Data Structures and Algorithms

# What is Prim’s Algorithm and Does it Work?

Prim’s algorithm is a greedy algorithm used to find the minimum spanning tree of a weighted, undirected graph. It works by selecting a starting vertex and growing the minimum spanning tree from this vertex by repeatedly adding the adjacent edge with the minimum weight that connects the tree to a vertex not yet in the tree, until all vertices are included in the tree.

At each step, Prim’s algorithm considers all edges that connect the vertices in the tree to the vertices not yet in the tree and selects the edge with the minimum weight. The vertex connected by this edge is then added to the tree, and the process is repeated until all vertices are included in the tree.

The time complexity of Prim’s algorithm is O(E log V), where E is the number of edges in the graph and V is the number of vertices. This makes it an efficient algorithm for finding the minimum spanning tree of large graphs. Prim’s algorithm is very similar to Kruskal’s algorithm, but it works by growing the minimum spanning tree from a single vertex, while Kruskal’s algorithm works by connecting disjoint sets of vertices.

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