How can you count strings formed under specific character constraints?
This problem involves counting valid strings based on limited occurrences of characters 'a', 'b', and 'c'. It tests dynamic programming skills.
Why Interviewers Ask This
Interviewers use this to gauge a candidate's proficiency in dynamic programming, specifically regarding state transitions and counting problems. It requires breaking down a complex combinatorial problem into smaller subproblems. The ability to define states based on remaining counts of characters and transition between them efficiently is key to solving this.
How to Answer This Question
Begin by defining the state of your DP table, likely involving the remaining lengths for each character. Explain how to form the recurrence relation based on choosing 'a', 'b', or 'c' at each step. Discuss memoization or tabulation to store results of overlapping subproblems. Highlight how to handle boundary conditions where a character count drops below zero. Finally, walk through a small example to illustrate the logic.
Key Points to Cover
- Defining multi-dimensional DP states for character counts
- Formulating the correct recurrence relation
- Handling boundary conditions for character limits
- Optimizing space if possible through state reduction
Sample Answer
I would approach this using dynamic programming with memoization. The state can be defined as dp[i][j][k], representing the number of ways to form a string given i 'a's, j 'b's, and k 'c's remaining. The recurrence relation would be the sum of ways if we pick 'a' (if i>0), plus ways if we pick 'b' (if j>0), plus ways if we pick 'c' (if k>0). The base case is when all counts are zero, returning 1. I would initialize a 3D array or use a hash map for memoization to avoid recalculating states. This reduces the complexity significantly compared to a naive recursive solution.
Common Mistakes to Avoid
- Overlooking the need for memoization leading to exponential time
- Incorrectly defining the base case
- Failing to check if character counts are non-negative before accessing DP states
- Confusing permutations with combinations in the logic
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