cs-125 — The Library Robot
| Field | Value |
|---|---|
| id | cs-125 |
| difficulty | Beginner |
| topics | integration, graphs, greedy |
| lecture | lecture-32 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | none |
| objective | state inputs, outputs, and assumptions, then solve a small instance by hand |
| solution | held by the instructor; discussed after the attempt |
Problem
A robot returns books to shelves minimising total walking, with a battery limit. Route planning meets knapsack-ish choice; full method: model, algorithm, tests.
Your deliverable is the stated assumptions, the rule list, the decision for the worked instance, and one contested case. 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: shelves along a corridor at positions [1, 4, 7, 10]; returns pile [4, 10, 1]; robot starts at 2, battery 12 m
- Output: greedy nearest-shelf route 2->4->7->10->1 = 2+3+3+9 = 17 > 12 battery -> infeasible; better order 2->1->4->7->10 = 1+3+3+3 = 10 <= 12
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
- Model: positions as a line, returns as a delivery list. Greedy nearest is the obvious policy - TEST it against the battery before trusting it.
- 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: Beginner (no prior experience assumed).
- Topics: integration, graphs, greedy.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes for a first attempt; partial answers with clear reasoning are worth more than silent struggling.
- 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: Write the one-page post-mortem: what the plan missed and what transfers.