Group Shifted Strings

class Solution {
public:
    char modifyChar(char letter, int offset) {
        return (letter - offset + 26) % 26 + 'a';
    }

    string calculateHash(string& s) {
        int offset = s[0];
        string hashKey;

        for (char letter : s) {
            hashKey += modifyChar(letter, offset);
        }

        return hashKey;
    }

    vector<vector<string>> groupStrings(vector<string>& strings) {
        unordered_map<string, vector<string>> hashToGroup;

        for (string str : strings) {
            string hashKey = calculateHash(str);
            hashToGroup[hashKey].push_back(str);
        }

        vector<vector<string>> groups;
        for (auto& mapEntry : hashToGroup) {
            groups.push_back(mapEntry.second);
        }

        return groups;
    }
};

The solution involves grouping strings that can be shifted to become each other. Here’s how the program in C++ achieves this:

The program defines a Solution class that contains methods for processing the strings.

• modifyChar: Adjusts a character's ASCII value using a formula based on an offset to normalize it against the first character of the string.
• calculateHash: Generates a unique hash for each string where all characters in the string are modified relative to the first character, making shifted versions of the same string result in the same hash.
• groupStrings: Arranges strings into groups based on their hashes. It uses an unordered map to associate each unique hash with a list of strings that have that hash.

To implement this:

1. For each string, compute a hash using calculateHash, which involves adjusting each character by shifting it back according to the offset value derived from the string's first character.

2. Insert each string into a hashToGroup map where the key is the hash and the value is a list of strings that share the same normalized pattern.

3. Once all strings have been processed, convert the unordered_map values into a vector of vector of strings, which represents groups of shifted strings.

This approach ensures that strings which can be shifted cyclically will end up in the same group, thus providing an efficient means to classify and group such strings based on their shifting patterns.

class Solution {
    char modifyChar(char ch, int delta) {
        return (char) ((ch - delta + 26) % 26 + 'a');
    }
    
    String createSignature(String input) {
        char[] elements = input.toCharArray();
        
        int shift = elements[0];
        for (int idx = 0; idx < elements.length; idx++) {
            elements[idx] = modifyChar(elements[idx], shift);
        }
        
        String signature = new String(elements);
        return signature;
    }
    
    public List<List<String>> categorizeStrings(String[] inputs) {
        Map<String, List<String>> signatureGroups = new HashMap<>();
        
        for (String item : inputs) {
            String signature = createSignature(item);
            if (!signatureGroups.containsKey(signature)) {
                signatureGroups.put(signature, new ArrayList<>());
            } 
            signatureGroups.get(signature).add(item);
        }
        
        List<List<String>> sortedGroups = new ArrayList<>();
        for (List<String> groupList : signatureGroups.values()) {
            sortedGroups.add(groupList);
        }
        
        return sortedGroups;
    }
}

The provided Java solution categorizes strings that are "shifted" versions of each other into groups. Shifted strings are those where each letter in the string is shifted by the same number of positions in the alphabet. The main components of the solution and how they operate are as follows:

• modifyChar Method:

  • This method adjusts a given character ch by a certain shift value delta.
  • It ensures the character remains a lowercase letter by subtracting delta from ch, adjusting by 26 (the number of letters in the alphabet) to handle negative results, and then normalizing within the 'a' to 'z' range.

• createSignature Method:

  • Takes a string input and generates a normalized form ("signature") where the shift difference between its first character and the rest of the characters is removed.
  • Converts the string to a character array, calculates the needed shift to normalize based on the first character, then uses modifyChar to adjust every character of input accordingly.
  • The resulting array, interpreted as a string, serves as the signature that groups strings together.

• categorizeStrings Method:

  • Takes an array of strings and categorizes them based on their signatures.
  • Utilizes a hashmap (signatureGroups) to group strings that share the same normalized form or signature.
  • For each string in the inputs, it computes the signature and adds the string to the corresponding group in the hashmap.
  • Finally, it collects all groups into a list and returns this list.

This approach efficiently groups shifted strings using the concept of signature-based mapping. Also, the use of a hashmap ensures that checking if a group already exists is done in constant time, making the method efficient even for larger data sets. The overall complexity of the solution largely depends on the number of strings and their maximum length, particularly due to the operations involved in generating signatures.

class Solution:
    def categorizeStrings(self, words: List[str]) -> List[List[str]]:
        
        def normalize_char(char: str, base: int):
            return chr((ord(char) - base) % 26 + ord('a'))
        
        # Define a function to calculate a unique hash for each string pattern
        def calculate_hash(word: str):
            base_shift = ord(word[0])
            return ''.join(normalize_char(ch, base_shift) for ch in word)
        
        # Using dictionary to group words with the same hash
        categorization = collections.defaultdict(list)
        for word in words:
            pattern_hash = calculate_hash(word)
            categorization[pattern_hash].append(word)
        
        # Compile the results into a list of lists
        return list(categorization.values())

This implementation in Python addresses the problem of grouping shifted strings. The solution involves defining a class Solution with a method categorizeStrings that categorizes each word into groups where each group contains words that are "shifted" versions of each other.

Follow these detailed points about the implemented code:

• Normalization Function: A helper function normalize_char computes the normalized version of characters based on their shifts from a base value. This function ensures a character is always shifted within the bounds of the alphabet, using modulo arithmetic.

• Hash Calculation: Another function calculate_hash computes a unique hash for each word. This hash represents the pattern of shifts applied to each character in the word relative to the first character. This effectively groups together words that are shifts of each other.

• Categorization Using Dictionary: The main process involves iterating over a list of words, computing each word's hash, and grouping words by these hashes in a dictionary (categorization). This grouping relies on a default dictionary from the collections module to handle the grouping automatically.

• Compiling Results: Finally, the method compiles and returns the grouped words as a list of lists, ensuring that each subgroup in the list contains words that are shifted versions of each other.

This solution effectively uses hashing and normalization to categorize shifted strings, making efficient use of Python’s data structures like lists and dictionaries. Ensure that the necessary modules (like collections) are imported to avoid runtime errors. Each function is carefully crafted to handle the string manipulation and categorization based on the defined problem constraints and requirements.