The match function being a black box was fine, what tripped me up was not knowing the grid dimensions.
Start by modeling the puzzle as a graph where each piece has four edges, and use the match function to determine adjacency. Then, build the grid incrementally by finding corner pieces (with two unmatched edges) and extending row by row, using backtracking to handle ambiguities. Finally, analyze time and space complexity and discuss trade-offs between different strategies.
Pro tip: Clarify with the interviewer whether pieces can be rotated and whether the match function is symmetric and transitive; these assumptions drastically affect the algorithm's complexity and correctness.
Ask about rotation, match function properties (symmetric, transitive), piece uniqueness, and input format. This ensures you solve the correct problem and avoids wasted effort.
Represent each piece as a node with four labeled edges (top, right, bottom, left). Use the match function to define compatibility between edges, forming a graph where edges represent possible connections.
Find pieces with two unmatched edges (corners) and pieces with one unmatched edge (edges). Use these to anchor the grid and determine its dimensions by counting pieces or extending from corners.
Start from a corner, place pieces row by row, using match to find compatible neighbors. If multiple candidates exist, use backtracking to explore possibilities until a consistent grid is formed.
Evaluate time and space complexity, considering worst-case scenarios. Discuss optimizations like caching match results, using heuristics to prioritize candidates, or parallelizing the search.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.