Bounded Heap for K Closest: Mental Model

Start with the idea

Begin with the concrete question: Return the two points closest to the origin, ordered by distance then coordinates. For the visible input [(1,3),(-2,2),(2,-2),(5,1)], the stated result is -2:2,2:-2. Before reading code, name the smallest piece of information that must survive from one step to the next. A heap keeps the current extremum accessible while new items arrive. Explain what belongs in the heap and what may be discarded. That is the mental model for Bounded Heap for K Closest; it gives you a reason for each update instead of a line of code to memorise.

The core mechanism is this: Keep the worst current winner at the root so a better candidate replaces it. 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.