Question: Suppose we implement the tree-based union-find data structure using the unionby-size and path-compression heuristics. Show that the total running time for performing a sequence of

Suppose we implement the tree-based union-find data structure using the unionby-size and path-compression heuristics. Show that the total running time for performing a sequence of m union and find operations, starting with n singleton sets, is O(n + m) if all the unions come before all the finds.

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