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    $\begingroup$ Where did you read that binomial heaps have $O(1)$ amortized time for insertion? I wonder if there's some context that is missing. Wikipedia's claim about amortized complexity only relates to consecutive insertions: en.wikipedia.org/wiki/Binomial_heap#Insert, so it doesn't apply to alternating insertions and pops. Can you credit the source where you read that and give full context on what that resource claims? $\endgroup$ Commented May 12, 2021 at 1:46
  • $\begingroup$ I'm going based on what I was taught when I took the course in data structures, but of course there is the possibility that I misunderstood that part of the material. If I've understood you correctly, it's possible that an operation can have one "amortized cost" when it's part of a specific series, but in a complete analysis of the data structure its actual amortized cost is different. If this is what you mean, it helps to clarify things a great deal. $\endgroup$ Commented May 12, 2021 at 2:40