For a sparse graph $G=(V,E)$ where $|E|=\Theta (V)$ is the implementation of Prim’s algorithm with a Fibonacci heap asymptotically faster than the binary-heap implementation? What about for a dense graph, where $|E|=\Theta (V)^{2}$? How must the sizes $|E|$ and $|V|$ be related for the Fibonacci-heap implementation to be asymptotically faster than the binary-heap implementation?
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Plz tell me difference between Sparse and Dense graph here? How Dense graph implemented and how it make difference for this question