To solve the problem, we need to find the maximum number of non-overlapping palindromic substrings of a given string with length at least k. A dynamic programming approach works well, and leveraging two pointers helps to efficiently check for palindromes and maintain state transitions.
Problem Statement
You are given a string s and a positive integer k. Your task is to find the maximum number of non-overlapping palindromic substrings that have a length of at least k.
A palindrome is a string that reads the same forwards and backwards. The substrings you select must be palindromic, and they cannot overlap with each other. Return the maximum number of such substrings in an optimal selection.
Examples
Example 1
Input: s = "abaccdbbd", k = 3
Output: 2
We can select the substrings underlined in s = "abaccdbbd". Both "aba" and "dbbd" are palindromes and have a length of at least k = 3. It can be shown that we cannot find a selection with more than two valid substrings.
Example 2
Input: s = "adbcda", k = 2
Output: 0
There is no palindrome substring of length at least 2 in the string.
Constraints
- 1 <= k <= s.length <= 2000
- s consists of lowercase English letters.
Solution Approach
Identify Palindromic Substrings
Start by identifying all possible palindromic substrings of length at least k. Use dynamic programming to check each substring and store results to avoid recomputation.
Use Two Pointers to Ensure Non-overlap
Once palindromic substrings are identified, employ a two-pointer technique to select non-overlapping substrings. As you select one, adjust the pointers to avoid overlap with previously selected substrings.
Optimize with Dynamic Programming
Optimize the solution using dynamic programming to track the maximum number of valid substrings, ensuring that the selections respect the condition of non-overlap and the length constraint.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time and space complexity depend on the dynamic programming approach used to identify palindromes and the efficiency of the two-pointer technique. Expect a time complexity of O(n^2) for palindrome identification, with additional complexity for dynamic programming and state transitions.
What Interviewers Usually Probe
- Candidate efficiently applies dynamic programming to solve the problem.
- Demonstrates understanding of state transitions and two-pointer technique.
- Can identify and optimize the problem by carefully considering substring overlap.
Common Pitfalls or Variants
Common pitfalls
- Failing to efficiently check for palindromes, leading to a slow solution.
- Not ensuring non-overlapping substrings, causing incorrect selections.
- Overcomplicating the dynamic programming approach without considering time complexity.
Follow-up variants
- Modify the problem by requiring palindromic substrings to be of an exact length, not just at least k.
- Limit the total number of palindromic substrings to a fixed number.
- Extend the problem to handle uppercase letters or non-ASCII characters.
How GhostInterview Helps
- GhostInterview helps by providing a structured dynamic programming approach tailored to finding palindromic substrings efficiently.
- It guides you through common pitfalls like overlapping selections and inefficient palindrome checking.
- GhostInterview optimizes your approach by encouraging the use of state transitions and careful optimization with two pointers.
Topic Pages
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- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How do I approach the Maximum Number of Non-overlapping Palindrome Substrings problem?
Start by identifying all possible palindromic substrings of length at least k, then use dynamic programming and a two-pointer technique to select non-overlapping substrings.
What is the time complexity for this problem?
The time complexity is typically O(n^2) due to palindrome checks and dynamic programming state transitions, though optimizations can be applied.
Can this problem be solved without dynamic programming?
Dynamic programming is highly effective for this problem, but alternative methods may exist, though they may be less efficient.
What should I consider to avoid overlapping palindromic substrings?
Use a two-pointer approach to track the positions of selected substrings and ensure they do not overlap.
How can I optimize the dynamic programming solution for this problem?
Focus on minimizing recomputation by storing previously computed results for palindromic substrings and maintaining state transitions for efficient selection.
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