62. Unique Paths

62. Unique PathsMedium1497104FavoriteShare

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:

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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:

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

Code:

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class Solution(object):
    def uniquePaths(self, m, n):
        if not m or not n:
            return 0
        cur = [1] * n
        for i in range(1, m):
            for j in range(1, n):
                cur[j] += cur[j-1]
        return cur[-1]

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return math.factorial(m+n-2)/(math.factorial(n-1) * math.factorial(m-1))