Sample Directed Graph and Topological Sort Code [c

问题:

Anyone know where I can obtain a sample implementation of a Directed Graph and sample code for performing a topological sort on a directed graph? (preferably in Java)

回答1:

Here is a simple implementation of the first algorithm from the Wikipedia page on Topological Sort:

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;

public class Graph {

  static class Node{
    public final String name;
    public final HashSet<Edge> inEdges;
    public final HashSet<Edge> outEdges;
    public Node(String name) {
      this.name = name;
      inEdges = new HashSet<Edge>();
      outEdges = new HashSet<Edge>();
    }
    public Node addEdge(Node node){
      Edge e = new Edge(this, node);
      outEdges.add(e);
      node.inEdges.add(e);
      return this;
    }
    @Override
    public String toString() {
      return name;
    }
  }

  static class Edge{
    public final Node from;
    public final Node to;
    public Edge(Node from, Node to) {
      this.from = from;
      this.to = to;
    }
    @Override
    public boolean equals(Object obj) {
      Edge e = (Edge)obj;
      return e.from == from && e.to == to;
    }
  }

  public static void main(String[] args) {
    Node seven = new Node("7");
    Node five = new Node("5");
    Node three = new Node("3");
    Node eleven = new Node("11");
    Node eight = new Node("8");
    Node two = new Node("2");
    Node nine = new Node("9");
    Node ten = new Node("10");
    seven.addEdge(eleven).addEdge(eight);
    five.addEdge(eleven);
    three.addEdge(eight).addEdge(ten);
    eleven.addEdge(two).addEdge(nine).addEdge(ten);
    eight.addEdge(nine).addEdge(ten);

    Node[] allNodes = {seven, five, three, eleven, eight, two, nine, ten};
    //L <- Empty list that will contain the sorted elements
    ArrayList<Node> L = new ArrayList<Node>();

    //S <- Set of all nodes with no incoming edges
    HashSet<Node> S = new HashSet<Node>(); 
    for(Node n : allNodes){
      if(n.inEdges.size() == 0){
        S.add(n);
      }
    }

    //while S is non-empty do
    while(!S.isEmpty()){
      //remove a node n from S
      Node n = S.iterator().next();
      S.remove(n);

      //insert n into L
      L.add(n);

      //for each node m with an edge e from n to m do
      for(Iterator<Edge> it = n.outEdges.iterator();it.hasNext();){
        //remove edge e from the graph
        Edge e = it.next();
        Node m = e.to;
        it.remove();//Remove edge from n
        m.inEdges.remove(e);//Remove edge from m

        //if m has no other incoming edges then insert m into S
        if(m.inEdges.isEmpty()){
          S.add(m);
        }
      }
    }
    //Check to see if all edges are removed
    boolean cycle = false;
    for(Node n : allNodes){
      if(!n.inEdges.isEmpty()){
        cycle = true;
        break;
      }
    }
    if(cycle){
      System.out.println("Cycle present, topological sort not possible");
    }else{
      System.out.println("Topological Sort: "+Arrays.toString(L.toArray()));
    }
  }
}

回答2:

An implementation I did based on second alternative on wikipedia page: http://en.wikipedia.org/wiki/Topological_sorting

public class Graph {

    Hashtable<Node, ArrayList<Node>> adjList = new Hashtable<Node, ArrayList<Node>>();
    ArrayList<Node> nodes = new ArrayList<Node>();
    LinkedList<Node> topoSorted;

    public Graph() {}

    public void add(Node node) { 
        if (adjList.contains(node)) { 
            return;
        } else { 
            adjList.put(node, new ArrayList<Node>());
            nodes.add(node);
        }
    }

    public void addNeighbor(Node from, ArrayList<Node> list) { 
        for (Node to: list) { 
            addNeighbor(from, to);
        }
    }

    public void addNeighbor(Node from, Node to) { 
        if (!adjList.containsKey(from)) { 
            add(from);
        }
        if (!adjList.containsKey(to)) { 
            add(to);
        }
        adjList.get(from).add(to);
        to.inDegree++;
        to.inNodes.add(from);
    }

    public void remove(Node node) { 
        for (Node n: nodes) { 
            for (Node x: adjList.get(n)) { 
                if (x.equals(node)) removeNeighbor(n, x);
            }
        }
        adjList.remove(node);
        nodes.remove(node);
    }

    public void removeNeighbor(Node from, Node to) { 
        adjList.get(from).remove(to);
        to.inDegree--;
        to.inNodes.remove(from);
    }

    public void resetVisited() { 
        for (Node node: nodes) { 
            node.visited = false;
        }
    }

    public boolean hasEdge(Node from, Node to) { 
        return adjList.get(from).contains(to) ? true : false;
    }

    /**
     * for DAGS only
     * @throws Exception
     */
    public void topologicalSort() throws Exception { 
        /* L <-- Empty list that will contain the sorted elements */
        topoSorted = new LinkedList<Node>();

        /* Use set to keep track of permanently visited nodes
         * in constant time. Does have pointer overhead */
        HashSet<Node> visited = new HashSet<Node>();

        /* while there are unmarked nodes do */
        for (Node n: nodes) { 

            /* select an unmarked node n
             * visit(n)
             */
            if (!visited.contains(n)) visit(n, visited);
        }
    }

    /* function: visit(node n) */
    public void visit(Node node, HashSet<Node> set) throws Exception { 
        /* if n has a temporary mark then stop (not a DAG) */
        if (node.visited) { 
            throw new Exception("graph cyclic");

        /* if n is not marked (i.e. has not been visited) then... */
        } else { 

            /* mark n temporarily [using boolean field in node]*/
            node.visited = true;

            /* for each node m with an edge n to m do... */
            for (Node m: adjList.get(node)) { 

                /* visit(m) */
                if (!set.contains(m)) visit(m, set);            
            }

            /* mark n permanently */
            set.add(node);

            /* unmark n temporarily */
            node.visited = false;

            /* add n to head of L */
            topoSorted.addFirst(node);
        }
    }

    public void printGraph() { 
        for (Node node: nodes) { 
            System.out.print("from: " + node.value + " |  to: ");
            for (Node m: adjList.get(node)) { 
                System.out.print(m.value + " ");
            }
            System.out.println();
        }
    }

    public void instantiateGraph() { 
        Node seven = new Node("7");
        Node five = new Node("5");
        Node three = new Node("3");
        Node eleven = new Node("11");
        Node eight = new Node("8");
        Node two = new Node("2");
        Node nine = new Node("9");
        Node ten = new Node("10");

        addNeighbor(seven, eleven);
        addNeighbor(seven, eight);
        addNeighbor(five, eleven);
        addNeighbor(three, eight);
        addNeighbor(three, ten);
        addNeighbor(eleven, two);
        addNeighbor(eleven, nine);
        addNeighbor(eleven, ten);
        addNeighbor(eight, nine);

        try {
            topologicalSort();
        } catch (Exception e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }

        for (Node node: topoSorted) { 
            System.out.print(node.value + " ");
        }   
    }

    public class Node { 
        String value; 
        boolean visited = false;
        int inDegree = 0;
        ArrayList<Node> inNodes = new ArrayList<Node>();


        public Node (String value) { 
            this.value = value;
        }
    }

    public static void main(String[] args) { 
        Graph g = new Graph();
        g.instantiateGraph();
    }
}

回答3:

You can also use third party open source projects, such as JGraphT. It provides many simple and complicated graph structures and their visual representation. Also you dont have to deal with structural issues with this way.

回答4:

Here goes a implementation I did some time ago:

/**
 * 
 * Sorts a directed graph, obtaining a visiting sequence ("sorted" list)
 * that respects the "Predecessors" (as in a job/task requirements list).
 * (when there is freedom, the original ordering is preferred)
 * 
 * The behaviour in case of loops (cycles) depends on the "mode":
 *    permitLoops == false : loops are detected, but result is UNDEFINED (simpler) 
 *    permitLoops == true  :  loops are detected, result a "best effort" try,   original ordering is privileged
 *    
 * http://en.wikipedia.org/wiki/Topological_sort
 */
public class TopologicalSorter<T extends DirectedGraphNode> {

    private final boolean permitLoops;
    private final Collection<T> graph; // original graph. this is not touched.
    private final List<T> sorted = new ArrayList<T>(); // result
    private final Set<T> visited = new HashSet<T>(); // auxiliar list
    private final Set<T> withLoops = new HashSet<T>();

    // auxiliar: all succesors (also remote) of each node; this is only used if permitLoops==true
    private HashMap<T, Set<T>> succesors = null;

    public TopologicalSorter(Collection<T> graph, boolean permitLoops) {
        this.graph = graph;
        this.permitLoops = permitLoops;
    }

    public void sort() {
        init();
        for( T n : graph ) {
            if( permitLoops ) visitLoopsPermitted(n);
            else visitLoopsNoPermitted(n, new HashSet<T>());
        }
    }

    private void init() {
        sorted.clear();
        visited.clear();
        withLoops.clear();
        // build succesors map: only it permitLoops == true 
        if( permitLoops ) {
            succesors = new HashMap<T, Set<T>>();
            HashMap<T, Set<T>> addTo = new HashMap();
            for( T n : graph ) {
                succesors.put(n, new HashSet<T>());
                addTo.put(n, new HashSet<T>());
            }
            for( T n2 : graph ) {
                for( DirectedGraphNode n1 : n2.getPredecessors() ) {
                    succesors.get(n1).add(n2);
                }
            }
            boolean change = false;
            do {
                change = false;
                for( T n : graph ) {
                    addTo.get(n).clear();
                    for( T ns : succesors.get(n) ) {
                        for( T ns2 : succesors.get(ns) ) {
                            if( !succesors.get(n).contains(ns2) ) {
                                change = true;
                                addTo.get(n).add(ns2);
                            }
                        }
                    }
                }
                for( DirectedGraphNode n : graph ) {
                    succesors.get(n).addAll(addTo.get(n));
                }
            } while(change);
        }
    }

    private void visitLoopsNoPermitted(T n, Set<T> visitedInThisCallStack) { // this is simpler than visitLoopsPermitted 
        if( visited.contains(n) ) {
            if( visitedInThisCallStack.contains(n) ) {
                withLoops.add(n); // loop!
            }
            return;
        }
        //System.out.println("visiting " + n.toString());
        visited.add(n);
        visitedInThisCallStack.add(n);
        for( DirectedGraphNode n1 : n.getPredecessors() ) {
            visitLoopsNoPermitted((T) n1, visitedInThisCallStack);
        }
        sorted.add(n);
    }

    private void visitLoopsPermitted(T n) {
        if( visited.contains(n) ) return;
        //System.out.println("visiting " + n.toString());
        visited.add(n);
        for( DirectedGraphNode n1 : n.getPredecessors() ) {
            if( succesors.get(n).contains(n1) ) {
                withLoops.add(n);
                withLoops.add((T) n1);
                continue;
            } // loop!
            visitLoopsPermitted((T) n1);
        }
        sorted.add(n);
    }

    public boolean hadLoops() {
        return withLoops.size() > 0;
    }

    public List<T> getSorted() {
        return sorted;
    }

    public Set<T> getWithLoops() {
        return withLoops;
    }

    public void showResult() { // for debugging
        for( DirectedGraphNode node : sorted ) {
            System.out.println(node.toString());
        }
        if( hadLoops() ) {
            System.out.println("LOOPS!:");
            for( DirectedGraphNode node : withLoops ) {
                System.out.println("  " + node.toString());
            }
        }
    }
}

/**
 * Node that conform a DirectedGraph 
 * It is used by TopologicalSorter
 */
public interface DirectedGraphNode {
    /** 
     * empty collection if no predecessors
     * @return
     */
    public Collection<DirectedGraphNode> getPredecessors();
}

And here one example of use:

public class TopologicalSorterExample {

    public static class Node implements DirectedGraphNode {
        public final String x;
        public ArrayList<DirectedGraphNode> antec = new ArrayList<DirectedGraphNode>(); // immediate antecesors
        public Node(String x) {this.x= x;}
        public Collection<DirectedGraphNode> getPredecessors() {
            return antec;
        }
        public String toString() {
            return x;
        }
    }

    public static void main(String[] args) {
        List<DirectedGraphNode> graph = new ArrayList<DirectedGraphNode>();
        Node na = new Node("A");
        Node nb = new Node("B");
        Node nc = new Node("C");
        Node nd = new Node("D");
        Node ne = new Node("E");
        nc.antec.add(na);
        nc.antec.add(nb);
        nd.antec.add(ne);
        ne.antec.add(na);
        na.antec.add(nd);

        graph.add(nc);
        graph.add(na);
        graph.add(nb);
        graph.add(ne);
        graph.add(nd);

        TopologicalSorter ts = new TopologicalSorter(graph, false);
        ts.sort();
        ts.showResult();
    }
 }

Two additional features (or complications) in my code: I needed to support loops (cycles) in my case, so that if the graph has loops it makes some "best effort" ordering. This behaviour is controlled by a flag passed to the constructor. In any case, you can (should) call hadLoops() to ask if there were cycles detected. Besides, I wanted the sorting algorithm to prefer the original ordering in case of freedom.

回答5:

Agree with jeremy.

I think here is a implementation to get the hashcode based on effective Java: http://www.javapractices.com/topic/TopicAction.do?Id=28

How about to add below method to override the hashcode?

@Override
    public int hashCode(){
         if (fHashCode == 0) {
              int result = HashCodeUtil.SEED;
              result = HashCodeUtil.hash(result, from);
              result = HashCodeUtil.hash(result, to);
         }
         return fHashCode;
    }

回答6:

Just to augment the great solution by @templatetypedef a bit, I added some unit tests to give some added confidence for myself and others to use. Hope this helps...

import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertTrue;
import java.util.List;
import org.junit.Test;

public class TestTopologicalSort {

    @Test (expected=java.lang.NullPointerException.class)
    public void testNullGraph() {
        final List<String> orderedLayers = TopologicalSort.sort(null);
    }

    @Test
    public void testEmptyGraph() {
        final DirectedGraph<String> dag = new DirectedGraph<String>();        
        final List<String> orderedLayers = TopologicalSort.sort(dag);
        assertEquals(0, orderedLayers.size());
    }

    @Test
    public void testSingleVertex() {
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("a");
        final List<String> orderedLayers = TopologicalSort.sort(dag);
        assertEquals(1, orderedLayers.size());
        assertTrue(orderedLayers.contains("a"));
    }

    @Test
    public void testMultipleVertices() {
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("a");
        dag.addNode("b");
        final List<String> orderedLayers = TopologicalSort.sort(dag);
        assertEquals(2, orderedLayers.size());
        assertTrue(orderedLayers.contains("a"));
        assertTrue(orderedLayers.contains("b"));
    }

    @Test (expected=java.util.NoSuchElementException.class)
    public void testBogusEdge() {
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("a");
        dag.addEdge("a", "b");
    }

    @Test
    public void testSimpleDag() {
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("b");        
        dag.addNode("a");
        dag.addEdge("a", "b");
        final List<String> orderedLayers = TopologicalSort.sort(dag);
        assertEquals(2, orderedLayers.size());
        assertTrue(orderedLayers.get(0).equals("a"));
        assertTrue(orderedLayers.get(1).equals("b"));
    }

    @Test
    public void testComplexGraph() {
        // node b has two incoming edges
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("a");        
        dag.addNode("b");
        dag.addNode("c");        
        dag.addNode("d");
        dag.addNode("e");        
        dag.addNode("f");
        dag.addNode("g");        
        dag.addNode("h");
        dag.addEdge("a", "b");
        dag.addEdge("a", "c");
        dag.addEdge("c", "d");
        dag.addEdge("d", "b");
        dag.addEdge("c", "e");
        dag.addEdge("f", "g");

        final List<String> orderedLayers = TopologicalSort.sort(dag);
        assertEquals(8, orderedLayers.size());
        assertTrue(orderedLayers.indexOf("a") < orderedLayers.indexOf("b")); 
        assertTrue(orderedLayers.indexOf("a") < orderedLayers.indexOf("c"));
        assertTrue(orderedLayers.indexOf("c") < orderedLayers.indexOf("d"));
        assertTrue(orderedLayers.indexOf("c") < orderedLayers.indexOf("e"));
        assertTrue(orderedLayers.indexOf("d") < orderedLayers.indexOf("b"));
        assertTrue(orderedLayers.indexOf("f") < orderedLayers.indexOf("g"));
    }

    @Test (expected=java.lang.IllegalArgumentException.class)
    public void testCycle() {
        // cycle between a, c, and d
        final DirectedGraph<String> dag = new DirectedGraph<String>();
        dag.addNode("a");        
        dag.addNode("b");
        dag.addNode("c");        
        dag.addNode("d");
        dag.addNode("e");        
        dag.addNode("f");
        dag.addNode("g");        
        dag.addNode("h");
        dag.addEdge("a", "b");
        dag.addEdge("a", "c");
        dag.addEdge("c", "d");
        dag.addEdge("d", "a");
        dag.addEdge("c", "e");
        dag.addEdge("f", "g");

        final List<String> orderedLayers = TopologicalSort.sort(dag);
    }
}

回答7:

You need to override hashCode() function as well since you are using HashSet in edges.

Otherwise, it will raise unexpected bugs.

EXP: Add two instances with same from and to into the hashset. The 2nd one won't be overritten without hashCode() which it's supposed to be overwritten.