UniversalIsomorphismTester.java

/* Copyright (C) 2002-2007  Stephane Werner <mail@ixelis.net>
 *
 *  This code has been kindly provided by Stephane Werner
 *  and Thierry Hanser from IXELIS mail@ixelis.net
 *
 *  IXELIS sarl - Semantic Information Systems
 *  17 rue des C???res 67200 Strasbourg, France
 *  Tel/Fax : +33(0)3 88 27 81 39 Email: mail@ixelis.net
 *
 *  CDK Contact: cdk-devel@lists.sf.net
 *
 *  This program is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public License
 *  as published by the Free Software Foundation; either version 2.1
 *  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 Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 */
package org.openscience.cdk.isomorphism;

import org.openscience.cdk.CDKConstants;
import org.openscience.cdk.exception.CDKException;
import org.openscience.cdk.interfaces.IAtom;
import org.openscience.cdk.interfaces.IAtomContainer;
import org.openscience.cdk.interfaces.IBond;
import org.openscience.cdk.isomorphism.matchers.IQueryAtom;
import org.openscience.cdk.isomorphism.matchers.IQueryAtomContainer;
import org.openscience.cdk.isomorphism.matchers.IQueryBond;
import org.openscience.cdk.isomorphism.mcss.RGraph;
import org.openscience.cdk.isomorphism.mcss.RMap;
import org.openscience.cdk.isomorphism.mcss.RNode;
import org.openscience.cdk.tools.manipulator.BondManipulator;

import java.util.ArrayList;
import java.util.BitSet;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.Map;

/**
 *  This class implements a multipurpose structure comparison tool.
 *  It allows to find maximal common substructure, find the
 *  mapping of a substructure in another structure, and the mapping of
 *  two isomorphic structures.
 *
 *  <p>Structure comparison may be associated to bond constraints
 *  (mandatory bonds, e.g. scaffolds, reaction cores,...) on each source graph.
 *  The constraint flexibility allows a number of interesting queries.
 *  The substructure analysis relies on the RGraph generic class (see: RGraph)
 *  This class implements the link between the RGraph model and the
 *  the CDK model in this way the {@link RGraph} remains independent and may be used
 *  in other contexts.
 *
 *  <p>This algorithm derives from the algorithm described in
 *  {@cdk.cite HAN90} and modified in the thesis of T. Hanser {@cdk.cite HAN93}.
 *
 *  <p>With the {@link #isSubgraph(IAtomContainer, IAtomContainer)} method,
 *  the second, and only the second argument <b>may</b> be a {@link IQueryAtomContainer},
 *  which allows one to do SMARTS or MQL like queries.
 *  The first {@link IAtomContainer} must never be an {@link IQueryAtomContainer}.
 *  An example:<pre>
 *  SmilesParser sp = new SmilesParser(DefaultChemObjectBuilder.getInstance());
 *  IAtomContainer atomContainer = sp.parseSmiles("CC(=O)OC(=O)C"); // acetic acid anhydride
 *  IAtomContainer SMILESquery = sp.parseSmiles("CC"); // ethane
 *  IQueryAtomContainer query = IQueryAtomContainerCreator.createBasicQueryContainer(SMILESquery);
 *  boolean isSubstructure = UniversalIsomorphismTester.isSubgraph(atomContainer, query);
 *  </pre>
 *
 *  <p><font color="#FF0000">WARNING</font>:
 *    As a result of the adjacency perception used in this algorithm
 *    there is a single limitation: cyclopropane and isobutane are seen as isomorph.
 *    This is due to the fact that these two compounds are the only ones where
 *    each bond is connected two each other bond (bonds are fully connected)
 *    with the same number of bonds and still they have different structures
 *    The algorithm could be easily enhanced with a simple atom mapping manager
 *    to provide an atom level overlap definition that would reveal this case.
 *    We decided not to penalize the whole procedure because of one single
 *    exception query. Furthermore isomorphism may be discarded since  the number of atoms are
 *    not the same (3 != 4) and in most case this will be already
 *    screened out by a fingerprint based filtering.
 *    It is possible to add a special treatment for this special query.
 *    Be reminded that this algorithm matches bonds only.
 * </p>
 * <p>
 * <b>Note</b>While most isomorphism queries involve a multi-atom query structure
 * there may be cases in which the query atom is a single atom. In such a case
 * a mapping of target bonds to query bonds is not feasible. In such a case, the RMap objects
 * correspond to atom indices rather than bond indices. In general, this will not affect user
 * code and the same sequence of method calls for matching multi-atom query structures will
 * work for single atom query structures as well.
 * </p>
 *
 * @author      Stephane Werner from IXELIS mail@ixelis.net
 * @cdk.created 2002-07-17
 * @cdk.require java1.4+
 * @cdk.module  standard
 * @cdk.githash
 */
public class UniversalIsomorphismTester {

    final static int ID1     = 0;
    final static int ID2     = 1;
    private long     start;
    private long     timeout = -1;

    public UniversalIsomorphismTester() {

    }

    ///////////////////////////////////////////////////////////////////////////
    //                            Query Methods
    //
    // This methods are simple applications of the RGraph model on atom containers
    // using different constrains and search options. They give an example of the
    // most common queries but of course it is possible to define other type of
    // queries exploiting the constrain and option combinations
    //

    ////
    // Isomorphism search

    /**
     * Tests if g1 and g2 are isomorph.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     true if the 2 molecule are isomorph
     * @throws     CDKException if the first molecule is an instance of IQueryAtomContainer
     */
    public boolean isIsomorph(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        if (g1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        if (g2.getAtomCount() != g1.getAtomCount()) return false;
        // check single atom case
        if (g2.getAtomCount() == 1) {
            IAtom atom = g1.getAtom(0);
            IAtom atom2 = g2.getAtom(0);
            if (atom instanceof IQueryAtom) {
                IQueryAtom qAtom = (IQueryAtom) atom;
                return qAtom.matches(g2.getAtom(0));
            } else if (atom2 instanceof IQueryAtom) {
                IQueryAtom qAtom = (IQueryAtom) atom2;
                return qAtom.matches(g1.getAtom(0));
            } else {
                String atomSymbol = atom2.getSymbol();
                return g1.getAtom(0).getSymbol().equals(atomSymbol);
            }
        }
        return (getIsomorphMap(g1, g2) != null);
    }

    /**
     * Returns the first isomorph mapping found or null.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the first isomorph mapping found projected of g1. This is a List of RMap objects containing Ids of matching bonds.
     */
    public List<RMap> getIsomorphMap(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        if (g1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        List<RMap> result = null;

        List<List<RMap>> rMapsList = search(g1, g2, getBitSet(g1), getBitSet(g2), false, false);

        if (!rMapsList.isEmpty()) {
            result = rMapsList.get(0);
        }

        return result;
    }

    /**
     * Returns the first isomorph 'atom mapping' found for g2 in g1.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the first isomorph atom mapping found projected on g1.
     * This is a List of RMap objects containing Ids of matching atoms.
     * @throws CDKException if the first molecules is not an instance of {@link IQueryAtomContainer}
     */
    public List<RMap> getIsomorphAtomsMap(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        if (g1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        List<RMap> list = checkSingleAtomCases(g1, g2);
        if (list == null) {
            return makeAtomsMapOfBondsMap(getIsomorphMap(g1, g2), g1, g2);
        } else if (list.isEmpty()) {
            return null;
        } else {
            return list;
        }
    }

    /**
     * Returns all the isomorph 'mappings' found between two
     * atom containers.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the list of all the 'mappings'
     */
    public List<List<RMap>> getIsomorphMaps(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        return search(g1, g2, getBitSet(g1), getBitSet(g2), true, true);
    }

    /////
    // Subgraph search

    /**
     * Returns all the subgraph 'bond mappings' found for g2 in g1.
     * This is an {@link List} of {@link List}s of {@link RMap} objects.
     *
     * Note that if the query molecule is a single atom, then bond mappings
     * cannot be defined. In such a case, the {@link RMap} object refers directly to
     * atom - atom mappings. Thus RMap.id1 is the index of the target atom
     * and RMap.id2 is the index of the matching query atom (in this case,
     * it will always be 0). Note that in such a case, there is no need
     * to call {@link #makeAtomsMapsOfBondsMaps(List, IAtomContainer, IAtomContainer)},
     * though if it is called, then the
     * return value is simply the same as the return value of this method.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the list of all the 'mappings' found projected of g1
     *
     * @see #makeAtomsMapsOfBondsMaps(List, IAtomContainer, IAtomContainer)
     */
    public List<List<RMap>> getSubgraphMaps(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        return search(g1, g2, new BitSet(), getBitSet(g2), true, true);
    }

    /**
     * Returns the first subgraph 'bond mapping' found for g2 in g1.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the first subgraph bond mapping found projected on g1. This is a {@link List} of
     *             {@link RMap} objects containing Ids of matching bonds.
     */
    public List<RMap> getSubgraphMap(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        List<RMap> result = null;
        List<List<RMap>> rMapsList = search(g1, g2, new BitSet(), getBitSet(g2), false, false);

        if (!rMapsList.isEmpty()) {
            result = rMapsList.get(0);
        }

        return result;
    }

    /**
     * Returns all subgraph 'atom mappings' found for g2 in g1, where g2 must be a substructure
     * of g1. If it is not a substructure, null will be returned.
     * This is an {@link List} of {@link List}s of {@link RMap} objects.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  substructure to be mapped. May be an {@link IQueryAtomContainer}.
     * @return     all subgraph atom mappings found projected on g1. This is a
     *             {@link List} of {@link RMap} objects containing Ids of matching atoms.
     */
    public List<List<RMap>> getSubgraphAtomsMaps(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        List<RMap> list = checkSingleAtomCases(g1, g2);
        if (list == null) {
            return makeAtomsMapsOfBondsMaps(getSubgraphMaps(g1, g2), g1, g2);
        } else {
            List<List<RMap>> atomsMap = new ArrayList<List<RMap>>();
            atomsMap.add(list);
            return atomsMap;
        }
    }

    /**
     * Returns the first subgraph 'atom mapping' found for g2 in g1, where g2 must be a substructure
     * of g1. If it is not a substructure, null will be returned.
     *
     * @param  g1 first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2 substructure to be mapped. May be an {@link IQueryAtomContainer}.
     * @return    the first subgraph atom mapping found projected on g1.
     *            This is a {@link List} of {@link RMap} objects containing Ids of matching atoms.
     */
    public List<RMap> getSubgraphAtomsMap(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        List<RMap> list = checkSingleAtomCases(g1, g2);
        if (list == null) {
            return makeAtomsMapOfBondsMap(getSubgraphMap(g1, g2), g1, g2);
        } else if (list.isEmpty()) {
            return null;
        } else {
            return list;
        }
    }

    /**
     * Tests if g2 a subgraph of g1.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     true if g2 a subgraph on g1
     */
    public boolean isSubgraph(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        if (g1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        if (g2.getAtomCount() > g1.getAtomCount()) return false;
        // test for single atom case
        if (g2.getAtomCount() == 1) {
            IAtom atom = g2.getAtom(0);
            for (int i = 0; i < g1.getAtomCount(); i++) {
                IAtom atom2 = g1.getAtom(i);
                if (atom instanceof IQueryAtom) {
                    IQueryAtom qAtom = (IQueryAtom) atom;
                    if (qAtom.matches(atom2)) return true;
                } else if (atom2 instanceof IQueryAtom) {
                    IQueryAtom qAtom = (IQueryAtom) atom2;
                    if (qAtom.matches(atom)) return true;
                } else {
                    if (atom2.getSymbol().equals(atom.getSymbol())) return true;
                }
            }
            return false;
        }
        if (!testSubgraphHeuristics(g1, g2)) return false;
        return (getSubgraphMap(g1, g2) != null);
    }

    ////
    // Maximum common substructure search

    /**
     * Returns all the maximal common substructure between two atom containers.
     *
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     the list of all the maximal common substructure
     *             found projected of g1 (list of AtomContainer )
     */
    public List<IAtomContainer> getOverlaps(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        start = System.currentTimeMillis();
        List<List<RMap>> rMapsList = search(g1, g2, new BitSet(), new BitSet(), true, false);

        // projection on G1
        List<IAtomContainer> graphList = projectList(rMapsList, g1, ID1);

        // reduction of set of solution (isomorphism and substructure
        // with different 'mappings'

        return getMaximum(graphList);
    }

    /**
     * Transforms an AtomContainer into a {@link BitSet} (which's size = number of bond
     * in the atomContainer, all the bit are set to true).
     *
     * @param  ac  {@link IAtomContainer} to transform
     * @return     The bitSet
     */
    public static BitSet getBitSet(IAtomContainer ac) {
        BitSet bs;
        int n = ac.getBondCount();

        if (n != 0) {
            bs = new BitSet(n);
            for (int i = 0; i < n; i++) {
                bs.set(i);
            }
        } else {
            bs = new BitSet();
        }

        return bs;
    }

    //////////////////////////////////////////////////
    //          Internal methods

    /**
     * Builds the {@link RGraph} ( resolution graph ), from two atomContainer
     * (description of the two molecules to compare)
     * This is the interface point between the CDK model and
     * the generic MCSS algorithm based on the RGRaph.
     *
     * @param  g1  Description of the first molecule
     * @param  g2  Description of the second molecule
     * @return     the rGraph
     */
    public static RGraph buildRGraph(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        RGraph rGraph = new RGraph();
        nodeConstructor(rGraph, g1, g2);
        arcConstructor(rGraph, g1, g2);
        return rGraph;
    }

    /**
     * General {@link RGraph} parsing method (usually not used directly)
     * This method is the entry point for the recursive search
     * adapted to the atom container input.
     *
     * @param  g1                first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2                second molecule. May be an {@link IQueryAtomContainer}.
     * @param  c1                initial condition ( bonds from g1 that
     *                           must be contains in the solution )
     * @param  c2                initial condition ( bonds from g2 that
     *                           must be contains in the solution )
     * @param  findAllStructure  if false stop at the first structure found
     * @param  findAllMap        if true search all the 'mappings' for one same
     *                           structure
     * @return                   a List of Lists of {@link RMap} objects that represent the search solutions
     */
    public List<List<RMap>> search(IAtomContainer g1, IAtomContainer g2, BitSet c1, BitSet c2,
            boolean findAllStructure, boolean findAllMap) throws CDKException {
        // remember start time
        start = System.currentTimeMillis();

        // handle single query atom case separately
        if (g2.getAtomCount() == 1) {
            List<List<RMap>> matches = new ArrayList<List<RMap>>();
            IAtom queryAtom = g2.getAtom(0);

            // we can have a IQueryAtomContainer *or* an IAtomContainer
            if (queryAtom instanceof IQueryAtom) {
                IQueryAtom qAtom = (IQueryAtom) queryAtom;
                for (IAtom atom : g1.atoms()) {
                    if (qAtom.matches(atom)) {
                        List<RMap> lmap = new ArrayList<RMap>();
                        lmap.add(new RMap(g1.indexOf(atom), 0));
                        matches.add(lmap);
                    }
                }
            } else {
                for (IAtom atom : g1.atoms()) {
                    if (queryAtom.getSymbol().equals(atom.getSymbol())) {
                        List<RMap> lmap = new ArrayList<RMap>();
                        lmap.add(new RMap(g1.indexOf(atom), 0));
                        matches.add(lmap);
                    }
                }
            }
            return matches;
        }

        // reset result
        List<List<RMap>> rMapsList = new ArrayList<List<RMap>>();

        // build the RGraph corresponding to this problem
        RGraph rGraph = buildRGraph(g1, g2);
        // Set time data
        rGraph.setTimeout(timeout);
        rGraph.setStart(start);
        // parse the RGraph with the given constrains and options
        rGraph.parse(c1, c2, findAllStructure, findAllMap);
        List<BitSet> solutionList = rGraph.getSolutions();

        // conversions of RGraph's internal solutions to G1/G2 mappings
        for (BitSet set : solutionList) {
            List<RMap> rmap = rGraph.bitSetToRMap(set);
            if (checkQueryAtoms(rmap, g1, g2)) rMapsList.add(rmap);
        }

        return rMapsList;
    }

    /**
     * Checks that {@link IQueryAtom}'s correctly match consistently.
     *
     * @param bondmap bond mapping
     * @param g1 target graph
     * @param g2 query graph
     * @return the atom matches are consistent
     */
    private boolean checkQueryAtoms(List<RMap> bondmap, IAtomContainer g1, IAtomContainer g2) {
        if (!(g2 instanceof IQueryAtomContainer)) return true;
        List<RMap> atommap = makeAtomsMapOfBondsMap(bondmap, g1, g2);
        for (RMap rmap : atommap) {
            IAtom a1 = g1.getAtom(rmap.getId1());
            IAtom a2 = g2.getAtom(rmap.getId2());
            if (a2 instanceof IQueryAtom) {
                if (!((IQueryAtom) a2).matches(a1)) return false;
            }
        }
        return true;
    }

    //////////////////////////////////////
    //    Manipulation tools

    /**
     * Projects a list of {@link RMap} on a molecule.
     *
     * @param  rMapList  the list to project
     * @param  g         the molecule on which project
     * @param  id        the id in the {@link RMap} of the molecule g
     * @return           an AtomContainer
     */
    public static IAtomContainer project(List<RMap> rMapList, IAtomContainer g, int id) {
        IAtomContainer ac = g.getBuilder().newInstance(IAtomContainer.class);

        Map<IAtom, IAtom> table = new HashMap<IAtom, IAtom>();
        IAtom a1;
        IAtom a2;
        IAtom a;
        IBond bond;

        for (Iterator<RMap> i = rMapList.iterator(); i.hasNext();) {
            RMap rMap = i.next();
            if (id == UniversalIsomorphismTester.ID1) {
                bond = g.getBond(rMap.getId1());
            } else {
                bond = g.getBond(rMap.getId2());
            }

            a = bond.getBegin();
            a1 = (IAtom) table.get(a);

            if (a1 == null) {
                try {
                    a1 = (IAtom) a.clone();
                } catch (CloneNotSupportedException e) {
                    e.printStackTrace();
                }
                ac.addAtom(a1);
                table.put(a, a1);
            }

            a = bond.getEnd();
            a2 = table.get(a);

            if (a2 == null) {
                try {
                    a2 = (IAtom) a.clone();
                } catch (CloneNotSupportedException e) {
                    e.printStackTrace();
                }
                ac.addAtom(a2);
                table.put(a, a2);
            }
            IBond newBond = g.getBuilder().newInstance(IBond.class, a1, a2, bond.getOrder());
            newBond.setFlag(CDKConstants.ISAROMATIC, bond.getFlag(CDKConstants.ISAROMATIC));
            ac.addBond(newBond);
        }
        return ac;
    }

    /**
     * Projects a list of RMapsList on a molecule.
     *
     * @param  rMapsList  list of RMapsList to project
     * @param  g          the molecule on which project
     * @param  id         the id in the RMap of the molecule g
     * @return            a list of AtomContainer
     */
    public static List<IAtomContainer> projectList(List<List<RMap>> rMapsList, IAtomContainer g, int id) {
        List<IAtomContainer> graphList = new ArrayList<IAtomContainer>();

        for (List<RMap> rMapList : rMapsList) {
            IAtomContainer ac = project(rMapList, g, id);
            graphList.add(ac);
        }
        return graphList;
    }

    /**
     * Removes all redundant solution.
     *
     * @param  graphList  the list of structure to clean
     * @return            the list cleaned
     * @throws CDKException if there is a problem in obtaining subgraphs
     */
    private List<IAtomContainer> getMaximum(List<IAtomContainer> graphList) throws CDKException {
        List<IAtomContainer> reducedGraphList = new ArrayList<IAtomContainer>();
        reducedGraphList.addAll(graphList);

        for (int i = 0; i < graphList.size(); i++) {
            IAtomContainer gi = graphList.get(i);

            for (int j = i + 1; j < graphList.size(); j++) {
                IAtomContainer gj = graphList.get(j);

                // Gi included in Gj or Gj included in Gi then
                // reduce the irrelevant solution
                if (isSubgraph(gj, gi)) {
                    reducedGraphList.remove(gi);
                } else if (isSubgraph(gi, gj)) {
                    reducedGraphList.remove(gj);
                }
            }
        }
        return reducedGraphList;
    }

    /**
     *  Checks for single atom cases before doing subgraph/isomorphism search.
     *
     * @param  g1  AtomContainer to match on. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  AtomContainer as query. May be an {@link IQueryAtomContainer}.
     * @return     {@link List} of {@link List} of {@link RMap} objects for the Atoms (not Bonds!), null if no single atom case
     * @throws     CDKException if the first molecule is an instance of IQueryAtomContainer
    */
    public static List<RMap> checkSingleAtomCases(IAtomContainer g1, IAtomContainer g2) throws CDKException {
        if (g1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        if (g2.getAtomCount() == 1) {
            List<RMap> arrayList = new ArrayList<RMap>();
            IAtom atom = g2.getAtom(0);
            if (atom instanceof IQueryAtom) {
                IQueryAtom qAtom = (IQueryAtom) atom;
                for (int i = 0; i < g1.getAtomCount(); i++) {
                    if (qAtom.matches(g1.getAtom(i))) arrayList.add(new RMap(i, 0));
                }
            } else {
                String atomSymbol = atom.getSymbol();
                for (int i = 0; i < g1.getAtomCount(); i++) {
                    if (g1.getAtom(i).getSymbol().equals(atomSymbol)) arrayList.add(new RMap(i, 0));
                }
            }
            return arrayList;
        } else if (g1.getAtomCount() == 1) {
            List<RMap> arrayList = new ArrayList<RMap>();
            IAtom atom = g1.getAtom(0);
            for (int i = 0; i < g2.getAtomCount(); i++) {
                IAtom atom2 = g2.getAtom(i);
                if (atom2 instanceof IQueryAtom) {
                    IQueryAtom qAtom = (IQueryAtom) atom2;
                    if (qAtom.matches(atom)) arrayList.add(new RMap(0, i));
                } else {
                    if (atom2.getSymbol().equals(atom.getSymbol())) arrayList.add(new RMap(0, i));
                }
            }
            return arrayList;
        } else {
            return null;
        }
    }

    /**
     *  This makes maps of matching atoms out of a maps of matching bonds as produced by the
     *  get(Subgraph|Ismorphism)Maps methods.
     *
     * @param  l   The list produced by the getMap method.
     * @param  g1  The first atom container. Must not be a {@link IQueryAtomContainer}.
     * @param  g2  The second one (first and second as in getMap). May be an {@link IQueryAtomContainer}.
     * @return     A List of {@link List}s of {@link RMap} objects of matching Atoms.
     */
    public static List<List<RMap>> makeAtomsMapsOfBondsMaps(List<List<RMap>> l, IAtomContainer g1, IAtomContainer g2) {
        if (l == null) {
            return l;
        }
        if (g2.getAtomCount() == 1) return l; // since the RMap is already an atom-atom mapping
        List<List<RMap>> result = new ArrayList<List<RMap>>();
        for (List<RMap> l2 : l) {
            result.add(makeAtomsMapOfBondsMap(l2, g1, g2));
        }
        return result;
    }

    /**
     *  This makes a map of matching atoms out of a map of matching bonds as produced by the
     *  get(Subgraph|Ismorphism)Map methods.
     *
     * @param  l   The list produced by the getMap method.
     * @param  g1  first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  g2  second molecule. May be an {@link IQueryAtomContainer}.
     * @return     The mapping found projected on g1. This is a {@link List} of {@link RMap} objects
     *             containing Ids of matching atoms.
     */
    public static List<RMap> makeAtomsMapOfBondsMap(List<RMap> l, IAtomContainer g1, IAtomContainer g2) {
        if (l == null) return (l);
        List<RMap> result = new ArrayList<RMap>();
        for (int i = 0; i < l.size(); i++) {
            IBond bond1 = g1.getBond(l.get(i).getId1());
            IBond bond2 = g2.getBond(l.get(i).getId2());
            IAtom[] atom1 = BondManipulator.getAtomArray(bond1);
            IAtom[] atom2 = BondManipulator.getAtomArray(bond2);
            for (int j = 0; j < 2; j++) {
                List<IBond> bondsConnectedToAtom1j = g1.getConnectedBondsList(atom1[j]);
                for (int k = 0; k < bondsConnectedToAtom1j.size(); k++) {
                    if (!bondsConnectedToAtom1j.get(k).equals(bond1)) {
                        IBond testBond = (IBond) bondsConnectedToAtom1j.get(k);
                        for (int m = 0; m < l.size(); m++) {
                            IBond testBond2;
                            if (((RMap) l.get(m)).getId1() == g1.indexOf(testBond)) {
                                testBond2 = g2.getBond(((RMap) l.get(m)).getId2());
                                for (int n = 0; n < 2; n++) {
                                    List<IBond> bondsToTest = g2.getConnectedBondsList(atom2[n]);
                                    if (bondsToTest.contains(testBond2)) {
                                        RMap map;
                                        if (j == n) {
                                            map = new RMap(g1.indexOf(atom1[0]), g2.indexOf(atom2[0]));
                                        } else {
                                            map = new RMap(g1.indexOf(atom1[1]), g2.indexOf(atom2[0]));
                                        }
                                        if (!result.contains(map)) {
                                            result.add(map);
                                        }
                                        RMap map2;
                                        if (j == n) {
                                            map2 = new RMap(g1.indexOf(atom1[1]), g2.indexOf(atom2[1]));
                                        } else {
                                            map2 = new RMap(g1.indexOf(atom1[0]), g2.indexOf(atom2[1]));
                                        }
                                        if (!result.contains(map2)) {
                                            result.add(map2);
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }
        }
        return result;
    }

    /**
     *  Builds  the nodes of the {@link RGraph} ( resolution graph ), from
     *  two atom containers (description of the two molecules to compare)
     *
     * @param  gr   the target RGraph
     * @param  ac1   first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  ac2   second molecule. May be an {@link IQueryAtomContainer}.
     * @throws CDKException if it takes too long to identify overlaps
     */
    private static void nodeConstructor(RGraph gr, IAtomContainer ac1, IAtomContainer ac2) throws CDKException {
        if (ac1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        // resets the target graph.
        gr.clear();

        // compares each bond of G1 to each bond of G2
        for (int i = 0; i < ac1.getBondCount(); i++) {
            for (int j = 0; j < ac2.getBondCount(); j++) {
                IBond bondA2 = ac2.getBond(j);
                if (bondA2 instanceof IQueryBond) {
                    IQueryBond queryBond = (IQueryBond) bondA2;
                    IQueryAtom atom1 = (IQueryAtom) (bondA2.getBegin());
                    IQueryAtom atom2 = (IQueryAtom) (bondA2.getEnd());
                    IBond bond = ac1.getBond(i);
                    if (queryBond.matches(bond)) {
                        // ok, bonds match
                        if (atom1.matches(bond.getBegin()) && atom2.matches(bond.getEnd())
                                || atom1.matches(bond.getEnd()) && atom2.matches(bond.getBegin())) {
                            // ok, atoms match in either order
                            gr.addNode(new RNode(i, j));
                        }
                    }
                } else {
                    // if both bonds are compatible then create an association node
                    // in the resolution graph
                    if (( // bond type conditions
                            ( // same bond order and same aromaticity flag (either both on or off)
                            ac1.getBond(i).getOrder() == ac2.getBond(j).getOrder() && ac1.getBond(i).getFlag(
                                    CDKConstants.ISAROMATIC) == ac2.getBond(j).getFlag(CDKConstants.ISAROMATIC)) || ( // both bond are aromatic
                            ac1.getBond(i).getFlag(CDKConstants.ISAROMATIC) && ac2.getBond(j).getFlag(
                                    CDKConstants.ISAROMATIC)))
                            && ( // atom type conditions
                            ( // a1 = a2 && b1 = b2
                              ac1.getBond(i).getBegin().getSymbol().equals(ac2.getBond(j).getBegin().getSymbol()) && ac1
                                    .getBond(i).getEnd().getSymbol().equals(ac2.getBond(j).getEnd().getSymbol())) || ( // a1 = b2 && b1 = a2
                                                                                                                       ac1.getBond(i).getBegin().getSymbol().equals(ac2.getBond(j).getEnd().getSymbol()) && ac1
                                    .getBond(i).getEnd().getSymbol().equals(ac2.getBond(j).getBegin().getSymbol())))) {
                        gr.addNode(new RNode(i, j));
                    }
                }
            }
        }
    }

    /**
     *  Build edges of the {@link RGraph}s.
     *  This method create the edge of the RGraph and
     *  calculates the incompatibility and neighborhood
     *  relationships between RGraph nodes.
     *
     * @param  gr   the rGraph
     * @param  ac1   first molecule. Must not be an {@link IQueryAtomContainer}.
     * @param  ac2   second molecule. May be an {@link IQueryAtomContainer}.
     * @throws CDKException if it takes too long to get the overlaps
     */
    private static void arcConstructor(RGraph gr, IAtomContainer ac1, IAtomContainer ac2) throws CDKException {
        // each node is incompatible with himself
        for (int i = 0; i < gr.getGraph().size(); i++) {
            RNode x = (RNode) gr.getGraph().get(i);
            x.getForbidden().set(i);
        }

        IBond a1;
        IBond a2;
        IBond b1;
        IBond b2;

        gr.setFirstGraphSize(ac1.getBondCount());
        gr.setSecondGraphSize(ac2.getBondCount());

        for (int i = 0; i < gr.getGraph().size(); i++) {
            RNode x = gr.getGraph().get(i);

            // two nodes are neighbors if their adjacency
            // relationship in are equivalent in G1 and G2
            // else they are incompatible.
            for (int j = i + 1; j < gr.getGraph().size(); j++) {
                RNode y = gr.getGraph().get(j);

                a1 = ac1.getBond(x.getRMap().getId1());
                a2 = ac2.getBond(x.getRMap().getId2());

                b1 = ac1.getBond(y.getRMap().getId1());
                b2 = ac2.getBond(y.getRMap().getId2());

                if (a2 instanceof IQueryBond) {
                    if (a1.equals(b1) || a2.equals(b2) || !queryAdjacencyAndOrder(a1, b1, a2, b2)) {
                        x.getForbidden().set(j);
                        y.getForbidden().set(i);
                    } else if (hasCommonAtom(a1, b1)) {
                        x.getExtension().set(j);
                        y.getExtension().set(i);
                    }
                } else {
                    if (a1.equals(b1) || a2.equals(b2) || (!getCommonSymbol(a1, b1).equals(getCommonSymbol(a2, b2)))) {
                        x.getForbidden().set(j);
                        y.getForbidden().set(i);
                    } else if (hasCommonAtom(a1, b1)) {
                        x.getExtension().set(j);
                        y.getExtension().set(i);
                    }
                }
            }
        }
    }

    /**
     * Determines if two bonds have at least one atom in common.
     *
     * @param  a  first bond
     * @param  b  second bond
     * @return    the symbol of the common atom or "" if
     *            the 2 bonds have no common atom
     */
    private static boolean hasCommonAtom(IBond a, IBond b) {
        return a.contains(b.getBegin()) || a.contains(b.getEnd());
    }

    /**
     *  Determines if 2 bond have 1 atom in common and returns the common symbol.
     *
     * @param  a  first bond
     * @param  b  second bond
     * @return    the symbol of the common atom or "" if
     *            the 2 bonds have no common atom
     */
    private static String getCommonSymbol(IBond a, IBond b) {
        String symbol = "";

        if (a.contains(b.getBegin())) {
            symbol = b.getBegin().getSymbol();
        } else if (a.contains(b.getEnd())) {
            symbol = b.getEnd().getSymbol();
        }

        return symbol;
    }

    /**
    *  Determines if 2 bond have 1 atom in common if second is a query AtomContainer.
    *
    * @param  a1  first bond
    * @param  b1  second bond
    * @return    the symbol of the common atom or "" if
    *            the 2 bonds have no common atom
    */
    private static boolean queryAdjacency(IBond a1, IBond b1, IBond a2, IBond b2) {

        IAtom atom1 = null;
        IAtom atom2 = null;

        if (a1.contains(b1.getBegin())) {
            atom1 = b1.getBegin();
        } else if (a1.contains(b1.getEnd())) {
            atom1 = b1.getEnd();
        }

        if (a2.contains(b2.getBegin())) {
            atom2 = b2.getBegin();
        } else if (a2.contains(b2.getEnd())) {
            atom2 = b2.getEnd();
        }

        if (atom1 != null && atom2 != null) {
            // well, this looks fishy: the atom2 is not always a IQueryAtom !
            return ((IQueryAtom) atom2).matches(atom1);
        } else
            return atom1 == null && atom2 == null;

    }

    /**
     *  Determines if 2 bond have 1 atom in common if second is a query AtomContainer
     *  and whether the order of the atoms is correct (atoms match).
     *
     * @param  bond1  first bond
     * @param  bond2  second bond
     * @param queryBond1 first query bond
     * @param queryBond2 second query bond
     * @return    the symbol of the common atom or "" if the 2 bonds have no common atom
     */
    private static boolean queryAdjacencyAndOrder(IBond bond1, IBond bond2, IBond queryBond1, IBond queryBond2) {

        IAtom centralAtom = null;
        IAtom centralQueryAtom = null;

        if (bond1.contains(bond2.getBegin())) {
            centralAtom = bond2.getBegin();
        } else if (bond1.contains(bond2.getEnd())) {
            centralAtom = bond2.getEnd();
        }

        if (queryBond1.contains(queryBond2.getBegin())) {
            centralQueryAtom = queryBond2.getBegin();
        } else if (queryBond1.contains(queryBond2.getEnd())) {
            centralQueryAtom = queryBond2.getEnd();
        }

        if (centralAtom != null && centralQueryAtom != null && ((IQueryAtom) centralQueryAtom).matches(centralAtom)) {
            IQueryAtom queryAtom1 = (IQueryAtom) queryBond1.getOther(centralQueryAtom);
            IQueryAtom queryAtom2 = (IQueryAtom) queryBond2.getOther(centralQueryAtom);
            IAtom atom1 = bond1.getOther(centralAtom);
            IAtom atom2 = bond2.getOther(centralAtom);
            if (queryAtom1.matches(atom1) && queryAtom2.matches(atom2) || queryAtom1.matches(atom2)
                    && queryAtom2.matches(atom1)) {
                return true;
            } else
                return false;
        } else
            return centralAtom == null && centralQueryAtom == null;

    }

    /**
     *  Checks some simple heuristics for whether the subgraph query can
     *  realistically be a subgraph of the supergraph. If, for example, the
     *  number of nitrogen atoms in the query is larger than that of the supergraph
     *  it cannot be part of it.
     *
     * @param  ac1  the supergraph to be checked. Must not be an {@link IQueryAtomContainer}.
     * @param  ac2  the subgraph to be tested for. May be an {@link IQueryAtomContainer}.
     * @return    true if the subgraph ac2 has a chance to be a subgraph of ac1
     * @throws CDKException if the first molecule is an instance of {@link IQueryAtomContainer}
     */
    private static boolean testSubgraphHeuristics(IAtomContainer ac1, IAtomContainer ac2) throws CDKException {
        if (ac1 instanceof IQueryAtomContainer)
            throw new CDKException("The first IAtomContainer must not be an IQueryAtomContainer");

        int ac1SingleBondCount = 0;
        int ac1DoubleBondCount = 0;
        int ac1TripleBondCount = 0;
        int ac1AromaticBondCount = 0;
        int ac2SingleBondCount = 0;
        int ac2DoubleBondCount = 0;
        int ac2TripleBondCount = 0;
        int ac2AromaticBondCount = 0;
        int ac1SCount = 0;
        int ac1OCount = 0;
        int ac1NCount = 0;
        int ac1FCount = 0;
        int ac1ClCount = 0;
        int ac1BrCount = 0;
        int ac1ICount = 0;
        int ac1CCount = 0;

        int ac2SCount = 0;
        int ac2OCount = 0;
        int ac2NCount = 0;
        int ac2FCount = 0;
        int ac2ClCount = 0;
        int ac2BrCount = 0;
        int ac2ICount = 0;
        int ac2CCount = 0;

        IBond bond;
        IAtom atom;
        for (int i = 0; i < ac1.getBondCount(); i++) {
            bond = ac1.getBond(i);
            if (bond.getFlag(CDKConstants.ISAROMATIC))
                ac1AromaticBondCount++;
            else if (bond.getOrder() == IBond.Order.SINGLE)
                ac1SingleBondCount++;
            else if (bond.getOrder() == IBond.Order.DOUBLE)
                ac1DoubleBondCount++;
            else if (bond.getOrder() == IBond.Order.TRIPLE) ac1TripleBondCount++;
        }
        for (int i = 0; i < ac2.getBondCount(); i++) {
            bond = ac2.getBond(i);
            if (bond instanceof IQueryBond) continue;
            if (bond.getFlag(CDKConstants.ISAROMATIC))
                ac2AromaticBondCount++;
            else if (bond.getOrder() == IBond.Order.SINGLE)
                ac2SingleBondCount++;
            else if (bond.getOrder() == IBond.Order.DOUBLE)
                ac2DoubleBondCount++;
            else if (bond.getOrder() == IBond.Order.TRIPLE) ac2TripleBondCount++;
        }

        if (ac2SingleBondCount > ac1SingleBondCount) return false;
        if (ac2AromaticBondCount > ac1AromaticBondCount) return false;
        if (ac2DoubleBondCount > ac1DoubleBondCount) return false;
        if (ac2TripleBondCount > ac1TripleBondCount) return false;

        for (int i = 0; i < ac1.getAtomCount(); i++) {
            atom = ac1.getAtom(i);
            if (atom.getSymbol().equals("S"))
                ac1SCount++;
            else if (atom.getSymbol().equals("N"))
                ac1NCount++;
            else if (atom.getSymbol().equals("O"))
                ac1OCount++;
            else if (atom.getSymbol().equals("F"))
                ac1FCount++;
            else if (atom.getSymbol().equals("Cl"))
                ac1ClCount++;
            else if (atom.getSymbol().equals("Br"))
                ac1BrCount++;
            else if (atom.getSymbol().equals("I"))
                ac1ICount++;
            else if (atom.getSymbol().equals("C")) ac1CCount++;
        }
        for (int i = 0; i < ac2.getAtomCount(); i++) {
            atom = ac2.getAtom(i);
            if (atom instanceof IQueryAtom) continue;
            if (atom.getSymbol().equals("S"))
                ac2SCount++;
            else if (atom.getSymbol().equals("N"))
                ac2NCount++;
            else if (atom.getSymbol().equals("O"))
                ac2OCount++;
            else if (atom.getSymbol().equals("F"))
                ac2FCount++;
            else if (atom.getSymbol().equals("Cl"))
                ac2ClCount++;
            else if (atom.getSymbol().equals("Br"))
                ac2BrCount++;
            else if (atom.getSymbol().equals("I"))
                ac2ICount++;
            else if (atom.getSymbol().equals("C")) ac2CCount++;
        }

        if (ac1SCount < ac2SCount) return false;
        if (ac1NCount < ac2NCount) return false;
        if (ac1OCount < ac2OCount) return false;
        if (ac1FCount < ac2FCount) return false;
        if (ac1ClCount < ac2ClCount) return false;
        if (ac1BrCount < ac2BrCount) return false;
        if (ac1ICount < ac2ICount) return false;
        return ac1CCount >= ac2CCount;

    }

    /**
     * Sets the time in milliseconds until the substructure search will be breaked.
     * @param timeout
     * Time in milliseconds. -1 to ignore the timeout.
     */
    public void setTimeout(long timeout) {
        this.timeout = timeout;
    }

}