Top K And Application Case Studies
Why This Matters
The goal is not to name an algorithm after code is written. It is to identify the invariant and choose the smallest structure that makes the required operation reliable.
Working Model
Top-K processing keeps only the best K items seen so far. Dependency resolution uses directed graphs. Schedulers combine eligibility, priority, and fairness. Search systems often use indexes rather than userland scans.
Practical Rules
- Write required operations before choosing a structure.
- Include update and deletion costs.
- Keep database-owned work in the database.
- Bound memory for streams.
- Prefer maintained libraries for specialized structures.
Failure Modes
- Fully sorting when only a few winners are needed.
- Using one structure for every operation.
- Ignoring consistency when cached indexes update.
- Implementing textbook structures inside latency-sensitive requests without measurement.
Verification
- Compare with a simple trusted implementation.
- Test ties and updates.
- Measure representative sizes.
- Document invariants in tests.
What You Should Be Able To Do
After this lesson, you should be able to explain combining data structures for practical ranking, scheduling, dependency, and search problems, choose a suitable approach for a real PHP project, and verify the result instead of relying on assumptions.
Practice
Practice: Rank Top Products
Design top-10 product ranking from a large event stream.
Your answer must:
- state the intended outcome;
- show the commands, data flow, or implementation shape;
- identify at least one unsafe alternative;
- explain how the result will be verified.
Show solution
Maintain aggregate counts in a map and a bounded ranking structure, define tie order, and plan how updates invalidate stale heap entries or rebuild periodically.
The important part is not memorising one command or vendor screen. The solution makes the invariant, failure behavior, and verification evidence explicit.
Practice: Resolve Plugin Order
Order plugins that declare dependencies.
Your answer must:
- state the intended outcome;
- show the commands, data flow, or implementation shape;
- identify at least one unsafe alternative;
- explain how the result will be verified.
Show solution
Build a directed graph, validate missing dependencies, topologically sort it, and report a concrete cycle when ordering is impossible.
The important part is not memorising one command or vendor screen. The solution makes the invariant, failure behavior, and verification evidence explicit.
Practice: Choose A Search Boundary
Choose between PHP scanning, a database index, and a search service for product search.
Your answer must:
- state the intended outcome;
- show the commands, data flow, or implementation shape;
- identify at least one unsafe alternative;
- explain how the result will be verified.
Show solution
Use PHP only for small in-memory data, database indexes for structured predicates and modest text needs, and a search service when relevance, typo tolerance, or scale justifies operational cost.
The important part is not memorising one command or vendor screen. The solution makes the invariant, failure behavior, and verification evidence explicit.