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Bounding the height of a tree in a variant of disjoint set union

Let me solve the case where you got stuck. Suppose $T_i$ with $\ell_i$ and $T_j$ with $\ell_j$ is merged into tree $T$, where $\ell_i$ = $\ell_j$. WLOG, suppose we make the root of $T_i$ point to the ...
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