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The runtime complexity of Kruskal's algorithm is O(E log V), where E is the number of edges and V is the number of vertices in the graph.

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Prims Algorithm is used when the given graph is dense , whereas Kruskals is used when the given is sparse,we consider this because of their time complexities even though both of them perform the same function of finding minimum spanning tree. ismailahmed syed


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What is the runtime of Prim's algorithm for finding the minimum spanning tree of a graph?

The runtime of Prim's algorithm for finding the minimum spanning tree of a graph is O(V2) with a simple implementation, or O(E log V) with a more efficient implementation using a priority queue.


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The runtime complexity of the Edmonds-Karp algorithm for finding the maximum flow in a network is O(VE2), where V is the number of vertices and E is the number of edges in the network.


What is the time complexity of the Edmonds-Karp algorithm for finding the maximum flow in a network?

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The time complexity of Dijkstra's algorithm for finding the shortest path in a graph is O(V2) with a simple implementation using an adjacency matrix, or O((V E) log V) with a more efficient implementation using a priority queue.


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The time complexity of Dijkstra's algorithm for finding the shortest path in a graph is O(V2) with a simple implementation using an adjacency matrix, and O(E V log V) with a more efficient implementation using a priority queue.


Why will the shortest paths tree returned by Dijkstra's algorithm never be a correct minimum spanning tree (MST)?

The shortest paths tree returned by Dijkstra's algorithm will never be a correct minimum spanning tree (MST) because Dijkstra's algorithm prioritizes finding the shortest path from a single source node to all other nodes, while a minimum spanning tree aims to connect all nodes in a graph with the minimum total edge weight without forming cycles. Dijkstra's algorithm does not consider the overall connectivity of the graph, leading to potential inconsistencies with the requirements of a minimum spanning tree.