Prims Algorithm in Go#553
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Add Prim's Algorithm for Minimum Spanning Tree (MST) in Go
Added an implementation of Prim's Algorithm to find the Minimum Spanning Tree (MST) of a connected, undirected, weighted graph. This version uses a min-heap to efficiently select the lowest-weight edge that connects a vertex in the MST to a vertex outside of it.
Features 🚀
Computes the set of edges in the MST and its total weight for a graph with integer node IDs.
Represents the graph using an adjacency list with weighted edges.
Uses Go's container/heap for an efficient priority queue of edges.
Correctly identifies disconnected graphs by returning nil when a spanning tree cannot be formed.
Includes a comprehensive test suite with checks for connected graphs, disconnected graphs, and other edge cases.
Complexity Analysis 📊
Time Complexity
O(ElogV), where E is the number of edges and V is the number of vertices. The complexity is driven by the min-heap operations, as each edge may be pushed onto the heap once.
Space Complexity
O(V+E) to store the graph's adjacency list, the visited set, and the edges in the min-heap.