How can you count strings formed using a, b, and c under constraints?
This task involves counting valid strings of a given length that adhere to specific rules regarding character usage. It tests dynamic programming and combinatorial logic.
Why Interviewers Ask This
Interviewers use this to test advanced dynamic programming skills and the ability to model complex constraints mathematically. They want to see if you can break down a counting problem into overlapping subproblems. It also checks optimization skills for large input sizes.
How to Answer This Question
Start by defining the state variables needed, such as current length and remaining counts of allowed characters. Explain the recurrence relation that builds the solution from smaller subproblems. Discuss memoization or tabulation to avoid recalculating states. Analyze the space and time complexity relative to the string length and constraints.
Key Points to Cover
- Identify overlapping subproblems in the counting process
- Define appropriate state variables for the DP table
- Establish a clear recurrence relation
- Optimize space if possible using rolling arrays
Sample Answer
I would define a DP state dp[length][count_a][count_b][count_c] representing the number of ways to form a string. However, since constraints might limit total length, I can simplify this to dp[len][last_char]. The transi…
Common Mistakes to Avoid
- Overcomplicating the state definition unnecessarily
- Failing to account for boundary conditions in constraints
- Missing the modulo operation if the answer exceeds integer limits
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