java实现有向图和判断是否存在循环

最新在看xwork的源代码,XmlConfigurationProvider这个类，用来实现解析xwork.xml配置文件。该类使用了有向图这种数据结构，来判断是否存在元素的循环包含。

 

有向图的实现如下：

import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Set;

public final class DirectedGraph implements Iterable 
{

    private final Map> mGraph = new HashMap>();
	
    /**
     * Adds a new node to the graph. If the node already exists, this function is a no-op.
     * 
     * @param node
     *            The node to add.
     * @return Whether or not the node was added.
     */
    public boolean addNode(T node) {
        /* If the node already exists, don't do anything. */
        if (mGraph.containsKey(node))
            return false;
        /* Otherwise, add the node with an empty set of outgoing edges. */
        mGraph.put(node, new HashSet());
        return true;
    }
    /**
     * Given a start node, and a destination, adds an arc from the start node to the destination. If an arc already exists, this operation is a no-op.
     * If either endpoint does not exist in the graph, throws a NoSuchElementException.
     * 
     * @param start
     *            The start node.
     * @param dest
     *            The destination node.
     * @throws NoSuchElementException
     *             If either the start or destination nodes do not exist.
     */
    public void addEdge(T start, T dest) {
        /* Confirm both endpoints exist. */
        if (!mGraph.containsKey(start)) {
            throw new NoSuchElementException("The start node does not exist in the graph.");
        } else if (!mGraph.containsKey(dest)) {
            throw new NoSuchElementException("The destination node does not exist in the graph.");
        }
        /* Add the edge. */
        mGraph.get(start).add(dest);
    }
	
	/**
     * Removes the edge from start to dest from the graph. If the edge does not exist, this operation is a no-op. If either endpoint does not exist,
     * this throws a NoSuchElementException.
     * 
     * @param start
     *            The start node.
     * @param dest
     *            The destination node.
     * @throws NoSuchElementException
     *             If either node is not in the graph.
     */
    public void removeEdge(T start, T dest) {
        /* Confirm both endpoints exist. */
        if (!mGraph.containsKey(start)) {
            throw new NoSuchElementException("The start node does not exist in the graph.");
        } else if (!mGraph.containsKey(dest)) {
            throw new NoSuchElementException("The destination node does not exist in the graph.");
        }
        mGraph.get(start).remove(dest);
    }
    /**
     * Given two nodes in the graph, returns whether there is an edge from the first node to the second node. If either node does not exist in the
     * graph, throws a NoSuchElementException.
     * 
     * @param start
     *            The start node.
     * @param end
     *            The destination node.
     * @return Whether there is an edge from start to end.
     * @throws NoSuchElementException
     *             If either endpoint does not exist.
     */
    public boolean edgeExists(T start, T end) {
        /* Confirm both endpoints exist. */
        if (!mGraph.containsKey(start)) {
            throw new NoSuchElementException("The start node does not exist in the graph.");
        } else if (!mGraph.containsKey(end)) {
            throw new NoSuchElementException("The end node does not exist in the graph.");
        }
        return mGraph.get(start).contains(end);
    }
	
	/**
     * Given a node in the graph, returns an immutable view of the edges leaving that node as a set of endpoints.
     * 
     * @param node
     *            The node whose edges should be queried.
     * @return An immutable view of the edges leaving that node.
     * @throws NoSuchElementException
     *             If the node does not exist.
     */
    public Set edgesFrom(T node) {
        /* Check that the node exists. */
        Set arcs = mGraph.get(node);
        if (arcs == null)
            throw new NoSuchElementException("Source node does not exist.");
        return Collections.unmodifiableSet(arcs);
    }
    /**
     * Returns an iterator that can traverse the nodes in the graph.
     * 
     * @return An iterator that traverses the nodes in the graph.
     */
    public Iterator iterator() {
        return mGraph.keySet().iterator();
    }
    /**
     * Returns the number of nodes in the graph.
     * 
     * @return The number of nodes in the graph.
     */
    public int size() {
        return mGraph.size();
    }
	
    /**
     * Returns whether the graph is empty.
     * 
     * @return Whether the graph is empty.
     */
    public boolean isEmpty() {
        return mGraph.isEmpty();
    }
}

 

通过上述源码发现：xwork框架采用的是有向图的邻接表方法进行存储的。

xwork使用CycleDetector用来判断有向图是否存在循环，实现如下：

public class CycleDetector
{
    private static final String marked = "marked";

    private static final String complete = "complete";

    private DirectedGraph graph;

    private Map marks;

    private List verticesInCycles;

    public CycleDetector(DirectedGraph graph)
    {
        this.graph = graph;
        marks = new HashMap();
        verticesInCycles = new ArrayList();
    }

    public boolean containsCycle()
    {
        for (T v : graph)
        {
            // 如果v正在遍历或者遍历完成,不需要进入mark(),因为mark是一个递归调用，使用的是深度优先搜索算法;
            // 这是为了保证1个顶点只会遍历一次
            if (!marks.containsKey(v))
            {
                if (mark(v))
                {
                    // return true;
                }
            }
        }

        return !verticesInCycles.isEmpty();
    }

    //DFS算法,遍历顶点vertex
    // @return 当前顶点是否在环上
    private boolean mark(T vertex)
    {
        List localCycles = new ArrayList();

        // 当前顶点vertex,遍历开始
        marks.put(vertex, marked);

        for (T u : graph.edgesFrom(vertex))
        {
            // u的遍历还没有结束,说明存在u->vertex的通路,也存在vertex->u的通路,形成了循环
            if (marks.containsKey(u) && marks.get(u).equals(marked))
            {
                localCycles.add(vertex);
                // return true;
            }
            else if (!marks.containsKey(u))
            {
                if (mark(u))
                {
                    localCycles.add(vertex);
                    // return true;
                }
            }
        }

        // 当前顶点vertex,遍历完成
        marks.put(vertex, complete);

        verticesInCycles.addAll(localCycles);
        return !localCycles.isEmpty();
    }

    public List getVerticesInCycles()
    {
        return verticesInCycles;
    }
}