Indexed Randomized Set: Mental Model

Start with the idea

Begin with the concrete question: After add 4, add 9, remove 4, add 7, return the dense storage in any valid order shown sorted. For the visible input add4 add9 remove4 add7, the stated result is 7,9. Before reading code, name the smallest piece of information that must survive from one step to the next. A key-derived representation lets later work reuse an earlier fact. It may be a set, a map from keys to state, compressed ranks, or a rolling fingerprint; name which one this pattern uses. That is the mental model for Indexed Randomized Set; it gives you a reason for each update instead of a line of code to memorise.

The core mechanism is this: Combine a dense vector with a value-to-index map; delete by swapping with the last item. 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.