Palindrome Partitioning
Given a string $s$, partition $s$ such that every substring of the partition is a palindrome. Return all possible palindrome partitioning schemes. Use Backtracking.
Why Interviewers Ask This
Meta asks Palindrome Partitioning to evaluate a candidate's mastery of recursion and backtracking algorithms. Interviewers specifically test the ability to explore all possible solution paths while pruning invalid branches efficiently. This problem assesses logical decomposition skills, understanding of string manipulation, and the capacity to manage state during complex recursive calls without external libraries.
How to Answer This Question
1. Clarify constraints: Ask about string length limits and character sets to determine if O(N*2^N) is acceptable. 2. Define the core logic: Explain that you will use a recursive function where each call tries every possible substring starting from the current index. 3. Implement palindrome checking: Describe an efficient helper function using two pointers to verify palindromes in linear time relative to substring length. 4. Execute backtracking: Detail how to add valid substrings to a temporary list, recurse for the remainder, and then remove the last element (backtrack) to try other partitions. 5. Optimize: Mention memoization or dynamic programming pre-computation for palindrome checks if the input size suggests repeated subproblems, aligning with Meta's focus on scalable solutions.
Key Points to Cover
- Explicitly stating the use of backtracking to explore all partitions
- Describing an efficient O(K) palindrome check using two pointers
- Demonstrating clear state management during recursion and backtracking steps
- Addressing time complexity analysis relative to input size N
- Mentioning potential optimizations like DP tables for repeated checks
Sample Answer
To solve this, I would first validate the input constraints. If the string length is up to 16, a pure backtracking approach is feasible. My strategy involves a main recursive function that takes the current start index and a path list. Inside this function, I iterate through all possible end indices from the start position. For each substring, I check if it is a palindrome using a two-pointer technique which runs in O(K) time. If it is a palindrome, I append it to my current path and recursively call the function for the remaining suffix. Once the base case is reached where the start index equals the string length, I add the current path to my results list. Crucially, after the recursive call returns, I must pop the last added substring to backtrack and explore other partition possibilities. This ensures we exhaustively find all valid combinations. I would also consider pre-calculating a DP table for palindrome checks to optimize repeated lookups, demonstrating attention to performance optimization which Meta values highly.
Common Mistakes to Avoid
- Failing to backtrack by removing elements from the current path after recursion
- Using inefficient O(K^2) methods to check palindromes instead of two pointers
- Ignoring edge cases like empty strings or single-character inputs
- Not clarifying time complexity assumptions before writing code
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