cs-099 — The Churn Story
| Field | Value |
|---|---|
| id | cs-099 |
| difficulty | Intermediate |
| topics | data, rates |
| lecture | lecture-25 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | loops, lists, and tracing from lectures 1-6 |
| objective | choose the technique, trace it faithfully, and defend the boundary behaviour |
| solution | held by the instructor; discussed after the attempt |
Problem
Monthly subscriber counts in and out. Define churn rate precisely (what's the base?), compute, and explain a month that 'looks bad but isn't'.
Your deliverable is the stated assumptions, churn defined precisely (base, window, unit), and one wording choice that changes the reported number. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: jan: 1000 start, 50 join, 40 leave, end 1010; feb: 1010 start, 60 leave
- Output: jan churn 40/1000 = 4.0% (base = starting subscribers); feb 60/1010 ~ 5.9% - define the base first
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- 'Churn' is meaningless until you name the denominator: start-of-month, average, or end - each gives a different rate.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Propose one extra rule that would change the verdict — is it an improvement?"
Constraints and assumptions
- Difficulty: Intermediate (loops and lists assumed).
- Topics: data, rates.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes for the plan and trace; finishing the details is a bonus, defending the method is the target.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Find the aggregation that answers a different stakeholder's question.