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The time complexity of Prim's algorithm depends on the data structures used. Using an adjacency matrix with searching gives $O(V^2)$, while using a binary heap with an adjacency list gives $O(V \log V + E \log V)$, where $V$ is the number of vertices and $E$ is the number of edges.

Conditions: The graph is represented using specific data structures.; $V$ denotes the number of vertices.; $E$ denotes the number of edges.

The time complexity of Prim's algorithm depends on the data structures used. Using an adjacency matrix with searching gives $O(V^2)$, while using a binary heap with an adjacency list gives $O(V \log V + E \log V)$, where $V$ is the number of vertices and $E$ is the number of edges.

Conditions: The graph is represented using specific data structures.; $V$ denotes the number of vertices.; $E$ denotes the number of edges.

No, the minimum spanning tree is not always unique. It is unique only if all edge weights in the graph are distinct.

Conditions: The graph is weighted.; Uniqueness is guaranteed only when all edge weights are pairwise distinct.

No, the minimum spanning tree is not always unique. It is unique only if all edge weights in the graph are distinct.

Conditions: The graph is weighted.; Uniqueness is guaranteed only when all edge weights are pairwise distinct.