能是从(i-1,j)或者是(i,j-1)来的，那么F(i,j)=F(i-1,j)+F(i,j-1)

一个二维数组现将第一行第一列都填成1，然后从（1，1）到（m-1,n-1）;

代码如下：

 1 public class Solution {

 2     public int uniquePaths(int m, int n) {

 3         int[][]result=new int[m][n];

 4         for(int i=0;i<m;i++){

 5             result[i][0]=1;

 6         }

 7         for(int i=0;i<n;i++){

 8             result[0][i]=1;

 9         }

10         for(int i=1;i<m;i++){

11             for(int j=1;j<n;j++){

12                 result[i][j]=result[i-1][j]+result[i][j-1];

13             }

14         }

15         return result[m-1][n-1];

16     }

17 }