Spatial algorithms and design

What is an algorithm in a spatial problem?

Explain what decomposition means when solving a large design problem.

Why should an algorithm be tested on a normal case and a boundary case?

Route A has weights 4, 7 and 3. Route B has weights 6, 5 and 2. Which route has the lower total weight?

What does it mean to refine a solution after testing?

A scale model uses 1 cm to represent 50 cm. How long should a model wall be for a real wall of 4 m?

Why can the shortest route be unsuitable if the problem requires coverage of all required locations?

Write a simple pseudocode instruction that would draw a square using repeated turns.

Give one limitation of a digital spatial model that looks correct on screen.

What information should be included when justifying that one spatial solution is better than another?

A delivery network has route options A-B-D with weights 5 and 6, A-C-D with weights 4 and 8, and A-E-D with weights 7 and 3. Compare the routes and choose the best route if lower weight means shorter time.

Design an algorithm for making a 1:25 scale model of a rectangular room that is 5 m by 3 m. Include conversion steps, a test case and one possible refinement if the model does not fit on the page.

A tessellation puzzle piece is repeated by translation. Explain an algorithm for testing whether the design leaves gaps or overlaps, and state how you would refine the piece if the test fails.

A shopping-centre layout has congestion near the entrance, checkouts and a narrow aisle. Decompose the problem into subproblems and describe one measurable constraint for each part.

Pseudocode says repeat 3 times: draw a segment, turn 120 degrees. Predict the shape produced, then explain how you would test whether the path closes.

A robot must place circular sensors of radius 1 m inside a rectangular strip from x = 0 to x = 10. Explain why centre positions must satisfy 1 ≤ x ≤ 9 and identify a boundary case to test.

A route algorithm finds the lowest total distance but misses one compulsory checkpoint. Explain the flaw and rewrite the decision rule so it accounts for both coverage and distance.

A local map combines roads, walking tracks, slopes and flood-prone areas. Explain which layers are useful for planning an emergency walking route and how the final route should be justified.

A design works for a small test grid but fails on a larger grid because two paths cross. Explain why testing only one case was not enough and describe two better tests.

Create a practical spatial algorithm problem involving routing, layout, scale modelling or pattern generation. Define the inputs, write the steps, test one case and refine the solution if needed.