Solution Explanation: Analyze User Website Visit Pattern

This problem requires finding the most frequent 3-website visit pattern among users, considering the order of visits. The solution uses a hash table to efficiently store and process user visit data, followed by pattern counting and lexicographical sorting to determine the final result.

Approach:

1. Data Organization: The input arrays (username, timestamp, website) are combined and sorted by timestamp. This ensures that visits for each user are in chronological order. A hash map (d in the code examples) is used to store the websites visited by each user, with the user's name as the key and a list of visited websites as the value.

2. Pattern Generation: The code iterates through the user-website data. For each user with at least three website visits, it generates all possible 3-website patterns. This involves nested loops to create all combinations of three websites from the user's visit history. Each generated pattern is a tuple (or string representation) of three websites.

3. Pattern Counting: A counter (cnt) keeps track of the frequency of each unique 3-website pattern across all users. The Counter object (Python) or HashMap (Java, C++, Go) efficiently counts occurrences.

4. Result Selection: After counting all patterns, the code finds the pattern(s) with the maximum count. If multiple patterns have the same maximum count, the lexicographically smallest pattern is selected.

Time Complexity Analysis:

The dominant factor in the time complexity is the generation of all possible 3-website patterns. For each user with m visits, there are O(m^3) possible 3-website patterns. In the worst case (all users have many visits), this could lead to a cubic time complexity. However, the exact complexity depends on the distribution of website visits across users. In practice, the runtime might be considerably less than O(n^3) if the average number of websites visited per user is relatively small.

• Sorting: Sorting the visits for each user by timestamp takes O(m log m) time where 'm' is the number of visits per user.
• Pattern Generation: This is the most expensive part, taking O(m³) time for each user.
• Counting: Counting patterns takes O(p) time, where 'p' is the number of unique patterns.
• Result Selection: This step takes O(p log p) time for sorting (if needed) or linear time for a simple scan.

Space Complexity Analysis:

• Hash Map (d): The space used for storing user-website visit data is proportional to the total number of visits, which is O(n), where n is the length of the input arrays.
• Pattern Counter (cnt): The space needed for counting patterns is proportional to the number of unique 3-website patterns generated. In the worst case, this could be O(n^3) but is likely to be much smaller in typical scenarios.

Code Examples (with detailed explanations inline):

The provided code examples in Python, Java, C++, and Go implement this approach. Each code snippet is well-commented to explain the logic of each step. The variations mainly stem from the different ways that hash maps and counters are handled in these languages.

The key steps (data organization, pattern generation, counting, and result selection) are consistent across all languages, although the syntax and specific data structures used might differ. The choice of a specific language primarily affects the way hash tables and sorting are implemented and the precise syntax of the code.