← MathWorks Interview Insights
My first instinct was backtracking and I went down that path for a few minutes before realizing I needed to think about what 'unique' actually means here.
Model the problem as a constraint satisfaction problem (CSP) where each entity's position is a variable with domain of all grid cells, and clues impose binary constraints. Use backtracking search with constraint propagation (e.g., AC-3) to find all valid placements, then check if the target entity's position is the same across all solutions. Alternatively, use a SAT solver or integer programming to determine uniqueness.
Pro tip: Emphasize that uniqueness requires checking all solutions, not just finding one; mention that you can stop early if you find two different positions for P. Also, discuss how to handle large grids by pruning domains aggressively.
Define variables for each entity with domain of all cells, and translate each clue into binary constraints (e.g., same row, left/right, above/below).
Use arc consistency (AC-3) to prune domains, removing values that cannot satisfy any constraint with a neighbor's domain.
Perform backtracking search with forward checking or maintaining arc consistency to find all valid placements, or until two solutions with different P positions are found.
Collect all positions of P from solutions; if exactly one distinct position exists, return it; otherwise, report no unique solution.
Analyze time/space complexity, suggest optimizations like symmetry breaking or using SAT/ILP solvers for large instances.
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