///////////////////////////////////////////////////////////////////////////////
// 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.TetradLogger;
import java.util.*;
/**
 * Extends Erin Korber's implementation of the Fast Causal Inference algorithm (found in FCI.java) with Jiji Zhang's
 * Augmented FCI rules (found in sec. 4.1 of Zhang's 2006 PhD dissertation, "Causal Inference and Reasoning in Causally
 * Insufficient Systems").
 * <p>
 * This class is based off a copy of FCI.java taken from the repository on 2008/12/16, revision 7306. The extension is
 * done by extending doFinalOrientation() with methods for Zhang's rules R5-R10 which implements the augmented search.
 * (By a remark of Zhang's, the rule applications can be staged in this way.)
 *
 * @author Erin Korber, June 2004
 * @author Alex Smith, December 2008
 * @author Joseph Ramsey
 * @author Choh-Man Teng
 */
public final class DagToPag {
    private final Graph dag;
//    private final IndTestDSep dsep;
    /*
     * The background knowledge.
     */
    private IKnowledge knowledge = new Knowledge2();
    /**
     * Glag for complete rule set, true if should use complete rule set, false otherwise.
     */
    private boolean completeRuleSetUsed = false;
    /**
     * The logger to use.
     */
    private TetradLogger logger = TetradLogger.getInstance();
    /**
     * True iff verbose output should be printed.
     */
    private boolean verbose = false;
    private int maxPathLength = -1;
    private Graph truePag;
    //============================CONSTRUCTORS============================//
    /**
     * Constructs a new FCI search for the given independence test and background knowledge.
     */
    public DagToPag(Graph dag) {
        this.dag = dag;
    }
    //========================PUBLIC METHODS==========================//
    public Graph convert() {
        if (dag == null) throw new NullPointerException();
        logger.log("info", "Starting DAG to PAG.");
        if (verbose) {
            System.out.println("DAG to PAG: Starting adjacency search");
        }
        Graph graph = calcAdjacencyGraph();
        if (verbose) {
            System.out.println("DAG to PAG: Starting collider orientation");
        }
        orientUnshieldedColliders2(graph, dag);
        if (verbose) {
            System.out.println("DAG to PAG: Starting final orientation");
        }
        final FciOrient fciOrient = new FciOrient(new DagSepsets(dag));
        fciOrient.setCompleteRuleSetUsed(completeRuleSetUsed);
        fciOrient.skipDiscriminatingPathRule(false);
        fciOrient.setChangeFlag(false);
        fciOrient.setMaxPathLength(maxPathLength);
        fciOrient.doFinalOrientation(graph);
        if (verbose) {
            System.out.println("Finishing final orientation");
        }
        return graph;
    }
    private Graph calcAdjacencyGraph() {
        List<Node> allNodes = dag.getNodes();
        List<Node> measured = new ArrayList<>();
        for (Node node : allNodes) {
            if (node.getNodeType() == NodeType.MEASURED) {
                measured.add(node);
            }
        }
        Graph graph = new EdgeListGraphSingleConnections(measured);
        for (int i = 0; i < measured.size(); i++) {
            addAdjacencies(measured.get(i), dag, graph);
        }
        return graph;
    }
    public static Set<Node> addAdjacencies(Node x, Graph dag, Graph builtGraph) {
        if (x.getNodeType() != NodeType.MEASURED) throw new IllegalArgumentException();
        final LinkedList<Node> path = new LinkedList<>();
        path.add(x);
        Set<Node> induced = new HashSet<>();
        for (Node b : dag.getAdjacentNodes(x)) {
            collectInducedNodesVisit2(dag, x, b, path, builtGraph);
        }
        return induced;
    }
    public static void collectInducedNodesVisit2(Graph dag, Node x, Node b, LinkedList<Node> path,
                                                 Graph builtGraph) {
        if (path.contains(b)) {
            return;
        }
        path.addLast(b);
        if (b.getNodeType() == NodeType.MEASURED && path.size() >= 2) {
            Node y = path.getLast();
            for (int i = 0; i < path.size() - 2; i++) {
                Node _a = path.get(i);
                Node _b = path.get(i + 1);
                Node _c = path.get(i + 2);
                if (_b.getNodeType() == NodeType.MEASURED) {
                    if (!dag.isDefCollider(_a, _b, _c)) {
                        path.removeLast();
                        return;
                    }
                }
                if (dag.isDefCollider(_a, _b, _c)) {
                    if (!(dag.isAncestorOf(_b, x) || dag.isAncestorOf(_b, y))) {
                        path.removeLast();
                        return;
                    }
                }
            }
            if (!builtGraph.isAdjacentTo(x, b)) {
                builtGraph.addEdge(Edges.nondirectedEdge(x, b));
            }
        }
        for (Node c : dag.getAdjacentNodes(b)) {
            collectInducedNodesVisit2(dag, x, c, path, builtGraph);
        }
        path.removeLast();
    }
    private void orientUnshieldedColliders(Graph graph, Graph dag) {
        graph.reorientAllWith(Endpoint.CIRCLE);
        List<Node> allNodes = dag.getNodes();
        List<Node> measured = new ArrayList<>();
        for (Node node : allNodes) {
            if (node.getNodeType() == NodeType.MEASURED) {
                measured.add(node);
            }
        }
        for (Node b : measured) {
            List<Node> adjb = graph.getAdjacentNodes(b);
            if (adjb.size() < 2) continue;
            for (int i = 0; i < adjb.size(); i++) {
                for (int j = i + 1; j < adjb.size(); j++) {
                    Node a = adjb.get(i);
                    Node c = adjb.get(j);
                    if (graph.isDefCollider(a, b, c)) {
                        continue;
                    }
                    if (graph.isAdjacentTo(a, c)) {
                        continue;
                    }
                    boolean found = foundCollider(dag, a, b, c);
                    if (found) {
                        if (verbose) {
                            System.out.println("Orienting collider " + a + "*->" + b + "<-*" + c);
                        }
                        graph.setEndpoint(a, b, Endpoint.ARROW);
                        graph.setEndpoint(c, b, Endpoint.ARROW);
                    }
                }
            }
        }
    }
    private void orientUnshieldedColliders2(Graph graph, Graph dag) {
//        graph.reorientAllWith(Endpoint.CIRCLE);
        List<Node> allNodes = dag.getNodes();
        List<Node> measured = new ArrayList<>();
        for (Node node : allNodes) {
            if (node.getNodeType() == NodeType.MEASURED) {
                measured.add(node);
            }
        }
        for (Node b : measured) {
            List<Node> adjb = graph.getAdjacentNodes(b);
            if (adjb.size() < 2) continue;
            for (int i = 0; i < adjb.size(); i++) {
                for (int j = i + 1; j < adjb.size(); j++) {
                    Node a = adjb.get(i);
                    Node c = adjb.get(j);
//                    List<Node> d = new ArrayList<>();
//                    d.add(a);
//                    d.add(c);
//
//                    List<Node> anc = dag.getAncestors(d);
                    if (!graph.isAdjacentTo(a, c) && !dag.isAncestorOf(b, a) && !dag.isAncestorOf(b, c)) {// !anc.contains(b)) {
//                        if (verbose) {
//                            System.out.println("Orienting collider " + a + "*->" + b + "<-*" + c);
//                        }
                        graph.setEndpoint(a, b, Endpoint.ARROW);
                        graph.setEndpoint(c, b, Endpoint.ARROW);
                    }
                }
            }
        }
    }
    private boolean foundCollider(Graph dag, Node a, Node b, Node c) {
        boolean ipba = existsInducingPathInto(b, a, dag);
        boolean ipbc = existsInducingPathInto(b, c, dag);
        if (!(ipba && ipbc)) {
            printTrueDefCollider(a, b, c, false);
            return false;
        }
        printTrueDefCollider(a, b, c, true);
        return true;
    }
    private void printTrueDefCollider(Node a, Node b, Node c, boolean found) {
        if (truePag != null) {
            final boolean defCollider = truePag.isDefCollider(a, b, c);
            if (verbose) {
                if (!found && defCollider) {
                    System.out.println("FOUND COLLIDER FCI");
                } else if (found && !defCollider) {
                    System.out.println("DIDN'T FIND COLLIDER FCI");
                }
            }
        }
    }
    public static boolean existsInducingPathInto(Node x, Node y, Graph graph) {
        if (x.getNodeType() != NodeType.MEASURED) throw new IllegalArgumentException();
        if (y.getNodeType() != NodeType.MEASURED) throw new IllegalArgumentException();


Answer:         final LinkedList<Node> path = new LinkedList<>();