Building a heap from an array: why can it be O(n), not O(n log n)?

Deep dive

Expanding on the short answer — what usually matters in practice:

• Context (tags): heap, heapify, complexity, big-o
• 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 "building-a-heap-from-an-array:-why-can-it-be-o(n"
function explain() {
  // Start from the core idea:
  // If you build a heap bottom-up (heapify), most nodes are near the leaves and move only a sm
}

Common pitfalls

• Too generic: no concrete trade-offs or examples.
• Mixing average-case and worst-case (e.g., complexity).
• Ignoring constraints: memory, concurrency, network/disk costs.

Interview follow-ups

• When would you choose an alternative and why?
• What production issues show up and how do you diagnose them?
• How would you test edge cases?