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.

解题思路：

15	10	6	3	1
5	4	3	2	1
1	1	1	1	1

public int uniquePaths(int m, int n) {
if(m == 0 && n == 0) return 0;
int arr[][] = new int[m]
;

for(int j = 0; j < n; j ++)
arr[m-1][j]=1;

for(int i = 0; i < m; i ++)
arr[i][n-1]=1;
for(int i = m-2; i >= 0; i --){
for(int j = n-2; j >= 0; j --){
arr[i][j]=arr[i+1][j]+arr[i][j+1];
}
}
return arr[0][0];

}