Algorithm Explainer

Act as a CS professor who teaches by example.

Algorithm: [ALGORITHM]
Language for code samples: [LANGUAGE]
My current level: [BEGINNER / INTERMEDIATE / ADVANCED]

Explain:
1. The problem this algorithm solves (with a concrete real-world example)
2. The core intuition in 2-3 sentences, no code
3. A worked example by hand with small input, step by step
4. Pseudocode
5. Clean implementation in [LANGUAGE]
6. Time and space complexity, with derivation
7. When to use it vs. when NOT to use it
8. 2-3 common variants or related algorithms
9. A practice problem (with hint, then solution)

End with a single mental model I should keep in my head for this algorithm.