The part that got me was the feasibility check.
Start by clarifying the constraints and edge cases, then propose a backtracking algorithm that fills cells probabilistically while ensuring each row has exactly 5 numbers and each column's numbers fall within its decade range. Discuss how to maintain satisfiability by checking row and column counts and using randomization with backtracking to avoid dead ends.
Pro tip: Mention that you can precompute the number of ways to fill each row given column constraints to guide probabilistic choices, and use a randomized backtracking approach with early pruning to ensure efficiency.
Confirm the board size, row/column constraints, and decade ranges. Discuss whether numbers within a column must be unique and whether the board should be uniformly random among all valid boards.
Propose a backtracking algorithm that fills cells row by row or column by column, using probabilistic choices (e.g., weighted by remaining capacity) and backtracking when constraints cannot be met.
At each step, check that the remaining empty cells can still satisfy the row's need for exactly 5 numbers and the column's decade range. Use pruning to avoid dead ends.
Write pseudocode or actual code, then test with multiple runs to ensure randomness and correctness. Consider performance for larger boards.
Compare backtracking with other approaches (e.g., precomputed templates, dynamic programming) in terms of randomness, efficiency, and complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.