Backtracking is the obvious move here and I went with it, but the variant part is what trips you up.
Clarify the exact variation and constraints, then model the puzzle as a constraint satisfaction problem and choose an appropriate algorithm (backtracking with pruning, constraint propagation, or exact cover). Discuss trade-offs between simplicity and efficiency, and outline how you would implement and test the solution.
Pro tip: Start by asking clarifying questions about the variation (e.g., grid size, additional constraints, whether a unique solution is guaranteed) to show you think before coding. Then, before diving into code, explain the algorithm at a high level and mention how you would handle edge cases and validate the solution.
Ask questions to understand the exact variation: grid dimensions, additional constraints (e.g., diagonals, irregular regions), input format, and expected output. Confirm whether a solution is guaranteed and if multiple solutions are possible.
Represent the puzzle as a constraint satisfaction problem: variables (cells), domains (possible values), and constraints (row, column, region, etc.). Identify any special constraints introduced by the variation.
Select an appropriate algorithm: backtracking with constraint propagation (e.g., forward checking, AC-3), or exact cover with Algorithm X. Discuss trade-offs between simplicity and performance, and justify your choice based on the variation's characteristics.
Describe the implementation steps: data structures (e.g., bitmasks for domains), recursive backtracking function, constraint checking, and pruning. Mention how to handle the variation's unique aspects.
Discuss time/space complexity, potential optimizations (e.g., MRV heuristic, constraint propagation), and how you would test the solution with edge cases and performance benchmarks.
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