Map data structures by the problems they solve

Organize around an operation

A map titled “Everything about data structures” can quickly become a wall of names. Start with a concrete task instead: “Which structure fits the way I access this data?” Branch into indexed access, membership lookup, ordered traversal, and first-in-first-out processing.

Place candidate structures under the operation you want to study. Keep a short note about the workload. A mostly read-only collection is a different problem from one that changes constantly.

For a rigorous companion to your own notes, MIT's Introduction to Algorithms course includes lectures, notes, and exercises. This outline is an organizational example, not a replacement for the course's definitions or analysis.

Give every structure the same questions

• Interface: which operations does the caller use?
• Representation: how is the information arranged?
• Cost: which operation is being measured, under which assumptions?
• Example: what happens to a small input, step by step?
• Trade-off: what becomes less convenient when this choice is made?

Be careful with labels such as “fast lookup.” Distinguish worst-case, average-case, and amortized claims wherever your course does. Keep the conditions next to the complexity notation instead of on a distant page.

Trace a queue before writing a large implementation

Start with an empty queue. Enqueue A, enqueue B, dequeue once, then enqueue C. The removed item is A and the remaining logical order is B, C. Put these states in the notes under “Queue behavior.”

Now separate that behavior from its implementation. A conceptual queue does not by itself tell you how a programming language stores the elements or what each operation costs. Write implementation-specific claims in their own node and verify them against the implementation you are studying.

In Mappy, short labels can name the structures while expanded notes hold traces, code blocks, and explanations. That keeps your map readable without losing the details you need for a problem set.

End with a choice you can defend

Invent a small workload and explain which operations dominate it. Choose a structure, state a disadvantage, and name a condition that would change your choice. Then check the decision against a worked problem or your lecture material.

Do not stop at recognizing terminology. The map becomes useful when it helps you explain why one representation fits a task, and why the same representation might be a poor fit elsewhere.