LeetCode 62. Unique Paths

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题目

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?

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

Constraints:

  • 1 <= m, n <= 100
  • It’s guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

思路

Math/DP.

代码

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class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if not m or not n:
            return 0
        return math.factorial(m+n-2)/(math.factorial(n-1) * math.factorial(m-1))

    
# class Solution(object):
#     def uniquePaths(self, m, n):
#         """
#         :type m: int
#         :type n: int
#         :rtype: int
#         """
#         dp = [[0] * n for _ in range(m)]
#         for i in range(m):
#             dp[i][0] = 1
#         for i in range(n):
#             dp[0][i] = 1
#         for i in range(1, m):
#             for j in range(1, n):
#                 dp[i][j] = dp[i][j - 1] + dp[i - 1][j]
#         return dp[m - 1][n - 1]