[LeetCode]题解（python）：062 Unique path

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题目来源

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https://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?

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题意分析

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Input:m、n

Output:the number of unique path

Conditions:输出所有可能的路径

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题目思路

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一看想起了全排列，注意到（m=3,n=7）时，表示要向下2步向右6步，那么全排列可得路径为f（2+6）/（f（2）*f（6）），f为阶乘函数

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AC代码（Python）

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__author__ = 'YE'

class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        def fac(n):
            f = 1
            for i in range(1, n + 1):
                f *= i
            return f

        m -= 1
        n -= 1
        if m == 0 or n == 0:
            return 1
        return fac(m + n) / (fac(m) * fac(n))

print(Solution().uniquePaths(3, 7))