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Problem of the week

Computational thinking is a habit, not a reading list — so it's practised on one real problem a week, broken down on paper. The subject can be anything (packing a trip, planning a cook, sorting the bookshelf); the skill is decomposition, pattern-spotting, and naming the classic algorithm hiding inside.

This week — worked example: packing for a weekend trip

1. Decompose — the goal ("everything needed, bag not overweight") splits into: list items, weigh/size them, rank by need, fit under the limit.
2. Spot the pattern — "maximise value under a weight limit" is the knapsack problem. Naming it means a hundred years of thinking is available.
3. Pick the strategy — full optimisation is overkill; a greedy rule ("most-needed per kilo first") is good enough, and knowing why it's good enough is the lesson.
4. Check — did the greedy rule miss anything a smarter method would catch? (Sometimes yes — that gap is the interesting part.)

Classic algorithms — met one at a time

Tick when it can be explained back and re-derived cold a week later.

• Binary search — the "guess the number" strategy, formalised
• Sorting — why some ways are fundamentally faster
• Graphs — shortest path (Maps does this every day)
• Hashing — how a name finds its data instantly

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