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Maximize unique characters from a word list

MetaMachine Learning Engineer · Onsite
MediumMachine Learning EngineerOnsiteCoding & Algorithms

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This problem tests your ability to use recursion with backtracking or bitmasking to find the optimal subset of strings that maximize the total count of unique characters.

Problem Statement

Given a list of strings words, find the maximum possible total length of a concatenated string formed by a subset of words such that every character in the resulting string is unique. A character is considered unique if it appears at most once across the entire concatenated subset.

Function Signature

def maxLength(words: List[str]) -> int:

Constraints

  • 1 <= words.length <= 16
  • 1 <= words[i].length <= 26
  • Each string in words consists of lowercase English letters.

Examples

Example 1: Input: words = ["un","iq","ue"] Output: 4 Explanation: The longest unique concatenation is "uniq" or "ique" (length 4).

Example 2: Input: words = ["cha","r","act","ers"] Output: 6 Explanation: Possible unique concatenations are "cha" + "ers" = "chaers" (length 6).

Considerations

  • A word itself may contain duplicate characters; if so, it can never be part of a valid subset.
  • Consider how bitmasks can represent the set of characters used in a string to optimize the inclusion check.
  • If a word contains duplicate characters, it is invalid for any subset.

Hints

Hint 1

First, filter out any words that contain duplicate characters themselves, as they can never be part of a valid subset.

Hint 2

Represent the character set of each remaining word as a 26-bit integer (bitmask), where the i-th bit is set if the i-th letter of the alphabet is present.

Hint 3

Use recursion with backtracking to explore all possible subsets of words, keeping track of the current 'used' bitmask and the current total length.

Follow-up questions

  • How would your solution change if you were required to return the actual concatenated string rather than just the maximum length?
  • What is the time complexity of your approach in terms of the number of words N and the average length of each word?
  • Could this problem be solved using dynamic programming instead of backtracking? What would the state representation be?