java - ordenamiento - topological sort

Muestra de gráfico dirigido y código de ordenamiento topológico

Question

¿Alguien sabe dónde puedo obtener una implementación de ejemplo de un Gráfico dirigido y un código de ejemplo para realizar una ordenación topológica en un gráfico dirigido? (preferiblemente en Java)

Answer 1

Aquí hay una implementación simple del primer algoritmo de la página de Wikipedia en Ordenación topológica :

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()));
    }
  }
}

Answer 2

Aquí va una implementación que hice hace un tiempo:

/**
 * 
 * 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();
}

Y aquí un ejemplo de uso:

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();
    }
 }

Dos características adicionales (o complicaciones) en mi código: necesitaba admitir bucles (ciclos) en mi caso, de modo que si la gráfica tiene bucles hace un pedido de "mejor esfuerzo". Este comportamiento es controlado por una bandera que se pasa al constructor. En cualquier caso, puede (debería) llamar a hadLoops() para preguntar si se detectaron ciclos. Además, quería que el algoritmo de clasificación prefiriera el orden original en caso de libertad.

Answer 3

De acuerdo con Jeremy.

Creo que aquí hay una implementación para obtener el código hash basado en Java efectivo: http://www.javapractices.com/topic/TopicAction.do?Id=28

¿Qué hay de agregar el método a continuación para anular el código hash?

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

Answer 4

Solo para aumentar un poco la gran solución con @templatetypedef, agregué algunas pruebas unitarias para dar un poco de confianza adicional para que yo y otros los utilicemos. Espero que esto ayude...

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);
    }
}

Answer 5

También debe anular la función hashCode() ya que está utilizando HashSet en los bordes.

De lo contrario, provocará errores inesperados.

EXP: Agrega dos instancias con igual desde y hacia el hashset . El segundo no se sobrescribirá sin el hashCode() que se supone que se debe sobrescribir.

Answer 6

También puede utilizar proyectos de código abierto de terceros, como JGraphT . Proporciona muchas estructuras gráficas simples y complicadas y su representación visual. Además, no tienes que lidiar con problemas estructurales de esta manera.

Answer 7

Una implementación que hice en base a la segunda alternativa en la página de wikipedia: 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();
    }
}