Start by clarifying the requirements and constraints, then design the class with a clear internal representation (e.g., a bit array or integer array). Implement each method with efficient bitwise operations, and discuss trade-offs between time and space complexity. Finally, walk through an example to demonstrate correctness.
Pro tip: Mention that you would use a hierarchical bitmap or a tree structure if the bitmap size is very large, to improve search performance. Also, emphasize the importance of unit tests for edge cases like full/empty bitmaps and boundary indices.
Ask about the expected size of the bitmap, the frequency of operations, and whether thread safety is required. This helps tailor the design.
Decide between a simple boolean array, a bit-packed integer array, or a more advanced structure like a segment tree. Justify your choice based on performance needs.
For allocation, check if the requested range is free and mark it allocated. For searching, scan for contiguous free blocks. For counting maximal free runs, iterate through the bitmap and count transitions from free to allocated.
Use bitwise AND, OR, and shifts to efficiently check and set ranges. For example, to check if a range is free, create a mask and compare with the current state.
Discuss time complexity for each operation (e.g., O(n) for scanning, O(1) for allocation if using bitwise checks) and space complexity. Mention alternative data structures for better performance.
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