Deadlock Detection in a Code Snippet

Start by clarifying the exact contract for Deadlock Detection: input representation, mutation rules, duplicate behavior, and what should happen on invalid or empty input. The core idea is whether a lock-acquisition schedule can create circular wait. Work a tiny example aloud and name the invariant after each step, because that is the proof that the approach stays correct as the input grows.

A dependable implementation plan is to list each thread lock order; build held-to-requested wait edges; show a concrete cycle; impose one global lock order. Blocked does not automatically mean deadlocked. Keep the code aligned with that invariant instead of adding special cases that silently change the contract. Test the smallest input, a normal case, duplicates or ties where relevant, an adversarial boundary, and a case that exercises the failure path. The expected complexity is linear in the modeled lock graph. Explain both time and auxiliary memory, including recursion or helper structures; do not hide sorting, copying, or repeated scans. If the title omits critical constraints, say what you need to know before committing to a more specialized solution.

Complexity: Building a wait-for graph with V threads or resources and E dependencies detects a cycle in O(V + E) time and O(V + E) space.