Spent way too long simulating the actual process in my head before realizing you just need to count distinct non-zero values.
First, clarify the problem by walking through a small example to ensure you understand the operation. Then, recognize that the number of operations equals the number of distinct non-zero values in the array, because each pass removes the smallest non-zero value, reducing all larger values by that amount. Finally, explain that the answer is simply the count of unique non-zero elements, and provide an efficient algorithm to compute it.
Pro tip: Mention that the order of elements doesn't matter and that the operation is equivalent to repeatedly subtracting the minimum non-zero value, which is why the answer is the number of distinct non-zero values. This shows you can abstract the problem to its core invariant.
Walk through a small example (e.g., [1,2,3]) to see how each pass subtracts the smallest non-zero element from all non-zero elements.
Observe that after each pass, the smallest non-zero element becomes zero, and all other non-zero elements are reduced by that value. The relative differences between elements remain unchanged.
Conclude that each distinct non-zero value in the original array will become the smallest non-zero exactly once, so the number of operations equals the number of distinct non-zero values.
Use a hash set to collect all non-zero elements, then return the size of the set. This runs in O(n) time and O(n) space.
Handle arrays with all zeros (answer 0), negative numbers (if allowed, clarify), and large arrays (efficiency of set approach).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.