Generating Minimum Spanning Trees Using Prim's Algorithm
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In graph theory, minimum spanning trees represent a fundamental concept. Among these, minimum spanning trees generated using Prim's algorithm stand as a key implementation. Prim's algorithm employs a greedy approach that begins with a single vertex and iteratively expands the spanning tree by adding the closest adjacent vertex. The algorithm typically utilizes a priority queue (min-heap) to efficiently select the next edge with minimum weight, ensuring optimal O(E log V) time complexity for connected graphs. Ultimately, all vertices become connected within the tree, forming a complete minimum spanning tree with the least total edge weight. Key implementation considerations include maintaining vertex sets for visited/unvisited nodes and updating edge weights dynamically during tree expansion.
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