Generate Synthetic Clickstream Data with Python Function

Scenario

The analytics team needs to generate synthetic click-stream records to test a new reporting pipeline before real traffic arrives.

Question

Write a Python function simulate_clickstream(num_users: int, days: int) that returns a Pandas DataFrame of simulated events with columns [user_id, event_ts, page, clicked]. Events should be timestamped within the past <days> days, each user should visit 1–10 random pages per day, and click probability is 0.15.

Hints

Use numpy.random for page counts and probabilities; build a list of dicts, then convert to DataFrame.

Deterministic Synthetic Clickstream Event Generator

Implement simulate_clickstream(num_users, days, seed=0) to generate a reproducible list of synthetic click-stream events. Return a list of dicts with keys [user_id, event_ts, page, clicked]. Use these rules: (1) Use BASE=1700000000 (Unix seconds) as a fixed 'now'. For each day d in [0..days-1], day_start = BASE - (d+1)86400. (2) Pages = ["home", "search", "product", "cart", "checkout"]. (3) For each user u in [1..num_users] and each day d, generate k = 1 + ((seed + 31u + 17d) % 10) events. For each event j in [0..k-1]: page_idx = (seed + 37u + 11d + 13j) % 5; offset = (seed + 97u + 101d + 103j) % 86400; clicked = 1 if ((seed + 131u + 137d + 139j) % 100) < 15 else 0; event_ts = day_start + offset. (4) Sort the final list by (event_ts asc, user_id asc, page asc). Return [] if num_users <= 0 or days <= 0.

Constraints

• 0 <= num_users <= 1000
• 0 <= days <= 30
• Each user generates 1..10 events per day
• event_ts is in [BASE - days*86400, BASE)
• Return events sorted by (event_ts, user_id, page)

Examples

Example 1

Input: num_users = 1, days = 1, seed = 0
Output: [{"user_id": 1, "event_ts": 1699913697, "page": "product", "clicked": 0}, {"user_id": 1, "event_ts": 1699913800, "page": "home", "clicked": 0}]

Explanation: For u=1,d=0: k=1+((0+311+170)%10)=2. j=0: page_idx=(0+371+110+130)%5=2=>product, offset=(0+971+1010+1030)%86400=97, clicked=(0+1311+1370+139*0)%100=31<15?0, ts=1699913600+97=1699913697. j=1: page_idx=0=>home, offset=200, clicked=(270%100)=70<15?0, ts=1699913800.

Example 2

Input: num_users = 1, days = 1, seed = 9
Output: [{"user_id": 1, "event_ts": 1699913706, "page": "search", "clicked": 0}]

Explanation: For u=1,d=0: k=1+((9+311+170)%10)=1. j=0: page_idx=(9+371)%5=1=>search, offset=(9+971)%86400=106, clicked=(9+131)%100=40<15?0, ts=1699913600+106=1699913706.

Hints

1. Iterate days then users; compute k events per user per day using the provided modular formulas.
2. Append dicts to a list and sort by (event_ts, user_id, page) before returning.
3. Return an empty list when num_users <= 0 or days <= 0.

Approach

The function deterministically simulates events per user per day using simple modular arithmetic driven by the seed, avoiding external libraries. Each event is assigned a page, an in-day second offset, and a Bernoulli-like click using a <15% threshold on a 0..99 residue. We construct the full list and sort it by (event_ts, user_id, page) to guarantee a stable order.

• Time complexity: O(N) where N is the total number of generated events
• Space complexity: O(N)