Biggest Window Between Visits

You are given a list of timestamps representing visits to a website. Your task is to find the largest time gap between consecutive visits from the same user. This is crucial for understanding user engagement patterns and identifying periods of inactivity.

Problem Description

The input is a list of visit records. Each record contains a user ID and a timestamp of their visit. You need to calculate the maximum difference between the timestamps of consecutive visits made by the same user.

Key Requirements:

• Process a list of visit records.
• Group visits by user ID.
• For each user, sort their visits by timestamp.
• Calculate the time difference between consecutive visits for each user.
• Determine the maximum of these differences across all users.

Expected Behavior:

The function should return a single integer representing the largest time difference found. If a user has only one visit, they do not contribute to any window calculation, and thus their visits don't affect the maximum window. If there are no users with more than one visit, the result should be 0.

Edge Cases:

• Empty input list.
• Input list with only one visit record.
• All visits are from different users.
• All visits are from the same user, but chronologically mixed.

Examples

Example 1:

Input: [("userA", 100), ("userB", 110), ("userA", 120), ("userC", 130), ("userA", 150), ("userB", 160)]
Output: 30
Explanation:
UserA visits: 100, 120, 150. Windows: 120-100=20, 150-120=30. Max for UserA is 30.
UserB visits: 110, 160. Window: 160-110=50. Max for UserB is 50.
UserC visits: 130. No windows.
The overall maximum window is max(30, 50) = 50.

Example 2:

Input: [("user1", 5), ("user2", 10), ("user1", 15), ("user3", 20)]
Output: 10
Explanation:
User1 visits: 5, 15. Window: 15-5=10. Max for User1 is 10.
User2 visits: 10. No windows.
User3 visits: 20. No windows.
The overall maximum window is 10.

Example 3: (Edge Case - Single visit per user)

Input: [("userX", 10), ("userY", 20), ("userZ", 30)]
Output: 0
Explanation:
Each user has only one visit, so no time windows can be calculated.

Example 4: (Edge Case - Empty input)

Input: []
Output: 0
Explanation: No visits, so no windows.

Constraints

• The number of visit records will be between 0 and 100,000.
• User IDs will be strings.
• Timestamps will be non-negative integers.
• Timestamps within the input list may not be sorted chronologically.
• The solution should aim for an efficient time complexity, ideally better than O(N^2) where N is the number of visit records.

Notes

• Consider how to efficiently group and sort visits by user.
• A Map or Dictionary data structure can be very helpful here.
• Remember that only users with two or more visits will contribute to the calculation of windows.