Pointer-Switch Intersection: Mental Model

Start with the idea

Begin with the concrete question: Return the first shared node value. For the visible input A=4->1->8->4->5; B=5->6->1->8->4->5, the stated result is 8. Before reading code, name the smallest piece of information that must survive from one step to the next. A list algorithm changes relationships between nodes, not just values. Draw the next pointers before and after each mutation. That is the mental model for Pointer-Switch Intersection; it gives you a reason for each update instead of a line of code to memorise.

The core mechanism is this: Switch each pointer to the other head so both traverse equal combined distance. 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 an invariant note rather than a complete program. Turn it into explicit state and transitions before coding.