Lab 5 — Cycles, Remainders, and Cold Starts (Lecture 05 follow-up)

Machine lab · 2 hours · Work in pairs. You will implement rotation schedules the way lecture 05 modelled them — with remainders, not calendars — and then attack the cold-start questions that break naive cycle code. Submit: a short report answering the checkpoints at the end.

Setup

Python 3 as python; work in lab5/ (see Python setup).
Style: pseudocode first, following the pseudocode style guide.

The task

A five-person support team shares on-call duty: person 1 on day 1, person 2 on day 2, …, person 5 on day 5, person 1 again on day 6.

Part A — Restate before you run (15 min)

A1. In two written lines: what does "day n" mean in remainder language? State what day 0 would be, and why the problem never asks for it. A2. Predict (before any code): who is on call on day 47? On day 100? Write both predictions down — they become your test oracle.

Part B — Implement (30 min)

B1. Write on_call(day, people) that returns the person number for any day ≥ 1. No if-chains over days; use the remainder operation. B2. Verify your Part A predictions by running them. If prediction and program disagree, find which one is wrong and say why in one line. B3. Extend: the team also waters the lab plants every 3rd day counting from day 4 (so days 4, 7, 10, …). Write waters(day) and state the trap your first attempt fell into (the cold start is day 4, not day 1).

Part C — Hostile inputs (30 min)

C1. What does your on_call return for day 0? For day −7? Decide and document: either define the behaviour (with a justification) or reject the input (with an error). "Crashes by accident" is the only wrong answer. C2. A seventh person joins the team on day 30. The rotation becomes 7-person from that day on. Does your function survive with a wrapper? Write on_call_v2(day) that handles the switch, and state the assumption that makes your answer a model rather than the model. C3. Swap hostile-input lists with another pair (three inputs each). Run theirs. Record every disagreement as input / observed / expected / one-line mechanism.

Part D — Trace and generalise (15 min)

D1. Hand-trace on_call for days 1, 2, 3 with people = 5 in a two-column table (day, remainder). Mark where the remainder "wraps". D2. One sentence: in lecture 05's language, what is the cycle length here, and what would change if the schedule skipped weekends?

Checkpoints (submit these as your report)

Your A1 remainder statement and your two A2 predictions.
The B2 comparison: predictions vs program, and who was wrong.
waters(day) with the cold-start trap you hit in B3.
Your C1 decision for day 0 and day −7, with justification.
on_call_v2 from C2 plus its stated assumption.
One row from the C3 exchange table.

What completion looks like

Completion-graded as in Lab 1: full credit for a serious, honest attempt at every checkpoint. A program that passes the two predictions but cannot say why day 100 wraps to person 5 earns less than a wrong program with the right remainder explanation.