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Unique Paths

andyaganrun edited this page Jul 9, 2017 · 1 revision

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?

class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        s=m+n-2
        k=n-1
        
        sum=1
        for i in range(1,k+1):
            sum=sum*(s-k+i)/i
        return sum

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