Problem Description
Given two integers n and k, consider a list of all happy strings of length n sorted in lexicographical order. A happy string is a string that consists only of letters from the set ['a', 'b', 'c'] and does not have consecutive identical characters. Return the k-th string of this list or return an empty string if there are less than k happy strings of length n.
Key Insights
- Happy strings can only contain the characters 'a', 'b', and 'c'.
- Consecutive characters in a happy string must differ.
- The total number of happy strings of length n can be computed based on the previous string's last character.
- The problem can be approached using backtracking to generate happy strings or by systematically counting valid strings.
Space and Time Complexity
Time Complexity: O(3^n) - In the worst case, generating all happy strings could take this time, but we can stop early if we reach k. Space Complexity: O(n) - Space required for the recursion stack and to store the current happy string being generated.
Solution
To solve this problem, we can use a backtracking approach to generate happy strings of length n. We start with an empty string and recursively add characters ('a', 'b', 'c') while ensuring no two consecutive characters are the same. We will keep track of the count of valid strings generated and stop once we reach the k-th string.