Analyzing Sequential Event Patterns with Advanced Window Functions

This challenge focuses on analyzing sequences of events within a dataset, specifically by calculating the time elapsed between consecutive events of a particular type for each user. This is crucial for understanding user behavior, identifying patterns, and potentially detecting anomalies in event streams.

Problem Description

You are tasked with analyzing a log of user events. For each user, you need to calculate the time difference between their most recent 'purchase' event and their previous 'purchase' event. This will help in understanding the purchase frequency of individual users.

Key Requirements:

1. Identify 'purchase' events: Filter the log to consider only events with the type 'purchase'.
2. Order events chronologically: For each user, events must be processed in the order they occurred.
3. Calculate time difference: For every 'purchase' event (except the very first one for a user), calculate the time elapsed since the immediately preceding 'purchase' event by the same user.
4. Handle first purchase: The first 'purchase' event for a user should have a null or a specific indicator for the time difference, as there is no prior purchase to compare against.

Expected Behavior:

The output should be a table containing:

• The user identifier.
• The timestamp of each 'purchase' event.
• The calculated time difference (in a consistent unit, e.g., seconds) from the previous 'purchase' event for that user.

Edge Cases:

• Users with no 'purchase' events: These users should not appear in the output.
• Users with only one 'purchase' event: The time difference should be null for their single purchase.
• Simultaneous events: If multiple 'purchase' events occur at the exact same timestamp for a user, the ordering within that timestamp might be arbitrary but consistent. The calculation should still aim to find the immediately preceding distinct event.

Examples

Example 1:

Input UserEvents table:

Output:

Explanation:

• For User A, the first purchase is at 10:10:00. The previous purchase doesn't exist, so NULL.
• For User B, the first purchase is at 10:15:00. The previous purchase doesn't exist, so NULL.
• User A's second purchase is at 10:30:00. The previous purchase was at 10:10:00. The difference is 20 minutes = 1200 seconds.
• User A's third purchase is at 10:45:00. The previous purchase was at 10:30:00. The difference is 15 minutes = 900 seconds.

Example 2: User with only one purchase

Input UserEvents table:

Output:

Explanation: User C has only one purchase, so the time since the previous purchase is NULL.

Example 3: Multiple purchases on the same day

Input UserEvents table:

Output:

Explanation: The first purchase at 08:00:00 has a NULL difference. The second purchase at 08:00:00 has a difference of 0 seconds from the previous one (assuming a stable order for simultaneous events). The third purchase at 08:15:00 has a difference of 900 seconds from the preceding 08:00:00 purchase.

Constraints

• The UserEvents table can contain up to 1,000,000 rows.
• UserID is a string, EventType is a string, and EventTimestamp is a datetime or timestamp data type.
• The solution should aim for a time complexity that scales reasonably with the number of rows, preferably avoiding O(n^2) operations.

Notes

• You will need to use a window function that allows you to access a previous row within a partition (defined by UserID).
• Consider how to partition your data and define the ordering within each partition.
• The "frame" of the window function will be crucial for defining which preceding row to look at.
• Think about the data types for time differences and how to handle the units of time.
• Your SQL dialect might have specific functions for timestamp differences (e.g., TIMESTAMPDIFF, DATEDIFF, or subtraction operators). Assume a way to calculate the difference in seconds.