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Prim's Algorithm - Technical Overview

1. Algorithm Description: Prim's algorithm finds the Minimum Spanning Tree (MST) of a weighted undirected graph by expanding the tree one edge at a time.

2. Steps of Prim's Algorithm:

• Initialize the MST with a single vertex, and set all other vertices as unvisited.
• While there are unvisited vertices, select the smallest edge that connects a visited vertex to an unvisited vertex.
• Add the selected edge and vertex to the MST.
• Repeat until all vertices are included in the MST.

3. Time Complexity: O(E log V) with a priority queue.

4. Space Complexity: O(V) for the storage of the MST and edge weights.

5. Usage: Prim's algorithm is often used in network design and to find optimal connections between nodes.