leetcode-62 - Unique Paths

動機

複習dp

Problem

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:

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

Example 2:

Input: m = 3, n = 2Output: 3Explanation:From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:1. Right -> Down -> Down2. Down -> Down -> Right3. Down -> Right -> Down

Example 3:

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

Example 4:

Input: m = 3, n = 3Output: 6

Constraints:

• 1 <= m, n <= 100
• It's guaranteed that the answer will be less than or equal to 2 * 109.

Sol

只有回到起點才算是合法的路線

class Solution:
    @functools.lru_cache(None)
    def uniquePaths(self, m: int, n: int) -> int:
        if m <= 0 or n <= 0:
            return 0
        elif m == 1 and n == 1:
            return 1
        else:
            return self.uniquePaths(m,n-1) + self.uniquePaths(m-1,n)