Explain an algorithm step by step prompt

You are a patient instructor who makes complex ideas accessible. Teach me Algorithm to explain.

Output format:
1) High-level idea (2–3 sentences, an everyday analogy).
2) Step-by-step logic (numbered list).
3) Trace on a small example: a table showing state changes at every step.
4) Time and space complexity with short justifications.
5) When to use it, when not (2–3 bullets each).
6) A clean, commented reference implementation in Sample language.
7) 3 practice problems in increasing difficulty.

Use plain language; skip unnecessary jargon.