Solution Explanation: Grouping Shifted Strings

The problem asks to group strings that belong to the same "shifting sequence." Strings are considered part of the same sequence if one can be obtained from another by repeatedly shifting each character forward or backward in the alphabet (wrapping around from 'z' to 'a' and vice-versa).

Approach:

The core idea is to create a canonical representation for each string within its shifting sequence. We can achieve this by shifting each character such that the first character of the string becomes 'a'. This normalized representation will be the same for all strings in the same shifting sequence. We can then use a hash table (dictionary in Python) to group strings based on their canonical representations.

Algorithm:

1. Initialization: Create a hash table (dictionary/map) to store the canonical representations as keys and lists of strings as values.

2. Iteration: Iterate through each string in the input list:

   • Calculate the shift amount: Find the difference between the ASCII value of the first character and the ASCII value of 'a'.
   • Shift the characters: Iterate through the characters of the string. For each character, subtract the shift amount from its ASCII value. If the result is less than the ASCII value of 'a', add 26 (to wrap around). Convert the shifted ASCII values back to characters.
   • Store in hash table: Use the shifted string (the canonical representation) as the key in the hash table. Append the original string to the list associated with that key.

3. Result: The values (lists of strings) in the hash table represent the groups of strings belonging to the same shifting sequence. Return these values as the final result.

Time Complexity: O(N * K), where N is the number of strings, and K is the maximum length of a string. This is because we iterate through each string once and perform a character-by-character shift operation for each string.

Space Complexity: O(N * K) in the worst case. The space used is dominated by the hash table, which could potentially store all the strings if each string belongs to a unique shifting sequence.

Code Examples:

The provided code examples demonstrate this approach in different programming languages. Each example follows the same algorithmic structure described above:

• Python: Uses defaultdict for concise hash table handling.
• Java: Uses HashMap and computeIfAbsent for efficient hash table operations.
• C++: Uses unordered_map for the hash table.
• Go: Uses map for the hash table.

The code in each language shows how to:

1. Iterate through the input strings.
2. Calculate the shift amount based on the first character.
3. Shift the characters and handle wrapping around.
4. Store the strings in the hash table based on their canonical representations.
5. Return the list of grouped strings.

The code examples are clear and efficient implementations of the described algorithm, effectively solving the problem of grouping shifted strings.