To solve Select K Disjoint Special Substrings, focus on using state transition dynamic programming combined with hash tables to track unique substrings. Identify at most 26 potential starting and ending points, then iteratively build valid selections while ensuring no overlap. This approach guarantees correct detection of k disjoint special substrings while maintaining efficient computation.
Problem Statement
Given a string s of length n and an integer k, determine whether it is possible to select exactly k disjoint special substrings. A special substring is defined by its uniqueness according to a given property, and all selected substrings must not overlap in s.
You need to return true if k such disjoint special substrings can be selected and false otherwise. Examples include s = "abcdbaefab", k = 2 returning true, and s = "cdefdc", k = 3 returning false. Constraints: 2 <= n <= 5 * 10^4, 0 <= k <= 26, s consists of lowercase English letters only.
Examples
Example 1
Input: s = "abcdbaefab", k = 2
Output: true
Example 2
Input: s = "cdefdc", k = 3
Output: false
There can be at most 2 disjoint special substrings: "e" and "f" . Since k = 3 , the output is false .
Example 3
Input: s = "abeabe", k = 0
Output: true
Example details omitted.
Constraints
- 2 <= n == s.length <= 5 * 104
- 0 <= k <= 26
- s consists only of lowercase English letters.
Solution Approach
Precompute Potential Substrings
Scan the string to identify first and last occurrences of each letter, giving at most 26 start and end points. Use these to generate candidate special substrings while respecting disjoint requirements.
Dynamic Programming Selection
Use a state transition DP array where dp[i] tracks the maximum number of disjoint special substrings up to index i. Transition by considering adding a new substring if it does not overlap the previous selections.
Validate Against k
Iterate through the DP table to check if it is possible to reach exactly k disjoint special substrings. Return true if dp[n] >= k, otherwise return false. This ensures efficient correctness with O(n) candidate evaluation.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on processing at most 26 start and end points for candidate substrings, giving O(n + 26^2) in practice. Space complexity includes DP array of size n and hash tables for substring checks, O(n + 26).
What Interviewers Usually Probe
- Check if you can precompute all potential start and end points efficiently.
- Clarify that substrings must be completely disjoint and cannot overlap in any index.
- Ask how DP can track the maximum number of valid special substrings up to each index.
Common Pitfalls or Variants
Common pitfalls
- Overcounting substrings that overlap partially or fully.
- Ignoring edge cases when k = 0 or k exceeds possible disjoint substrings.
- Using brute-force substring comparison instead of leveraging start and end points.
Follow-up variants
- Maximize the number of disjoint special substrings instead of checking a fixed k.
- Select disjoint substrings with additional length constraints or patterns.
- Count disjoint substrings with overlapping allowed but limited to a threshold.
How GhostInterview Helps
- Provides step-by-step state transition DP guidance tailored to disjoint substring selection.
- Highlights candidate substring generation with hash tables to avoid overlaps.
- Validates your approach against k efficiently and flags common pitfalls in real time.
Topic Pages
Related GhostInterview Pages
- 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
What defines a special substring in this problem?
A special substring is one that meets the uniqueness property specified, typically tracked via first and last occurrences of letters.
How does state transition dynamic programming apply here?
DP tracks the maximum number of disjoint special substrings up to each index, allowing safe addition of new substrings without overlap.
Can k be zero or exceed possible disjoint substrings?
Yes, k = 0 should return true, and if k exceeds the maximum possible disjoint substrings, the answer is false.
Why are hash tables useful for this problem?
Hash tables help quickly locate first and last occurrences, reducing the search space for candidate substrings.
What is the main failure mode to avoid?
Selecting overlapping substrings or miscounting potential candidates, which leads to incorrect true/false results.
Need direct help with Select K Disjoint Special Substrings instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Select K Disjoint Special Substrings from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
You need to delete characters in a string to reduce its distinct characters to at most k.
Open problem page#3557 Find Maximum Number of Non Intersecting SubstringsDetermine the maximum number of non-overlapping substrings in a word, each at least four characters and matching start-end letters.
Open problem page#3085 Minimum Deletions to Make String K-SpecialMinimize deletions to make a string k-special by adjusting character frequencies.
Open problem page