[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.

方法数就是求组合数，在（m-n-2）步中找出（m-1）步竖着走就可以了。写计算组合数写了好久，要用long来存储才不会溢出，同时注意从后面往前乘就不会出现精度问题。

    public int uniquePaths(int m, int n) {
        if(m == 1 || n == 1) return 1;
        long i = n, j = 1, res = 1;
        while(j <= m-1) {
            res = res * i / j;
            i++; j++;
        }
        return (int)res;
    }