<P> Different variations of the algorithm differ from each other in how the set Q is implemented: as a simple linked list or array of vertices, or as a more complicated priority queue data structure . This choice leads to differences in the time complexity of the algorithm . In general, a priority queue will be quicker at finding the vertex v with minimum cost, but will entail more expensive updates when the value of C (w) changes . </P> <P> The time complexity of Prim's algorithm depends on the data structures used for the graph and for ordering the edges by weight, which can be done using a priority queue . The following table shows the typical choices: </P> <Table> <Tr> <Th> Minimum edge weight data structure </Th> <Th> Time complexity (total) </Th> </Tr> <Tr> <Td> adjacency matrix, searching </Td> <Td> O (V 2) (\ displaystyle O (V ^ (2))) </Td> </Tr> <Tr> <Td> binary heap and adjacency list </Td> <Td> O ((V + E) log ⁡ V) = O (E log ⁡ V) (\ displaystyle O ((V + E) \ log V) = O (E \ log V)) </Td> </Tr> <Tr> <Td> Fibonacci heap and adjacency list </Td> <Td> O (E + V log ⁡ V) (\ displaystyle O (E + V \ log V)) </Td> </Tr> </Table> <Tr> <Th> Minimum edge weight data structure </Th> <Th> Time complexity (total) </Th> </Tr>

Time complexity of prim's minimum spanning tree
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