Week 1 Tutorial: Check a legal route
Hand-compute the available candidate routes on the ten-node block graph, find the edge that passes through a building, and draw the task state diagram.
24 February 2027
Open Week 1 in the Lab →Try your own change on this week's case.
Two-hour tutorial: preparation, coding and checks
This week’s task#
Model: The ten-node kitchen block; two computed alternatives to #03 and proposed connections near #03/#05. Costs are flight seconds, without battery constraints.
Before you start · 15 minutes#
Read W1 and sketch load → outward → service → return. Predict which proposed segment crosses a building.
Trace the example · 25 minutes#
Inspect a blocked connection. Name both endpoints and the highlighted building, then inspect the legal-route table.
Implement and compare · 55 minutes#
Add the edge times for each available route on paper. Use the published graph to check every directed edge. Reject the blocked proposal; the browser does not edit the canonical graph.
Use Open full Lab for editable inputs, strategy code, exports and the practice pack. The example on this page compares this week’s published cases; your local student runner must call the functions you complete.
Check and explain · 25 minutes#
Write one route-cost table, the task-phase sketch and a geometric counterexample. Check a reverse direction separately.
What to keep: A1: problem definition and legal-edge reasoning. Show the tutor your prediction, experiment and explanation for this week’s participation point; keep the record to develop your assignment.
Optional extension#
Try a geometrically clear proposal that is still absent from the graph. Explain why “clear” does not add a legal edge.
W1 · Check the whole connection.
Two legal endpoints: can the edge still cross a building?
Dinner #03 goes from the kitchen to Home 03. Compare two legal routes with a shortcut through a building.
Select a connection to see exactly where it crosses the block. Legal endpoints do not prove that the line between them is a legal edge.
Computed from this case · 1.07 ms · lab-1.0 · block
A and B reach Home 03. Pink marks the inspected connection.
Two routes and one tempting shortcut
| Connection | Cost | Can we use it? |
|---|---|---|
| Route A | 30 s | Legal route |
| Route B | 84 s | Legal route |
| Shortcut | — | Blocked by Building 2 |
Start at the kitchen. Both legal routes reach Home 03. The shortcut crosses a building even though its endpoints are clear.
Explore the evidence, replay or open full Lab
Open full Lab ↗ for editable inputs, strategy code and saved comparisons.
Locate the proposed edge and the building it crosses. A shorter illegal connection is not a route.
Read the example above
Locate the proposed edge and the building it crosses. A shorter illegal connection is not a route.
Flight time only · No shared charging in this model · Corridor reservations not active
| Inspect | Connection | Geometry check | Building |
|---|---|---|---|
| Meadow / West Lane → Home 03 | Clear geometry; absent from graph | — | |
| Meadow / Garden Lane → Orchard / West Lane | Clear geometry; absent from graph | — | |
| Meadow / Garden Lane → South Block Approach | Clear geometry; absent from graph | — | |
| Orchard / West Lane → Kitchen Lane | Clear geometry; absent from graph | — | |
| Orchard / West Lane → Home 05 | Clear geometry; absent from graph | — | |
| Home 03 → Kitchen Lane | Clear geometry; absent from graph | — | |
| Home 03 → Home 17 | Building intersection | Building 2 | |
| South Block Approach → Home 05 | Clear geometry; absent from graph | — | |
| Kitchen Lane → Home 05 | Clear geometry; absent from graph | — | |
| Kitchen → Meadow / West Lane | Clear geometry; absent from graph | — | |
| Kitchen → Home 03 | Clear geometry; absent from graph | — | |
| Kitchen → Home 05 | Clear geometry; absent from graph | — |
Continue in the Lab →The same case, with every input open to change.
The spec
What you bring to the session. Written so a reader can tell whether it has been met without asking you.
- you can say whether a given object changes the legal edge set, and which edge
- you can name the leg a task description is missing
- your candidate routes have the costs the workbench reports
Teaching team
- Kofi Marchetti — tutor