[英]Generate a Connected Graph java
I want to write a function, which is given a set of vertices and then develops an edge between 2 vertices and repeats this until the graph becomes a connected graph). 我想编写一个函数,该函数具有一组顶点,然后在2个顶点之间展开边并重复此过程,直到该图成为连接的图为止)。 How can I tell when the graph has become connected?
我如何知道图形何时已连接?
This would be a basic idea: Every time you add a new edge, you run BFS or DFS to check the connectivity. 这将是一个基本思想:每次添加新边缘时,您都运行BFS或DFS来检查连接性。 This solution is can be further optimized.
该解决方案可以进一步优化。
import java.util.Deque;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Random;
import java.util.Set;
import org.jgrapht.graph.DefaultEdge;
import org.jgrapht.graph.SimpleGraph;
public class Main {
public static boolean isConnected(SimpleGraph<Integer, DefaultEdge> graph) {
Set<Integer> vertexSet = graph.vertexSet();
if(vertexSet.size()==0) {
//graph is connected by definition
return true;
}
if(vertexSet.size()-1>graph.edgeSet().size()) {
//not enough edges, must be disconnected
return false;
}
Set<Integer> traversed = new HashSet<>();
Deque<DefaultEdge> toTraverse = new LinkedList<DefaultEdge>();
//pick one random element to start search
Integer startVertex = vertexSet.iterator().next();
traversed.add(startVertex);
graph.edgesOf(startVertex).forEach(x->toTraverse.addLast(x));
while(traversed.size()!=vertexSet.size() && toTraverse.size()!=0) {
DefaultEdge currentEdge = toTraverse.pollFirst();
Integer src = graph.getEdgeSource(currentEdge);
Integer dst = graph.getEdgeSource(currentEdge);
//it can be at most one new vertex
Integer targetVertex = traversed.contains(src)?dst:src;
if(!traversed.contains(targetVertex)) {
traversed.add(targetVertex);
//BFS
graph.edgesOf(targetVertex).forEach(x->toTraverse.addLast(x));
//DFS
//graph.edgesOf(targetVertex).forEach(x->toTraverse.addFirst(x));
}
}
if(traversed.size()==vertexSet.size()) {
return true;
}else {
return false;
}
}
public static SimpleGraph<Integer, DefaultEdge> buildGraph(int numberOfVertices) {
SimpleGraph<Integer, DefaultEdge> g =
new SimpleGraph<Integer, DefaultEdge>(DefaultEdge.class);
for(int i = 0; i < numberOfVertices; i++) {
g.addVertex(i);
}
Random r = new Random();
do {
int a = r.nextInt(numberOfVertices);
int b = r.nextInt(numberOfVertices);
while(a == b) {
b = r.nextInt(numberOfVertices);
}
g.addEdge(a, b);
}while(!isConnected(g));
return g;
}
public static void main(String[] args) {
SimpleGraph<Integer, DefaultEdge> g = buildGraph(10);
System.out.println("Number of edges");
System.out.println(g.edgeSet().size());
System.out.println("Edges:");
for(DefaultEdge e: g.edgeSet()){
String a = g.getEdgeSource(e).toString();
String b = g.getEdgeTarget(e).toString();
System.out.println(a+" "+b);
}
}
}
For an arbitrary graph, checking connectivity requires at least O(V) (V - number of vertices, E - number of edges). 对于任意图,检查连通性至少需要O(V)(V-顶点数,E-边数)。 BFS and DFS run in O(V+E).
BFS和DFS在O(V + E)中运行。 This might be fine if you want to create relatively small graphs.
如果要创建相对较小的图形,这可能会很好。 Here is a smarter idea how to do it.
这是一个更聪明的想法。 At the beginning you create V separate graphs.
在开始时,您将创建V个独立的图。 Now you want to add edge between A and B, you find the graph where A belongs and the other where B belongs.
现在要在A和B之间添加边,您将找到A所属的图和B所属的另一个图。 If those are two different graphs, merge them.
如果这些是两个不同的图,请合并它们。 Repeat this process until only one graph remains.
重复此过程,直到只剩下一个图形。
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