Most Frequent User Website Visit Pattern

This challenge asks you to analyze user website visit data to identify the most frequently occurring three-page visit sequence. This is a common task in web analytics, helping businesses understand user navigation patterns and optimize website design or marketing strategies.

Problem Description

You are given a dataset of user website visits. Each record in the dataset contains a user's ID, the website they visited, and a timestamp for that visit. Your task is to find the sequence of three distinct websites that a single user visited most frequently.

• Input: A list of visit records. Each record has the following structure: (user_id, website, timestamp).
• Output: A list of three website names, sorted alphabetically, representing the most frequent three-page visit sequence. If there are multiple sequences with the same highest frequency, return the one that comes first lexicographically (alphabetically).
• Key Requirements:
  • A "visit sequence" refers to three distinct websites visited by the same user in chronological order.
  • The timestamps are crucial for determining the order of visits for a given user.
  • You need to count the occurrences of each unique three-page sequence across all users.
  • The output sequence must be sorted alphabetically.
• Edge Cases:
  • A user might visit the same website multiple times; only distinct website visits within a sequence of three count towards a unique three-page sequence.
  • A user might have fewer than three distinct website visits; these users will not contribute to any three-page sequences.
  • If no user visits at least three distinct websites, or if there are no valid three-page sequences, the behavior for the output should be defined (e.g., return an empty list or a specific indicator). For this challenge, assume there will always be at least one valid three-page sequence.

Examples

Example 1:

Input:
[
  ("user1", "home", 10),
  ("user2", "about", 11),
  ("user1", "products", 12),
  ("user1", "home", 13),
  ("user2", "contact", 14),
  ("user1", "products", 15),
  ("user1", "about", 16),
  ("user2", "home", 17),
  ("user2", "about", 18),
  ("user2", "contact", 19),
  ("user1", "home", 20),
  ("user1", "about", 21),
  ("user1", "products", 22),
  ("user1", "services", 23)
]

Output:
["about", "home", "products"]

Explanation:
Let's analyze the visits for each user:

User1:
Visits in chronological order of distinct websites:
- (home, 10)
- (products, 12)
- (about, 16)
- (services, 23)
Distinct website sequences of length 3:
- ("home", "products", "about") - occurs twice (based on timestamps 10, 12, 16 and 10, 15, 16)
- ("home", "products", "services") - occurs once (based on timestamps 10, 12, 23)
- ("home", "about", "services") - occurs once (based on timestamps 10, 16, 23)
- ("products", "about", "services") - occurs once (based on timestamps 12, 16, 23)

User2:
Visits in chronological order of distinct websites:
- (about, 11)
- (contact, 14)
- (home, 17)
Distinct website sequences of length 3:
- ("about", "contact", "home") - occurs once (based on timestamps 11, 14, 17)

Overall frequencies:
- ("home", "products", "about"): 2 times
- ("about", "contact", "home"): 1 time
- ("home", "products", "services"): 1 time
- ("home", "about", "services"): 1 time
- ("products", "about", "services"): 1 time

The most frequent sequence is ("home", "products", "about"). Sorted alphabetically, this is ["about", "home", "products"].

Example 2:

Input:
[
  ("user1", "a", 1),
  ("user1", "b", 2),
  ("user1", "c", 3),
  ("user1", "d", 4),
  ("user2", "a", 5),
  ("user2", "b", 6),
  ("user2", "c", 7),
  ("user2", "d", 8),
  ("user3", "a", 9),
  ("user3", "b", 10),
  ("user3", "c", 11),
  ("user3", "d", 12)
]

Output:
["a", "b", "c"]

Explanation:
User1 visits: a -> b -> c -> d. Sequences: (a, b, c), (a, b, d), (a, c, d), (b, c, d)
User2 visits: a -> b -> c -> d. Sequences: (a, b, c), (a, b, d), (a, c, d), (b, c, d)
User3 visits: a -> b -> c -> d. Sequences: (a, b, c), (a, b, d), (a, c, d), (b, c, d)

All possible 3-page sequences occur 3 times.
Lexicographically, "a", "b", "c" comes before "a", "b", "d", etc.
Therefore, ["a", "b", "c"] is the output.

Constraints

• The number of visits can be between 0 and 10^5.
• The number of unique users can be between 0 and 10^4.
• The number of unique websites can be between 0 and 10^4.
• Website names are strings and consist of lowercase English letters.
• Timestamps are integers.
• Performance: The solution should be efficient enough to handle the given constraints within a reasonable time limit (e.g., a few seconds).

Notes

• The core of this problem involves grouping visits by user, sorting them by timestamp, generating all possible three-page sequences for each user, and then aggregating and counting these sequences.
• Remember to handle duplicate website visits within a user's history carefully when forming sequences. A user visiting "home", "home", "products", "about" should generate sequences based on the distinct website visits in chronological order: "home", "products", "about".
• Pay attention to the sorting requirements for both the input data (by timestamp for each user) and the final output (alphabetical order of websites within the sequence, and lexicographical order of sequences if there's a tie in frequency).
• Consider using data structures that allow for efficient grouping and counting, such as hash maps (dictionaries).