[LeetCode] [Python] [Math] Unique Paths

题目:

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?

这是一道数学题，也可以用dp来做，但是理解为数学题更容易做，可以看成一道排列组合题目

机器人一定会走m-1次右边和n-1次下边，答案则为C(m+n-2) 上面为m-1

代码如下：

class Solution:
# @return an integer
def uniquePaths(self, m, n):
s = min(m,n) - 1
mn = m + n - 2;
k = 1
for i in range(s) :
k *= mn-i;
for i in range(s) :
k /= i+1;
return k