Offline dynamic connectivity: Process edge insertions, then answer "were u and v connected after operation k?" Rollback operations: Undo union operations by reverting to an earlier version. Branching histories: Create different "timelines" from the same base state. Comparison with Link-Cut trees: - Link-Cut: amortized, supports cut - Persistent UF: worst case, no cut support, version history Use persistent UF when you need version queries but not edge deletion.
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$ curl repovive.com/roadmaps/data-structures/persistent-data-structures/persistent-uf-applications
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