cs-015 — The Change Maker
| Field | Value |
|---|---|
| id | cs-015 |
| difficulty | Intermediate |
| topics | python, state, arithmetic |
| lecture | lecture-04 |
| 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
Compute change in coins (25/10/5/1) for an amount. Emphasise state updates of remaining amount and each coin count, and why order of subtraction matters.
Your deliverable is the computed aggregates for the worked instance, the accumulator update rules, and one test input that breaks a careless initialisation. 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: amount 87 cents
- Output: 25x3, 10x1, 5x0, 1x2
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
- Biggest coin first: subtract as many as fit, then move down; the remaining amount is the only state.
- Every aggregate here is a small machine: state + update rule.
- The initial value is part of the algorithm, not a detail.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which accumulator was hardest to get right, and what test would have caught the mistake?"
Constraints and assumptions
- Difficulty: Intermediate (loops and lists assumed).
- Topics: python, state, arithmetic.
- 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: Implement your pseudocode and verify it against your hand trace.