NP-complete problems are both in NP (a solution can be verified in polynomial time) and NP-hard. NP-hard means “at least as hard as NP problems” but it might not be in NP (e.g., optimization versions). If any NP-complete problem has a polynomial-time algorithm, then P = NP.
Advanced answer
Deep dive
Expanding on the short answer — what usually matters in practice:
Complexity: compare typical operations (average vs worst-case).
Invariants: what must always hold for correctness.
When the choice is wrong: production symptoms (latency, GC, cache misses).
Explain the "why", not just the "what" (intuition + consequences).
Trade-offs: what you gain/lose (time, memory, complexity, risk).
Edge cases: empty inputs, large inputs, invalid inputs, concurrency.
Examples
A tiny example (an explanation template):
// Example: discuss trade-offs for "np-hard-vs-np-complete:-what's-the-difference?"
function explain() {
// Start from the core idea:
// NP-complete problems are both in NP (a solution can be verified in polynomial time) and NP
}
Common pitfalls
Too generic: no concrete trade-offs or examples.
Mixing average-case and worst-case (e.g., complexity).