// Point : Forest to Tree
//
// While T has more than one component
// For each component C of T :
// Begin with an empty set of edges S
// For each vertex v in C :
// Find the cheapest edge from v to a vertex outside of C, and add it to S
// Add the cheapest edge in S to T
public WeightUnDirectedGraph MSTBySollin() {
LinkedList<WeightUnDirectedGraph> graphLinkedList = new LinkedList<>();
for (int i = 0; i < vertices.size(); i++) {
graphLinkedList.add(new WeightUnDirectedGraph());
}
// 각각의 vertex에 대해서 graph라고 만듦
for (int i = 0; i < vertices.size(); i++) {
graphLinkedList.get(i).insertVertex(new Data(vertices.get(i).getData().id));
}
int index = 0;
WeightUnDirectedGraph currentGraph;
// While T has more than one component:
while (graphLinkedList.size() > 1) {
if (index >= graphLinkedList.size()) index = 0;
// For each component C of T:
currentGraph = graphLinkedList.get(index);
// Begin with an empty set of edges S
LinkedList<Edge> edgeList = new LinkedList<>();
// For each vertex v in C:
for (Vertex currentVertex : currentGraph.vertices) {
// Find the cheapest edge from v to a vertex outside of C, and add it to S
// 현재 큰 그래프에서 찾음
Vertex vertex = retrieveVertex(currentVertex.getData().id);
for (Edge edge : vertex.getEdges()) {
if (currentGraph.retrieveVertex(edge.getToVertex().getData().id) == null)
insertEdgeToList(edgeList, edge);
}
}
int graphIndex = findGraphIndex(graphLinkedList, edgeList.getFirst().getToVertex());
// Add the cheapest edge in S to T
if (mergeGraph(currentGraph, graphLinkedList.get(graphIndex), edgeList.removeFirst()))
graphLinkedList.remove(graphIndex);
index++;
}
return graphLinkedList.getFirst();
}
// Point : Vertex
// 1. Remove Edge from PQ
// 2. check edge's toVertex is in Graph
// 3. if toVertex is not exist then add that vertex to the graph and edges
// 3-1. if to Vertex is exist in Graph then ignore this Edge
public WeightUnDirectedGraph MSTByPrim() {
if (vertices.size() == 0) return null;
WeightUnDirectedGraph tmpGraph = new WeightUnDirectedGraph();
LinkedList<Edge> edgeList = new LinkedList<>();
// Insert First Vertex to Graph
tmpGraph.insertVertex(new Data(vertices.getFirst().getData().id));
// Get First tmpGraph Vertex
Vertex currentVertex = vertices.getFirst();
Vertex nextVertex;
// Insert First Vertex Edges
for (Edge edge : currentVertex.getEdges()) {
insertEdgeToList(edgeList, edge);
}
// keep make graph(actually tree) until edgeList size get to 0
while (edgeList.size() != 0) {
// First One is lowest Weight Edge
Edge edge = edgeList.removeFirst();
// Vertex Exist => Already lowest weight path exist
if (tmpGraph.retrieveVertex(edge.getToVertex().getData().id) != null) continue;
// insert Vertex
tmpGraph.insertVertex(new Data(edge.getToVertex().getData().id));
nextVertex = edge.getToVertex();
// insert edge between two vertices
tmpGraph.insertEdge(
tmpGraph.retrieveVertex(edge.getFromVertex().getData().id),
tmpGraph.retrieveVertex(edge.getToVertex().getData().id),
edge.getWeight());
// insert next Vertex's Edges
for (Edge tmpEdge : nextVertex.getEdges()) {
insertEdgeToList(edgeList, tmpEdge);
}
}
return tmpGraph;
}
// merge toGraph and fromGraph, and put edge to the toGraph
private boolean mergeGraph(
WeightUnDirectedGraph toGraph, WeightUnDirectedGraph fromGraph, Edge edge) {
// Add "fromGraph" To "toGraph"
// Both graphs are disjoint!!
LinkedList<Edge> edgeList = new LinkedList<>();
// move all vertices from fromGraph to toGraph
for (int i = 0; i < fromGraph.size; i++) {
if (!toGraph.vertices.contains(fromGraph.vertices.get(i)))
toGraph.insertVertex(new Data(fromGraph.vertices.get(i).getData().id));
// add all edges from fromGraph to toGraph
for (Edge tmpEdge : fromGraph.vertices.get(i).getEdges()) {
insertEdgeToList(edgeList, tmpEdge);
}
} // add all vertices to toGraph
// insert all edges to the toGraph
for (Edge tmpEdge : edgeList) {
toGraph.insertEdge(
toGraph.retrieveVertex(tmpEdge.getFromVertex().getData().id),
toGraph.retrieveVertex(tmpEdge.getToVertex().getData().id),
tmpEdge.getWeight());
}
// insert "edge"(see above parameter) to the toGraph
toGraph.insertEdge(
toGraph.retrieveVertex(edge.getFromVertex().getData().id),
toGraph.retrieveVertex(edge.getToVertex().getData().id),
edge.getWeight());
return true;
}
// Point : Edge
// 1. Put edges to the edgeList(sort by weight) (frankly it is Minimum Heap)
// 2. remove edge element from heap and add to the graph
// 3. if there is a cycle then remove that edge(which we inserted at step 2)
public WeightUnDirectedGraph MSTByKruskal() {
if (vertices.size() == 0) return null;
WeightUnDirectedGraph tmpGraph = new WeightUnDirectedGraph();
// Use this as a Heap
LinkedList<Edge> edgeList = new LinkedList<>();
// Put edges to the edgeList(sort by weight)
for (Vertex currentVertex : vertices) {
for (Edge currentEdge : currentVertex.getEdges()) {
insertEdgeToList(edgeList, currentEdge);
}
}
// Make new Graph(Tree) by using edgeList
while (!edgeList.isEmpty()) {
Edge edge = edgeList.removeFirst();
// Make new vertex for tmpGraph
if (tmpGraph.retrieveVertex(edge.getFromVertex().getData().id) == null)
tmpGraph.insertVertex(new Data(edge.getFromVertex().getData().id));
if (tmpGraph.retrieveVertex(edge.getToVertex().getData().id) == null)
tmpGraph.insertVertex(new Data(edge.getToVertex().getData().id));
// insert Edge and Weight between vertices
tmpGraph.insertEdge(
tmpGraph.retrieveVertex(edge.getFromVertex().getData().id),
tmpGraph.retrieveVertex(edge.getToVertex().getData().id),
edge.getWeight());
// Check if there is a cycle
if (tmpGraph.hasCycle()) {
// if there is a cycle
// then delete edge
tmpGraph.deleteEdge(
tmpGraph.retrieveVertex(edge.getFromVertex().getData().id),
tmpGraph.retrieveVertex(edge.getToVertex().getData().id));
System.out.println("Cycle Exist");
}
}
return tmpGraph;
}