The basic version was fine, just a counter times k, nothing to it.
Start by designing a simple MultiplesStream class that maintains a current value and increments by k on each next() call. For multiple base integers, use a min-heap to merge the streams, tracking the last emitted value to skip duplicates, and advance only the streams that produced the minimum.
Pro tip: Discuss the trade-offs between using a heap versus other approaches (like a priority queue with lazy deletion) and mention how to handle large k or many streams efficiently. Also, clarify whether the stream should be infinite and how to handle overflow.
Ask about constraints: number of base integers, range of k, memory limits, and whether duplicates should be skipped globally or per stream. Confirm that next() should return the next multiple in ascending order.
Implement MultiplesStream(k) with a current variable initialized to k, and next() returns current and then adds k. This is O(1) time and O(1) space.
Use a min-heap to store the next multiple from each base integer. Initially push each base integer. On next(), pop the smallest, record it as the result, and push the next multiple for that base (i.e., add the base to the popped value).
Keep track of the last emitted value. When popping from the heap, if the value equals the last emitted, skip it and push the next multiple for that base. Repeat until a new value is found.
Time per next() is O(log m) where m is the number of base integers, due to heap operations. Space is O(m). Discuss edge cases: k=0 (infinite zeros?), negative k, overflow, and large m.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.