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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.

Dijkstra's algorithm is a method for finding the shortest path from a single starting node to all other nodes in a weighted directed graph. It is distinct from minimum spanning tree algorithms like Prim's and Kruskal's, which connect all nodes with the minimum total edge weight rather than finding paths from a specific source.

Conditions: The graph must be weighted.; The graph can be directed or undirected, though the video primarily demonstrates it on a directed graph.

Dijkstra's algorithm is a method for finding the shortest path from a single starting node to all other nodes in a weighted directed graph. It is distinct from minimum spanning tree algorithms like Prim's and Kruskal's, which connect all nodes with the minimum total edge weight rather than finding paths from a specific source.

Conditions: The graph must be weighted.; The graph can be directed or undirected, though the video primarily demonstrates it on a directed graph.