leetcode-Uniqe Paths

题目

https://oj.leetcode.com/problems/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?

思路

每个到达终点的方案需要向右m-1步，向下n-1步，一共m+n-2步；

从组合角度，可以理解为从m+n-2中选择m-1步向右走，剩下n-1步向下走。

代码

1 class Solution:
 2     # @return an integer
 3     def uniquePaths(self, m, n):
 4         return int(self.combination(m+n-2, n-1))
 5     
 6     def combination(self, n, k):
 7         res = 1.0
 8         for i in range(1, k+1):
 9             res = res * (n - k + i) / i
10         return res

参考地址

1. https://oj.leetcode.com/discuss/9110/my-ac-solution-using-formula