code: ///////////////////////////////////////////////////////////////////////////////
  // For information as to what this class does, see the Javadoc, below.       //
  // Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
  // 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
  // Ramsey, and Clark Glymour.                                                //
  //                                                                           //
  // This program is free software; you can redistribute it and/or modify      //
  // it under the terms of the GNU General Public License as published by      //
  // the Free Software Foundation; either version 2 of the License, or         //
  // (at your option) any later version.                                       //
  //                                                                           //
  // This program is distributed in the hope that it will be useful,           //
  // but WITHOUT ANY WARRANTY; without even the implied warranty of            //
  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the             //
  // GNU General Public License for more details.                              //
  //                                                                           //
  // You should have received a copy of the GNU General Public License         //
  // along with this program; if not, write to the Free Software               //
  // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
  ///////////////////////////////////////////////////////////////////////////////
  
  package edu.cmu.tetrad.search;
  
  import edu.cmu.tetrad.data.IKnowledge;
  import edu.cmu.tetrad.data.Knowledge2;
  import edu.cmu.tetrad.graph.*;
  import edu.cmu.tetrad.util.DepthChoiceGenerator;
  import edu.cmu.tetrad.util.TetradLogger;
  
  import java.util.ArrayList;
  import java.util.List;
  import java.util.Set;
  
  /**
   * Implements the PC Local algorithm.
   *
   * @author Joseph Ramsey (this version).
   */
  public class CpcLocal implements GraphSearch {
  
      /**
       * The independence test used for the PC search.
       */
      private IndependenceTest independenceTest;
  
      /**
       * Forbidden and required edges for the search.
       */
      private IKnowledge knowledge = new Knowledge2();
  
      /**
       * True if cycles are to be aggressively prevented. May be expensive for large graphs (but also useful for large
       * graphs).
       */
      private boolean aggressivelyPreventCycles = false;
  
      /**
       * The logger for this class. The config needs to be set.
       */
      private TetradLogger logger = TetradLogger.getInstance();
  
      /**
       * Elapsed time of the most recent search.
       */
      private long elapsedTime;
  
      private Graph graph;
      private MeekRules meekRules;
  
      //=============================CONSTRUCTORS==========================//
  
      /**
       * Constructs a PC Local search with the given independence oracle.
       */
      public CpcLocal(IndependenceTest independenceTest) {
          if (independenceTest == null) {
              throw new NullPointerException();
          }
  
          this.independenceTest = independenceTest;
      }
  
      //==============================PUBLIC METHODS========================//
  
      public boolean isAggressivelyPreventCycles() {
          return this.aggressivelyPreventCycles;
      }
  
      public void setAggressivelyPreventCycles(boolean aggressivelyPreventCycles) {
          this.aggressivelyPreventCycles = aggressivelyPreventCycles;
      }
  
  
      public IndependenceTest getIndependenceTest() {
          return independenceTest;
      }
  
      public IKnowledge getKnowledge() {
          return knowledge;
      }
  
      public void setKnowledge(IKnowledge knowledge) {
          if (knowledge == null) {
              throw new NullPointerException();
          }
  
          this.knowledge = knowledge;
      }
  
      public long getElapsedTime() {
          return elapsedTime;
      }
  
      /**
       * Runs PC starting with a fully connected graph over all of the variables in the domain of the independence test.
       */
      public Graph search() {
          long time1 = System.currentTimeMillis();
  
          graph = new EdgeListGraph(getIndependenceTest().getVariables());
          meekRules = new MeekRules();
          meekRules.setAggressivelyPreventCycles(isAggressivelyPreventCycles());
          meekRules.setKnowledge(knowledge);
          meekRules.setUndirectUnforcedEdges(true);
  
  
          // This is the list of all changed nodes from the last iteration
          List<Node> nodes = graph.getNodes();
  
          Graph outGraph = null;
  
          int numEdges = nodes.size() * (nodes.size() - 1) / 2;
          int index = 0;
  
          for (int i = 0; i < nodes.size(); i++) {
              for (int j = i + 1; j < nodes.size(); j++) {
                  ++index;
  
                  if (index % 1000 == 0) {
                      log("info", index + " of " + numEdges);
                  }
  
                  Node x = nodes.get(i);
                  Node y = nodes.get(j);
  
                  tryAddingEdge(x, y);
              }
          }
  
          outGraph = graph;
  
          this.logger.log("graph", "\nReturning this graph: " + graph);
  
          long time2 = System.currentTimeMillis();
          this.elapsedTime = time2 - time1;
  
          return outGraph;
      }
  
      private void log(String info, String message) {
          TetradLogger.getInstance().log(info, message);
          if ("info".equals(info)) {
              System.out.println(message);
          }
      }
  
      private void tryAddingEdge(Node x, Node y) {
          if (graph.isAdjacentTo(x, y)) {
              return;
          }
  
          List<Node> sepset = sepset(x, y);
  
          if (sepset == null) {
              if (getKnowledge().isForbidden(x.getName(), y.getName()) && getKnowledge().isForbidden(y.getName(), x.getName())) {
                  return;
              }
  
              Edge edge = Edges.undirectedEdge(x, y);
              graph.addEdge(edge);
              orientNewColliders(x, y);
  
              for (Node w : graph.getAdjacentNodes(x)) {
                  tryRemovingEdge(w, x);
              }
  
              for (Node w : graph.getAdjacentNodes(y)) {
                  tryRemovingEdge(w, y);
              }
          }
      }
  
      private void tryRemovingEdge(Node x, Node y) {
          if (!graph.isAdjacentTo(x, y)) return;
  
          List<Node> sepsetX = sepset(x, y);
  
          if (sepsetX != null) {
              if (!getKnowledge().noEdgeRequired(x.getName(), y.getName())) {
                  return;
              }
  
              graph.removeEdge(x, y);
  
              List<Node> start = new ArrayList<>();
              start.add(x);
              start.add(y);
  
              meekRules.orientImplied(graph, start);
  
              renderUnambiguousWherePossible();
          }
      }
  
      private void renderUnambiguousWherePossible() {
          Set<Node> visited = meekRules.getVisited();
  
          for (Node v : visited) {
              List<Node> adj = graph.getAdjacentNodes(v);
  
              for (int i = 0; i < adj.size(); i++) {
                  for (int j = i + 1; j < adj.size(); j++) {
                      Node _x = adj.get(i);
                      Node _z = adj.get(j);
                      if (Edges.isDirectedEdge(graph.getEdge(_x, v)) && Edges.isDirectedEdge(graph.getEdge(v, _z))) {
                          graph.removeAmbiguousTriple(_x, v, _z);
                      }
                  }
              }
          }
      }
  
      //================================PRIVATE METHODS=======================//
  
      private List<Node> sepset(Node x, Node y) {
          List<Node> adj = graph.getAdjacentNodes(x);
          adj.remove(y);
  
          DepthChoiceGenerator gen = new DepthChoiceGenerator(adj.size(), adj.size());
          int[] choice;
  
          while ((choice = gen.next()) != null) {
              List<Node> cond = GraphUtils.asList(choice, adj);
  
              if (getIndependenceTest().isIndependent(x, y, cond)) {
                  return cond;
              }
          }
  
          adj = graph.getAdjacentNodes(y);
          adj.remove(x);
  
          gen = new DepthChoiceGenerator(adj.size(), adj.size());
  
          while ((choice = gen.next()) != null) {
              List<Node> cond = GraphUtils.asList(choice, adj);
  
              if (getIndependenceTest().isIndependent(x, y, cond)) {
                  return cond;
              }
          }
  
          return null;
      }
  
      private void orientNewColliders(Node x, Node y) {
          boolean oriented = orientColliders(x, y);
  
          if (!oriented) {
              orientColliders(y, x);
          }
  
          List<Node> start = new ArrayList<>();
  //        start.add(x);
          start.add(y);
  
          meekRules.orientImplied(graph, start);
      }
  
      private boolean orientCollider1(Node x, Node y) {
          boolean oriented = false;
  
          for (Node z : graph.getAdjacentNodes(y)) {
              if (z == x) continue;
  
              List<Node> cond = sepset(z, x);
  
              if (cond != null && !cond.contains(y) && !graph.isParentOf(y, x) && !graph.isParentOf(y, z)) {
                  graph.setEndpoint(x, y, Endpoint.ARROW);
                  graph.setEndpoint(z, y, Endpoint.ARROW);
                  oriented = true;
              }
          }
  
          List<Node> start = new ArrayList<>();
          start.add(y);
  
          meekRules.orientImplied(graph, start);
          return oriented;
      }
  
      private boolean orientColliders(Node x, Node y) {
          boolean oriented = false;
          List<Node> start = new ArrayList<>();
          start.add(y);
  
          for (Node z : graph.getAdjacentNodes(y)) {
              if (z == x) continue;
  
              SearchGraphUtils.CpcTripleType type = SearchGraphUtils.getCpcTripleType2(x, y, z, getIndependenceTest(), -1, graph);
  
              if (type == SearchGraphUtils.CpcTripleType.COLLIDER &&
                      isArrowpointAllowed(x, y, knowledge) &&
                      isArrowpointAllowed(z, y, knowledge)) {
                  graph.removeEdge(x, y);
                  graph.removeEdge(z, y);
                  graph.addDirectedEdge(x, y);
                  graph.addDirectedEdge(z, y);
                  oriented = true;
              } else if (type == SearchGraphUtils.CpcTripleType.AMBIGUOUS) {
                  graph.addAmbiguousTriple(x, y, z);
              }
  
              start.add(z);
  
              for (Node w : graph.getAdjacentNodes(z)) {
                  if (w == y) continue;
  
                  SearchGraphUtils.CpcTripleType _type = SearchGraphUtils.getCpcTripleType2(w, z, y, getIndependenceTest(), -1, graph);
  
                  if (_type == SearchGraphUtils.CpcTripleType.COLLIDER &&
                          isArrowpointAllowed(x, y, knowledge) &&
                          isArrowpointAllowed(z, y, knowledge)) {
                      graph.removeEdge(w, z);
                      graph.removeEdge(y, z);
                      graph.addDirectedEdge(w, z);
                      graph.addDirectedEdge(y, z);
                      oriented = true;
                  } else if (_type == SearchGraphUtils.CpcTripleType.AMBIGUOUS) {
                      graph.addAmbiguousTriple(x, y, z);
                  }
              }
          }
  
          meekRules.orientImplied(graph, start);
          renderUnambiguousWherePossible();
          return oriented;
      }
  
      /**
       * Checks if an arrowpoint is allowed by background knowledge.
       */
      public static boolean isArrowpointAllowed(Object from, Object to,
                                                IKnowledge knowledge) {
          if (knowledge == null) {
              return true;
          }
          return !knowledge.isRequired(to.toString(), from.toString()) &&
                  !knowledge.isForbidden(from.toString(), to.toString());
      }
  }
  
  
  