How do you count strings formed under specific character constraints?
This problem involves calculating the number of valid strings that can be constructed using a set of characters subject to frequency or adjacency constraints. It tests dynamic programming or combinatorics.
Why Interviewers Ask This
Interviewers use this to test advanced problem-solving skills involving counting principles and state transitions. It reveals whether a candidate can model complex constraints mathematically and implement them using dynamic programming. It also checks their ability to handle large numbers and modulo arithmetic if required.
How to Answer This Question
Start by defining the state variables needed, such as the current length of the string and the last character used. Explain how to transition between states based on allowed characters. Discuss the recurrence relation clearly. If the constraints involve adjacency, mention how to track the previous character in the DP state. Conclude with an analysis of time and space complexity.
Key Points to Cover
- Define DP state based on length and constraints
- Establish clear transition rules between states
- Handle frequency or adjacency restrictions explicitly
- Sum valid end states for the final count
Sample Answer
I would use dynamic programming where dp[i][last_char] represents the number of valid strings of length i ending with last_char. For each position, I iterate through allowed next characters and update the DP table based on transition rules. If there are frequency constraints, I might need additional state variables for remaining counts. The final answer is the sum of all valid states at the target length. This approach ensures we count only valid configurations efficiently.
Common Mistakes to Avoid
- Overlooking state dependencies in the recurrence
- Incorrectly modeling constraint interactions
- Ignoring modulo operations for large counts
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