Count paths to stair n using one- or two-step moves.
A good solution should
- State the invariant or decision rule that makes the approach correct.
- Explain time and space costs in terms of input size and required output.
- Handle empty, minimal, duplicate, and boundary-shaped inputs.
Reasoning prompt
Define base cases and use the sum of the previous two counts. Keep only two values if no path reconstruction is needed.
Use the linked judge for the canonical challenge. The examples above are compact TRT checks; create additional tests around the boundary most likely to break your invariant.