To solve this problem, we need to identify the longest subsequence repeated k times in the string. Backtracking search with pruning is a suitable approach for this problem, and pruning helps cut down unnecessary search paths. Efficient handling of subsequences and lexicographical order is crucial to finding the correct solution.
Problem Statement
Given a string s and an integer k, you are tasked with finding the longest subsequence repeated exactly k times in s. A subsequence is derived from the string by removing characters while maintaining the original order of the remaining characters.
The problem requires finding the longest subsequence seq such that seq repeated k times is a valid subsequence of s. Your goal is to identify the lexicographically largest subsequence if there are multiple candidates. Note that the length of the longest subsequence will not exceed n/k.
Examples
Example 1
Input: s = "letsleetcode", k = 2
Output: "let"
There are two longest subsequences repeated 2 times: "let" and "ete". "let" is the lexicographically largest one.
Example 2
Input: s = "bb", k = 2
Output: "b"
The longest subsequence repeated 2 times is "b".
Example 3
Input: s = "ab", k = 2
Output: ""
There is no subsequence repeated 2 times. Empty string is returned.
Constraints
- n == s.length
- 2 <= k <= 2000
- 2 <= n < min(2001, k * 8)
- s consists of lowercase English letters.
Solution Approach
Backtracking Search with Pruning
Start with a backtracking search to explore possible subsequences and attempt to form seq repeated k times. Use pruning to discard invalid or unnecessary paths early in the search process.
Greedy Selection for Lexicographical Order
To handle multiple subsequences of the same length, employ a greedy approach to select the lexicographically largest subsequence among the valid options.
Efficient Pruning Strategy
As the subsequence is built, prune paths that cannot possibly lead to a valid sequence repeated k times. This reduces the search space and improves efficiency.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n \cdot {\lfloor \dfrac{n}{k} \rfloor}!) |
| Space | O(\lfloor \dfrac{n}{k} \rfloor!) |
The time complexity is O(n · ⌊n/k⌋!), where n is the length of the string, and ⌊n/k⌋ is the upper limit on the length of the subsequence. The space complexity is O(⌊n/k⌋!), driven by the recursive depth and subsequence storage.
What Interviewers Usually Probe
- Can the candidate identify the importance of pruning in reducing the search space?
- Does the candidate understand the relationship between subsequence length and k?
- How well does the candidate handle lexicographical ordering in the subsequence selection?
Common Pitfalls or Variants
Common pitfalls
- Failing to prune search paths that cannot possibly yield valid subsequences.
- Overlooking the lexicographical order requirement when multiple valid subsequences exist.
- Incorrectly assuming the subsequence length can exceed n/k.
Follow-up variants
- Modify the problem to find subsequences repeated m times for a different integer m.
- Change the problem to find the shortest subsequence repeated k times.
- Consider the case where the subsequence must be contiguous instead of a general subsequence.
How GhostInterview Helps
- GhostInterview assists by offering detailed explanations of backtracking with pruning for subsequence problems.
- It provides examples and step-by-step strategies for handling lexicographical order in subsequences.
- GhostInterview aids in understanding how to handle pruning effectively, making your solution more efficient.
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 is the primary pattern to solve the Longest Subsequence Repeated k Times problem?
The primary pattern is backtracking search with pruning, which explores subsequences efficiently while eliminating unnecessary paths.
How does pruning help in the Longest Subsequence Repeated k Times problem?
Pruning reduces the search space by discarding subsequences that cannot possibly form a valid sequence repeated k times, improving efficiency.
What is the time complexity of the Longest Subsequence Repeated k Times problem?
The time complexity is O(n · ⌊n/k⌋!), where n is the length of the string and ⌊n/k⌋ is the upper bound on subsequence length.
How do you handle lexicographical order in this problem?
Use a greedy strategy to select the lexicographically largest subsequence when multiple subsequences of the same length are possible.
What does it mean for a subsequence to be repeated k times?
A subsequence is repeated k times if concatenating the subsequence k times results in a valid subsequence of the string s.
Need direct help with Longest Subsequence Repeated k Times instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Longest Subsequence Repeated k Times 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
Find the smallest numerically balanced number greater than a given integer using backtracking search and pruning.
Open problem page#2131 Longest Palindrome by Concatenating Two Letter WordsFind the maximum-length palindrome by combining two-letter words using array scanning and hash table lookups efficiently.
Open problem page#1849 Splitting a String Into Descending Consecutive ValuesCheck if a string of digits can be split into descending consecutive values where the difference between them is 1.
Open problem page