My first instinct was to sort and greedily consume sequences, which is wrong and I knew it was wrong while doing it.
Start by sorting the tiles and using a recursive backtracking algorithm that tries each possible pair and then recursively checks if the remaining tiles can form four melds. Use memoization to avoid redundant computations and ensure efficiency.
Pro tip: Emphasize that the order of processing matters: always handle the smallest tile first to reduce branching, and consider using a frequency array for O(1) tile lookups. Mention that this problem is a constrained version of the classic Mahjong hand decomposition, and demonstrating awareness of edge cases (like multiple identical tiles) shows depth.
Clarify that there are exactly 14 tiles, and we need to partition them into 4 melds (triplets or sequences) and 1 pair. Note that tiles are integers, likely representing suits and ranks, but for simplicity, assume they are just numbers.
Decide on a data structure to store tile counts, such as a sorted list or a frequency map (e.g., array of size 34 for standard Mahjong tiles). This allows efficient checks for triplets and sequences.
Iterate over possible pairs (tiles with count >= 2), remove them, and then recursively attempt to form melds from the remaining tiles. For melds, always take the smallest tile and try to form a triplet or a sequence, backtracking if unsuccessful.
Use memoization to cache results for a given tile count state, and prune branches early if counts become negative or if remaining tiles cannot form valid melds. Also, consider symmetry and avoid duplicate pair choices.
Discuss time complexity (exponential in worst case but small due to constraints) and space complexity. Mention edge cases like multiple pairs, sequences spanning gaps, and invalid tile counts.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.