The pop behavior is what makes this weird.
Clarify the operations and constraints, then design a data structure that supports O(log n) insertions and O(log n) deletions from either end while maintaining sorted order. A balanced BST with min-max pointers or two heaps can work, but consider simpler options like a sorted array with two pointers if the operation sequence is known. Simulate the operations and output the remaining elements in order.
Pro tip: Discuss trade-offs between different implementations (e.g., balanced BST vs. two heaps vs. sorted array) and choose based on expected operation mix. Mention that if the sequence is known, you can sometimes process offline for efficiency.
Ask about the range of values, number of operations, and whether the sequence is known in advance. Confirm that 'popping randomly' means choosing either head or tail arbitrarily, not uniformly at random.
Evaluate options: balanced BST (e.g., TreeSet) with min/max access, two heaps (min-heap and max-heap) with lazy deletion, or a sorted array with two pointers if operations are known. Consider time and space complexity.
Outline how to process each operation: insert adds to the structure, pop removes either the smallest or largest element, size returns the count. Ensure the structure remains sorted or can retrieve min/max efficiently.
Iterate through the operations, updating the structure. After all operations, extract remaining elements in ascending order and return them.
State the time complexity per operation and overall, and discuss edge cases like empty structure, duplicate values, and large inputs. Mention potential optimizations.
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