# Analysis of Weighted Quick Union with Path Compression

I have searched the internet for an analysis of why WQUPC is amortized $O( m \alpha (n) )$ for m operations on n nodes ( $\alpha ( n)$ is the inverse Ackerman function).

I understand why it is $O ( m \log^{\ast} ( n ) )$ as it is proven on wikipedia.

So the question is, why is WQUPC $O( m \alpha (n) )$? I would prefer a rigorous analysis, but an intuitive explanation would also be useful.