For a sparse graph G = (V, E), where |E| = (V), is the implementation of Prims algorithm with a Fibonacci heap asymptotically faster than

For a sparse graph G = (V, E), where |E| = Θ(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| = Θ(V²)? How must the sizes |E| and |V| be related for the Fibonacci-heap implementation to be asymptotically faster than the binary-heap implementation?