I asked if iterative bottom-up was fine and the interviewer said yes, but then casually mentioned recursion would be much simpler.
Clarify the tournament structure and elimination rules, then model the problem as constructing a binary tree where leaves are players and internal nodes represent matches. Use a greedy strategy to assign lower-ranked players to positions that delay their elimination, ensuring they face higher-ranked players as late as possible.
Pro tip: Discuss the trade-offs between different bracket shapes (e.g., balanced vs. unbalanced) and how they affect the earliest and latest elimination rounds, showing you consider practical constraints like fairness and efficiency.
Ask questions to confirm the tournament format: Is it single-elimination? How are matches scheduled? What exactly does 'eliminated later' mean in terms of rounds?
Represent the tournament as a binary tree where leaves are players and each internal node is a match. The depth of a leaf indicates the round in which the player is eliminated (if they lose).
For each pair of players with ranks i < j, ensure that player i is eliminated in a later round than player j. This imposes constraints on the relative depths of leaves in the tree.
Use a greedy approach: place the lowest-ranked player (highest number) in the shallowest leaf, then recursively build subtrees ensuring that lower-ranked players are placed deeper. Alternatively, sort players by rank and assign them to leaves in a specific order (e.g., in-order traversal).
Check that the constructed bracket satisfies the condition for all pairs. Analyze time and space complexity, and discuss potential optimizations or alternative approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.