In prim’s algorithm, if a graph G(V,E) is represented by its adjacency list and the priority...

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In prim’s algorithm, if a graph G(V,E) is represented by its adjacency list and the priority...

In prim’s algorithm, if a graph G(V,E) is represented by its adjacency list and the priority queue is implemented using min-heap data structure, find the time complexity of the algorithm using big-oh asymptotic notation. Justify your answer in detail how you get the time complexity

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Answer 1

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Using min-heap data structure, In prim’s algorithm a graph G(V,E) is represented by its adjacency list.
Prim's algorithm has three loops.
The first loop seeks the proximity of all nodes requiring O (n) space (big-Oh asymptotic notation).
The second for loop, after adding a vertex to MST, now to find the remaining n-2 edges and
The third for loop updates close to each node.
while the third loop is in the second loop, i.e., O (n^2) time is required.
Hence, Prim's algorithm's overall time complexity is O (n^2).

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In prim’s algorithm, if a graph G(V,E) is represented by its adjacency list and the priority...

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