Start by formalizing the puzzle as a constraint satisfaction problem (CSP) with variables for each cell's height and constraints from row/column clues. Then propose a backtracking search with constraint propagation (e.g., maintaining possible values) and pruning techniques like forward checking and arc consistency. Finally, discuss uniqueness verification via exhaustive search or by checking for multiple solutions, and analyze complexity.
Pro tip: Emphasize the trade-offs between different modeling choices (e.g., cell-based vs. permutation-based) and how they affect pruning effectiveness and complexity. Mention that for N up to 5 or 6, brute-force with pruning is fine, but for larger N, more advanced techniques like SAT solvers or exact cover may be needed.
Define variables (cells) with domains {1..N} and constraints: each row/column is a permutation, and clue constraints (visible skyscrapers from each direction).
Use backtracking search with variable ordering (e.g., most constrained variable) and value ordering (e.g., least constraining value).
Implement forward checking, arc consistency (AC-3), and clue-based pruning to reduce the search space.
After finding a solution, continue search to see if another exists; if none, solution is unique. Alternatively, use a SAT solver with a blocking clause.
Discuss worst-case complexity (exponential in N^2) and expected input/output format (e.g., grid of clues, solution grid).
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