Problem Description
You are given an array of strings arr. A string s is formed by the concatenation of a subsequence of arr that has unique characters. Return the maximum possible length of s.
Key Insights
- A subsequence can be formed by deleting some or no elements from the array without changing the order of the remaining elements.
- The goal is to concatenate strings from the subsequence such that all characters in the concatenated string are unique.
- We can use backtracking to explore all possible combinations of strings in
arr. - Bit manipulation can be used to efficiently check for unique characters in the concatenated string.
Space and Time Complexity
Time Complexity: O(2^n * k) where n is the number of strings in arr and k is the average length of the strings. This accounts for all possible subsequences and the time to check for unique characters in each concatenation.
Space Complexity: O(n) for the recursion stack and additional space for maintaining the current string being formed.
Solution
To solve this problem, we will use a backtracking approach combined with bit manipulation. We will iterate through each string in the array and decide whether to include it in the current concatenation. We will maintain a bitmask to track the characters that have already been used. If adding a new string results in duplicate characters, we will backtrack and try the next option.