Place n queens on an n-by-n board so no pair shares a row, column, or diagonal.
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
Track occupied columns and the two diagonal keys. Build one row at a time so row conflicts are excluded by construction.
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.