Number of Ways to Divide a Long Corridor — LeetCode 2147 Python Solution

The problem

Along a long library corridor, there is a line of seats and decorative plants. You are given a 0-indexed string corridor of length n consisting of letters 'S' and 'P' where each 'S' represents a seat and each 'P' represents a plant.

Example

Input

corridor = "SSPPSPS"

Output

3

Explanation

There are 3 different ways to divide the corridor.

Python solution

class Solution:
    def numberOfWays(self, corridor: str) -> int:
        @cache
        def dfs(i: int, k: int) -> int:
            if i >= len(corridor):
                return int(k == 2)
            k += int(corridor[i] == "S")
            if k > 2:
                return 0
            ans = dfs(i + 1, k)
            if k == 2:
                ans = (ans + dfs(i + 1, 0)) % mod
            return ans

        mod = 10**9 + 7
        ans = dfs(0, 0)
        dfs.cache_clear()
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2147. Number of Ways to Divide a Long Corridor is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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