【LeetCode with Python】 Unique Paths

来源：互联网发布：登陆淘宝open平台 , 编辑：程序博客网时间：2024/05/16 14:14

博客域名：http://www.xnerv.wang
原题页面：https://oj.leetcode.com/problems/unique-paths/
题目类型：排列组合，动态规划
难度评价：★
本文地址：http://blog.csdn.net/nerv3x3/article/details/38928973

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.

用数学中的排列组合来解题，从(m+n)次选择中选出m次向下走。
这道题跟“n阶台阶，每次一步或两步，总共多少种走法”一样，也可以用动态规划解题，不过这里是二维动态规划，而后者是一维动态规划。Unique Paths还比较简单，所以可用排列组合快速解题，但是Unique Paths II这道题，就只能用动态规划了。

class Solution:    # @return an integer    def uniquePaths(self, m, n):        if 0 == m or 0 == n:            return 1        up = 1        for i in range(m + n - 2, n - 1, -1):            up *= i        down = 1        for j in range(1, m):            down *= j        return up / down

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