Start by exploring all possible subsequences of the input array while tracking used characters with a bitmask. At each step, decide whether to include a string based on character overlap, pruning paths that create duplicates. The maximum length across all valid concatenations is returned efficiently using this approach, avoiding unnecessary computations.
Problem Statement
Given an array of strings arr, generate a string s by concatenating a subsequence of arr such that s contains only unique characters. Your task is to find the maximum possible length of s. Each string in arr consists of lowercase English letters, and a valid subsequence may skip elements without changing their order.
Return an integer representing the maximum length of a string formed by concatenating elements from any subsequence of arr with all distinct characters. Consider that some strings in arr may contain overlapping characters, so careful selection and pruning of subsequences is required to avoid duplicates.
Examples
Example 1
Input: arr = ["un","iq","ue"]
Output: 4
All the valid concatenations are:
- ""
- "un"
- "iq"
- "ue"
- "uniq" ("un" + "iq")
- "ique" ("iq" + "ue") Maximum length is 4.
Example 2
Input: arr = ["cha","r","act","ers"]
Output: 6
Possible longest valid concatenations are "chaers" ("cha" + "ers") and "acters" ("act" + "ers").
Example 3
Input: arr = ["abcdefghijklmnopqrstuvwxyz"]
Output: 26
The only string in arr has all 26 characters.
Constraints
- 1 <= arr.length <= 16
- 1 <= arr[i].length <= 26
- arr[i] contains only lowercase English letters.
Solution Approach
Backtracking with Bitmask
Use a backtracking search to explore all possible subsequences. Track used characters with a 26-bit integer mask. If adding a string would cause a duplicate, skip that branch, pruning unnecessary paths.
Pruning Invalid Combinations Early
Before concatenating a string, check if it contains duplicate characters or overlaps with the current mask. This reduces the number of recursive calls and ensures only valid unique-character strings are considered.
Compute Maximum Length Efficiently
During recursion, keep updating the maximum length encountered so far. At the end, return the largest length found. This approach leverages both backtracking and pruning to handle the exponential search space effectively.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(2^n * m) where n is arr.length and m is the average string length, due to exploring all subsequences with bitmask checks. Space complexity is O(n) for recursion stack, plus O(1) for bitmask storage.
What Interviewers Usually Probe
- Does the candidate consider character uniqueness across combined strings?
- Does the solution prune paths where duplicates would occur instead of exploring blindly?
- Are bitmask techniques or efficient character tracking applied for faster checks?
Common Pitfalls or Variants
Common pitfalls
- Not checking for duplicate characters inside individual strings before combining.
- Failing to prune subsequences early, leading to timeouts on larger arrays.
- Using string concatenation repeatedly instead of a bitmask or set, increasing runtime unnecessarily.
Follow-up variants
- Find the maximum length where characters can repeat at most k times.
- Return all possible concatenated strings with maximum length and unique characters.
- Solve the problem when strings contain uppercase letters and digits as well.
How GhostInterview Helps
- Automatically applies backtracking with pruning to find the maximum length efficiently.
- Tracks character usage via bitmask internally, reducing manual error in overlaps.
- Highlights which subsequences fail due to duplicate characters to refine your strategy.
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 main pattern used in Maximum Length of a Concatenated String with Unique Characters?
The core pattern is backtracking search with pruning, checking character uniqueness via a bitmask.
Can I use sets instead of bitmasks?
Yes, sets work for tracking used characters, but bitmasks are faster and use less memory.
How does pruning help in this problem?
Pruning stops recursion early when a string would introduce duplicate characters, saving exponential computations.
What is the maximum array length constraint?
The input array length is between 1 and 16, which allows backtracking without exceeding reasonable computation time.
Do I need to check for duplicates inside a single string?
Yes, strings with repeated characters cannot contribute to a valid unique-character concatenation.
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