Time Complexity
| Minimum edge weight data structure | Time complexity (total) |
|---|---|
| adjacency matrix, searching | O(V2) |
| binary heap and adjacency list | O((V + E) log V) = O(E log V) |
| Fibonacci heap and adjacency list | O(E + V log V) |
A simple implementation using an adjacency matrix graph representation and searching an array of weights to find the minimum weight edge to add requires O(V2) running time. Using a simple binary heap data structure and an adjacency list representation, Prim's algorithm can be shown to run in time O(E log V) where E is the number of edges and V is the number of vertices. Using a more sophisticated Fibonacci heap, this can be brought down to O(E + V log V), which is asymptotically faster when the graph is dense enough that E is ω(V).
Read more about this topic: Prim's Algorithm
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