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There are lots of sources about amortized complexity or union-find, quick-find operations but I couldn't find anything about the proof of single union operation complexity.

So, how can I prove that the amortized complexity of the union operation is O(log n).

Thanks.

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  • Union-find has 3 main operations: MakeSet, Find and Union. If you prove the complexity for each, you 'll reach complexity for the entire algorithm. In the case of the union, you could use path compression, splitting/halving in union by size/rank and prove that the amortized complexity will be O(α log n). Commented Aug 19, 2021 at 17:25
  • You have to show some kind of effort you did yourself to get the answer. After that, you should post your question along with that effort to get a solution. Commented Aug 29, 2021 at 19:57
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