The row/column uniqueness part felt like N-queens to me immediately, so I went straight to backtracking.
Model the problem as a constraint satisfaction problem where each row and column must have exactly one flower, and each house must have exactly one adjacent flower. Use backtracking with constraint propagation, placing flowers row by row while checking row, column, and house constraints, and prune early when constraints are violated.
Pro tip: Start by discussing the problem's complexity and potential NP-hardness, then propose a backtracking solution with pruning, and mention how you would optimize using bitmasks or DLX for large N.
Clarify the constraints: exactly one flower per row and column, and each house must have exactly one flower among its four orthogonal neighbors. Confirm that flowers can only be placed on empty cells ('0').
Model as a constraint satisfaction problem: variables are rows (or columns) with domain of possible column positions for the flower. Constraints: all-different on columns, and for each house, exactly one adjacent flower.
Use backtracking with pruning. Represent the grid and track used columns, and for each house, count adjacent flowers. Use bitmasks for rows/columns and precompute house adjacency to speed up checks.
Implement recursive backtracking: for each row, try placing a flower in each unused column that doesn't violate house constraints. Prune if any house already has more than one adjacent flower or if a house cannot get a flower. Optimize with constraint propagation (e.g., forward checking).
Discuss time complexity (worst-case exponential) and space complexity. Mention trade-offs between backtracking and other methods like SAT solvers or integer programming, and when each might be preferable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.