Unexpected Results with Prim's Algorithm in Java - Issues with Sparse Graphs
After trying multiple solutions online, I still can't figure this out. I've been struggling with this for a few days now and could really use some help... I've been working on this all day and I'm converting an old project and Hey everyone, I'm running into an issue that's driving me crazy. I'm currently implementing Prim's algorithm to find the minimum spanning tree of a graph using Java, but I'm encountering unexpected results when the graph is sparse. I've set up my adjacency list representation and am using a priority queue to select the next edge with the minimum weight. However, when I test it on a sparse graph, the algorithm seems to produce edges that don't form a valid spanning tree. For example, if I run it on the following edge list: ```java List<Edge> edges = Arrays.asList( new Edge(1, 2, 3), new Edge(2, 3, 1), new Edge(3, 4, 5), new Edge(1, 4, 4) ); ``` I expect to get a minimum spanning tree covering all vertices, but I'm getting edges that connect only some of them. My implementation looks like this: ```java public class PrimAlgorithm { public static Set<Edge> prim(List<Edge> edges, int numVertices) { Set<Edge> mst = new HashSet<>(); boolean[] visited = new boolean[numVertices + 1]; PriorityQueue<Edge> minHeap = new PriorityQueue<>(Comparator.comparingInt(e -> e.weight)); visited[1] = true; // Starting from vertex 1 for (Edge edge : edges) { if (edge.from == 1) minHeap.offer(edge); } while (!minHeap.isEmpty()) { Edge edge = minHeap.poll(); if (visited[edge.to]) continue; visited[edge.to] = true; mst.add(edge); for (Edge nextEdge : edges) { if (nextEdge.from == edge.to && !visited[nextEdge.to]) { minHeap.offer(nextEdge); } } } return mst; } } ``` I've tried modifying the way I add edges into the priority queue, but it doesn't seem to help. Here’s the output I'm getting when I run the algorithm on the sparse graph: `[(1, 2, 3), (2, 3, 1)]`, which fails to connect vertex 4. I also confirmed that the graph is connected, but the algorithm doesn't seem to build the complete minimum spanning tree. Am I missing something in the edge addition logic or the priority queue handling? Any insights would be greatly appreciated! The project is a CLI tool built with Java. Thanks for your help in advance! This is for a service running on Ubuntu 20.04. Could this be a known issue? For context: I'm using Java on Linux. This is my first time working with Java latest. Any ideas what could be causing this?