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Consider the classic minimum‑spanning‑tree (MST) problem. Kruskal’s algorithm, with a complexity of (O(E\log E)) where (E) is the number of edges, is optimal for dense graphs, whereas Prim’s algorithm with a binary‑heap implementation also achieves (O(E\log V)). No algorithm can beat these bounds asymptotically for the general case, because each edge must be examined at least once.