← MathWorks Interview Insights
Model the problem as a constraint satisfaction problem (CSP) and use backtracking with constraint propagation to find the unique target position. Represent the grid and constraints explicitly, then apply pruning techniques like forward checking and MRV heuristic to efficiently narrow down possibilities. Finally, analyze the complexity and provide clear pseudocode.
Pro tip: Emphasize that the 'exactly one of a set is adjacent' constraint is a global cardinality constraint that can be handled with specialized propagation, and mention that uniqueness of the solution can be verified by continuing the search after finding one solution.
Define variables for each person's grid position (row, column) and translate each constraint into a formal relation (e.g., directional, adjacency, row/column exclusion, exactly-one-adjacent).
Use a 2D array or dictionary to represent the grid, sets for domains of possible positions, and adjacency lists or bitmasks for efficient constraint checking.
Implement backtracking search with constraint propagation: start with all positions possible, apply constraints to prune domains, and recursively assign positions using MRV and forward checking.
Discuss worst-case time complexity (exponential in number of people) and space complexity (O(N*M) for grid and domains), noting that propagation reduces practical runtime.
Provide clear pseudocode for the backtracking search with propagation, including handling of the 'exactly one adjacent' constraint via counting.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.