Leetcode 63 Unique Paths

Leetcode 63 Unique Paths"/>

Leetcode 63 Unique Paths

Leetcode 63 Unique Paths

题目描述

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 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

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思路解析

题目要求统计到达终点的不同路径数。

易知若达到终点处，所走步数为 m + n − 2 m+n-2 m+n−2，若要保证到达终点数，则需保证只向下走 m − 1 m-1 m−1或只向右走 n − 1 n-1 n−1，得到不同路径数为 C m + n − 2 m − 1 C_{m+n-2}^{m-1} Cm+n−2m−1​，代码如下：

from math import factorial
class Solution:def uniquePaths(self, m: int, n: int) -> int:return int(factorial(m+n-2) / (factorial(m-1) * factorial(n-1)))

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