Number of Ways to Divide a Long Corridor

Problem Description

Given a string corridor consisting of letters 'S' (seats) and 'P' (plants), determine the number of ways to divide the corridor into non-overlapping sections, where each section has exactly two seats. Return the number of ways modulo 10^9 + 7. If no valid divisions exist, return 0.

Key Insights

• Each section must contain exactly two 'S' characters.
• The number of 'S' characters must be even for any divisions to be possible.
• The sections can be separated by installing dividers at positions between 'S' characters.
• The number of ways to install dividers is determined by the gaps between the pairs of 'S'.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can follow these steps:

1. Count 'S' Characters: Traverse the string to count the number of 'S'. If the count is odd, return 0 immediately.
2. Identify Positions of 'S': Store the indices of all 'S' characters in a list for easier access.
3. Calculate the Number of Ways:
   • Group the 'S' into pairs.
   • For each pair of 'S', calculate the number of ways to place dividers based on the gaps between the pairs.
   • The number of gaps between each pair of 'S' can be used to calculate combinations.
4. Return Result: Use modular arithmetic to return the result.

Code Solutions