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The add and remove parts are fine, just a min-heap.
Use a min-heap to track pod loads and a global offset to handle the increment operation lazily. When adding a pod, insert its load minus the offset; when removing, extract the minimum and add the offset back. This yields O(log n) per operation and O(1) for increments.
Pro tip: Mention that the global offset trick avoids O(n) updates, and discuss how this pattern generalizes to other lazy update scenarios. Also, clarify that the heap stores adjusted values to maintain correct ordering.
Identify that add and remove are heap operations, while increment affects all elements. Recognize that a naive increment would be O(n), so we need a lazy approach.
Choose a min-heap to store pod loads and maintain a global offset variable. The heap stores values adjusted by subtracting the offset.
For add, push (load - offset). For increment, increment offset by 1. For remove, pop the minimum, add offset, and return it.
Add and remove are O(log n) due to heap operations; increment is O(1). Overall amortized O(log n) per operation.
Consider empty heap for remove, and ensure offset doesn't cause integer overflow. Discuss potential alternatives like balanced BST.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.