Start by clarifying requirements and edge cases, then propose a data structure that maintains free intervals in a balanced BST or skip list for O(log n) allocation and release. Explain how to handle tags with a hash map from tag to allocated intervals, and discuss trade-offs like fragmentation and memory overhead.
Pro tip: Mention that using a balanced BST (e.g., red-black tree) for free intervals and a hash map for tags gives O(log n) operations, but also consider a segment tree with lazy propagation if the array size is fixed and known. Show awareness of real-world constraints like memory fragmentation and concurrency.
Ask about array size, whether tags can be reused, what happens if allocate fails, and if release should handle multiple tags. Confirm that allocate returns the start index or a handle, and release returns the number of cells freed.
Propose a balanced BST (e.g., red-black tree) to store free intervals keyed by start index, supporting O(log n) find, insert, and delete. Use a hash map from tag to a list of allocated intervals for O(1) average tag lookup.
Search the BST for the lowest-start free interval with size >= len. If found, split it: allocate the first len cells, update the free interval, and record the allocation in the tag map. If not found, return failure.
Look up the tag in the hash map to get all allocated intervals. For each, remove from the map and insert back into the free BST, merging with adjacent free intervals to combat fragmentation. Return the total count of released cells.
Explain that each operation is O(log n) due to BST operations, with O(1) average for tag lookup. Discuss fragmentation, memory overhead of the data structures, and potential improvements like using a segment tree for fixed-size arrays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.