I jumped straight to a sorted structure which was the right instinct, but I fumbled explaining why removal had to happen atomically and how I'd find the triplet efficiently.
Clarify the problem constraints and requirements first, then propose a solution using a balanced BST or two heaps to maintain sorted order and efficiently find valid triplets. Discuss trade-offs between different data structures and algorithms, and analyze time and space complexity.
Pro tip: Mention that you can optimize by checking only consecutive elements in sorted order, since if any triplet satisfies the condition, three consecutive elements will also satisfy it. This shows deep insight and can simplify the implementation.
Ask about the expected frequency of operations, memory constraints, and whether the threshold is fixed or can change. Confirm that the triplet must be sorted and removed immediately upon detection.
Propose using a balanced binary search tree (e.g., TreeSet in Java) or two heaps (min-heap and max-heap) to maintain sorted order and allow efficient insertion and deletion. Discuss the trade-offs between these options.
After each insertion, check for a valid triplet. Since any valid triplet implies three consecutive elements in sorted order also satisfy the condition, check consecutive triples in the sorted structure. If found, return and remove them.
Analyze the time complexity of insertion, checking, and removal. For a balanced BST, insertion and deletion are O(log n), and checking consecutive triples can be done in O(1) if we maintain pointers or O(k) where k is the number of elements, but we can optimize by checking only around the inserted element.
Consider optimizations like lazy deletion or maintaining a separate structure for quick min/max access. Handle edge cases such as fewer than three items, multiple valid triplets, and duplicate values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.