Undirected Cycle Detection: Mental Model

Start with the idea

Begin with the concrete question: Return true when the undirected graph contains a cycle. For the visible input edges=(0,1),(1,2),(2,0),(2,3), the stated result is true. Before reading code, name the smallest piece of information that must survive from one step to the next. A graph method needs an explicit vertex-and-edge representation. For traversal, define when a vertex becomes seen: on insertion into the frontier or on removal. That is the mental model for Undirected Cycle Detection; it gives you a reason for each update instead of a line of code to memorise.

The core mechanism is this: During traversal ignore the edge back to the parent; any other seen neighbor closes a cycle. Treat it as a claim to test after every operation. Write down the state before the first operation, update it once, and ask which part of the claim is still true. If an item is skipped, inserted, or removed, explain why that action cannot destroy an answer that should be retained. A useful trace has columns for the current input position, the state before the step, the action, and the state afterward. Use the visible sample until the expected result becomes inevitable rather than merely plausible.

Now inspect the Rust sketch, not just its final expression. The supplied Rust sketch is a starting point. Identify what it stores, how one iteration changes it, and whether it already solves the exact task or only demonstrates a related operation.