/*******************************************************************************
    * SAT4J: a SATisfiability library for Java Copyright (C) 2004, 2012 Artois University and CNRS
    *
    * All rights reserved. This program and the accompanying materials
    * are made available under the terms of the Eclipse Public License v1.0
    * which accompanies this distribution, and is available at
    *  http://www.eclipse.org/legal/epl-v10.html
    *
    * Alternatively, the contents of this file may be used under the terms of
   * either the GNU Lesser General Public License Version 2.1 or later (the
   * "LGPL"), in which case the provisions of the LGPL are applicable instead
   * of those above. If you wish to allow use of your version of this file only
   * under the terms of the LGPL, and not to allow others to use your version of
   * this file under the terms of the EPL, indicate your decision by deleting
   * the provisions above and replace them with the notice and other provisions
   * required by the LGPL. If you do not delete the provisions above, a recipient
   * may use your version of this file under the terms of the EPL or the LGPL.
   *
   * Based on the original MiniSat specification from:
   *
   * An extensible SAT solver. Niklas Een and Niklas Sorensson. Proceedings of the
   * Sixth International Conference on Theory and Applications of Satisfiability
   * Testing, LNCS 2919, pp 502-518, 2003.
   *
   * See www.minisat.se for the original solver in C++.
   *
   * Contributors:
   *   CRIL - initial API and implementation
   *******************************************************************************/
  
  package org.sat4j.pb.tools;
  
  import java.math.BigInteger;
  import java.util.ArrayList;
  import java.util.Collection;
  import java.util.HashMap;
  import java.util.Iterator;
  import java.util.Map;
  import java.util.Set;
  import java.util.TreeSet;
  
  import org.sat4j.core.Vec;
  import org.sat4j.core.VecInt;
  import org.sat4j.pb.IPBSolver;
  import org.sat4j.pb.ObjectiveFunction;
  import org.sat4j.specs.ContradictionException;
  import org.sat4j.specs.IConstr;
  import org.sat4j.specs.IVec;
  import org.sat4j.specs.IVecInt;
  import org.sat4j.specs.IteratorInt;
  import org.sat4j.specs.TimeoutException;
  import org.sat4j.tools.Backbone;
  import org.sat4j.tools.GateTranslator;
  
  /**
   * Helper class intended to make life easier to people to feed a sat solver
   * programmatically.
   * 
   * @author daniel
   * 
   * @param <T>
   *            The class of the objects to map into boolean variables.
   * @param <C>
   *            The class of the object to map to each constraint.
   */
  public class DependencyHelper<T, C> {
  
  	public static final INegator NO_NEGATION = new INegator() {
  
  		public boolean isNegated(Object thing) {
  			return false;
  		}
  
  		public Object unNegate(Object thing) {
  			return thing;
  		}
  	};
  
  	public static final INegator BASIC_NEGATION = new INegator() {
  
  		public boolean isNegated(Object thing) {
  			return thing instanceof Negation;
  		}
  
  		public Object unNegate(Object thing) {
  			return ((Negation) thing).getThing();
  		}
  	};
  
  	private static final class Negation {
  		private final Object thing;
  
  		Negation(Object thing) {
  			this.thing = thing;
  		}
  
  		Object getThing() {
  			return this.thing;
  		}
 
 		@Override
 		public String toString() {
 			return "-" + thing;
 		}
 	}
 
 	/**
 	 * 
 	 */
 	private static final long serialVersionUID = 1L;
 
 	private final Map<T, Integer> mapToDimacs = new HashMap<T, Integer>();
 	private final Map<Integer, T> mapToDomain = new HashMap<Integer, T>();
 	final Map<IConstr, C> descs = new HashMap<IConstr, C>();
 
 	private final XplainPB xplain;
 	private final GateTranslator gator;
 	final IPBSolver solver;
 	private INegator negator = BASIC_NEGATION;
 
 	private ObjectiveFunction objFunction;
 	private IVecInt objLiterals;
 	private IVec<BigInteger> objCoefs;
 
 	private final boolean explanationEnabled;
 	private final boolean canonicalOptFunction;
 
 	/**
 	 * 
 	 * @param solver
 	 *            the solver to be used to solve the problem.
 	 */
 	public DependencyHelper(IPBSolver solver) {
 		this(solver, true);
 	}
 
 	/**
 	 * 
 	 * @param solver
 	 *            the solver to be used to solve the problem.
 	 * @param explanationEnabled
 	 *            if true, will add one new variable per constraint to allow the
 	 *            solver to compute an explanation in case of failure. Default
 	 *            is true. Usually, this is set to false when one wants to check
 	 *            the encoding produced by the helper.
 	 */
 	public DependencyHelper(IPBSolver solver, boolean explanationEnabled) {
 		this(solver, explanationEnabled, true);
 	}
 
 	/**
 	 * 
 	 * @param solver
 	 *            the solver to be used to solve the problem.
 	 * @param explanationEnabled
 	 *            if true, will add one new variable per constraint to allow the
 	 *            solver to compute an explanation in case of failure. Default
 	 *            is true. Usually, this is set to false when one wants to check
 	 *            the encoding produced by the helper.
 	 * @param canonicalOptFunctionEnabled
 	 *            when set to true, the objective function sum up all the
 	 *            coefficients for a given literal. The default is true. It is
 	 *            useful to set it to false when checking the encoding produced
 	 *            by the helper.
 	 * @since 2.2
 	 */
 	public DependencyHelper(IPBSolver solver, boolean explanationEnabled,
 			boolean canonicalOptFunctionEnabled) {
 		if (explanationEnabled) {
 			this.xplain = new XplainPB(solver);
 			this.solver = this.xplain;
 		} else {
 			this.xplain = null;
 			this.solver = solver;
 		}
 		this.gator = new GateTranslator(this.solver);
 		this.explanationEnabled = explanationEnabled;
 		this.canonicalOptFunction = canonicalOptFunctionEnabled;
 	}
 
 	public void setNegator(INegator negator) {
 		this.negator = negator;
 	}
 
 	/**
 	 * Translate a domain object into a dimacs variable.
 	 * 
 	 * @param thing
 	 *            a domain object
 	 * @return the dimacs variable (an integer) representing that domain object.
 	 */
 	protected int getIntValue(T thing) {
 		return getIntValue(thing, true);
 	}
 
 	/**
 	 * Translate a domain object into a dimacs variable.
 	 * 
 	 * @param thing
 	 *            a domain object
 	 * @param create
 	 *            to allow or not the solver to create a new id if the object in
 	 *            unknown. If set to false, the method will throw an
 	 *            IllegalArgumentException if the object is unknown.
 	 * @return the dimacs variable (an integer) representing that domain object.
 	 */
 	protected int getIntValue(T thing, boolean create) {
 		T myThing;
 		boolean negated = this.negator.isNegated(thing);
 		if (negated) {
 			myThing = (T) this.negator.unNegate(thing);
 		} else {
 			myThing = thing;
 		}
 		Integer intValue = this.mapToDimacs.get(myThing);
 		if (intValue == null) {
 			if (create) {
 				intValue = this.solver.nextFreeVarId(true);
 				this.mapToDomain.put(intValue, myThing);
 				this.mapToDimacs.put(myThing, intValue);
 			} else {
 				throw new IllegalArgumentException("" + myThing
 						+ " is unknown in the solver!");
 			}
 		}
 		if (negated) {
 			return -intValue;
 		}
 		return intValue;
 	}
 
 	/**
 	 * Retrieve the solution found.
 	 * 
 	 * Note that this method returns a Sat4j specific data structure (IVec).
 	 * People willing to retrieve a more common data structure should use
 	 * {@link #getASolution()} instead.
 	 * 
 	 * THAT METHOD IS EXPECTED TO BE CALLED IF hasASolution() RETURNS TRUE.
 	 * 
 	 * @return the domain object that must be satisfied to satisfy the
 	 *         constraints entered in the solver.
 	 * @see {@link #hasASolution()}
 	 * @see {@link #getASolution()}
 	 */
 	public IVec<T> getSolution() {
 		int[] model = this.solver.model();
 		IVec<T> toInstall = new Vec<T>();
 		if (model != null) {
 			for (int i : model) {
 				if (i > 0) {
 					toInstall.push(this.mapToDomain.get(i));
 				}
 			}
 		}
 		return toInstall;
 	}
 
 	/**
 	 * Retrieve a collection of objects satisfying the constraints.
 	 * 
 	 * It behaves basically the same as {@link #getSolution()} but returns a
 	 * common Collection instead of a Sat4j specific IVec.
 	 * 
 	 * THAT METHOD IS EXPECTED TO BE CALLED IF hasASolution() RETURNS TRUE.
 	 * 
 	 * @return the domain object that must be satisfied to satisfy the
 	 *         constraints entered in the solver.
 	 * @see {@link #hasASolution()}
 	 * @see {@link #getSolution()}
 	 * @since 2.3.1
 	 */
 	public Collection<T> getASolution() {
 		int[] model = this.solver.model();
 		Collection<T> toInstall = new ArrayList<T>();
 		if (model != null) {
 			for (int i : model) {
 				if (i > 0) {
 					toInstall.add(this.mapToDomain.get(i));
 				}
 			}
 		}
 		return toInstall;
 	}
 
 	public BigInteger getSolutionCost() {
 		return this.objFunction.calculateDegree(this.solver);
 	}
 
 	/**
 	 * Retrieve the boolean value associated with a domain object in the
 	 * solution found by the solver. THAT METHOD IS EXPECTED TO BE CALLED IF
 	 * hasASolution() RETURNS TRUE.
 	 * 
 	 * @param t
 	 *            a domain object
 	 * @return true iff the domain object has been set to true in the current
 	 *         solution.
 	 * @throws IllegalArgumentException
 	 *             If the argument of the method is unknown to the solver.
 	 */
 	public boolean getBooleanValueFor(T t) {
 		int dimacsValue = getIntValue(t, false);
 		if (dimacsValue > 0) {
 			return this.solver.model(dimacsValue);
 		} else {
 			return !this.solver.model(-dimacsValue);
 		}
 	}
 
 	/**
 	 * 
 	 * @return true if the set of constraints entered inside the solver can be
 	 *         satisfied.
 	 * @throws TimeoutException
 	 */
 	public boolean hasASolution() throws TimeoutException {
 		return this.solver.isSatisfiable();
 	}
 
 	/**
 	 * 
 	 * @return true if the set of constraints entered inside the solver can be
 	 *         satisfied.
 	 * @throws TimeoutException
 	 */
 	public boolean hasASolution(IVec<T> assumps) throws TimeoutException {
 		IVecInt assumptions = new VecInt();
 		for (Iterator<T> it = assumps.iterator(); it.hasNext();) {
 			assumptions.push(getIntValue(it.next()));
 		}
 		return this.solver.isSatisfiable(assumptions);
 	}
 
 	/**
 	 * 
 	 * @return true if the set of constraints entered inside the solver can be
 	 *         satisfied.
 	 * @throws TimeoutException
 	 */
 	public boolean hasASolution(Collection<T> assumps) throws TimeoutException {
 		IVecInt assumptions = new VecInt();
 		for (T t : assumps) {
 			assumptions.push(getIntValue(t));
 		}
 		return this.solver.isSatisfiable(assumptions);
 	}
 
 	/**
 	 * Explain the reason of the inconsistency of the set of constraints.
 	 * 
 	 * THAT METHOD IS EXPECTED TO BE CALLED IF hasASolution() RETURNS FALSE.
 	 * 
 	 * @return a set of objects used to "name" each constraint entered in the
 	 *         solver.
 	 * @throws TimeoutException
 	 * @see {@link #hasASolution()}
 	 */
 	public Set<C> why() throws TimeoutException {
 		if (!this.explanationEnabled) {
 			throw new UnsupportedOperationException("Explanation not enabled!");
 		}
 		Collection<IConstr> explanation = this.xplain.explain();
 		Set<C> ezexplain = new TreeSet<C>();
 		for (IConstr constr : explanation) {
 			C desc = this.descs.get(constr);
 			if (desc != null) {
 				ezexplain.add(desc);
 			}
 		}
 		return ezexplain;
 	}
 
 	/**
 	 * Explain a domain object has been set to true in a solution.
 	 * 
 	 * @return a set of objects used to "name" each constraint entered in the
 	 *         solver.
 	 * @throws TimeoutException
 	 * @see {@link #hasASolution()}
 	 */
 	public Set<C> why(T thing) throws TimeoutException {
 		IVecInt assumps = new VecInt();
 		assumps.push(-getIntValue(thing));
 		return why(assumps);
 	}
 
 	/**
 	 * Explain a domain object has been set to false in a solution.
 	 * 
 	 * @return a set of objects used to "name" each constraint entered in the
 	 *         solver.
 	 * @throws TimeoutException
 	 * @see {@link #hasASolution()}
 	 */
 	public Set<C> whyNot(T thing) throws TimeoutException {
 		IVecInt assumps = new VecInt();
 		assumps.push(getIntValue(thing));
 		return why(assumps);
 	}
 
 	private Set<C> why(IVecInt assumps) throws TimeoutException {
 		if (this.xplain.isSatisfiable(assumps)) {
 			return new TreeSet<C>();
 		}
 		return why();
 	}
 
 	/**
 	 * Add a constraint to set the value of a domain object to true.
 	 * 
 	 * @param thing
 	 *            the domain object
 	 * @param name
 	 *            the name of the constraint, to be used in an explanation if
 	 *            needed.
 	 * @throws ContradictionException
 	 *             if the set of constraints appears to be trivially
 	 *             inconsistent.
 	 */
 	public void setTrue(T thing, C name) throws ContradictionException {
 		IConstr constr = this.gator.gateTrue(getIntValue(thing));
 		if (constr != null) {
 			this.descs.put(constr, name);
 		}
 	}
 
 	/**
 	 * Add a constraint to set the value of a domain object to false.
 	 * 
 	 * @param thing
 	 *            the domain object
 	 * @param name
 	 *            the name of the constraint, to be used in an explanation if
 	 *            needed.
 	 * @throws ContradictionException
 	 *             if the set of constraints appears to be trivially
 	 *             inconsistent.
 	 */
 	public void setFalse(T thing, C name) throws ContradictionException {
 		IConstr constr = this.gator.gateFalse(getIntValue(thing));
 		// constraints duplication detection may end up with null constraint
 		if (constr != null) {
 			this.descs.put(constr, name);
 		}
 
 	}
 
 	/**
 	 * Create a logical implication of the form lhs -> rhs
 	 * 
 	 * @param lhs
 	 *            some domain objects. They form a conjunction in the left hand
 	 *            side of the implication.
 	 * @return the right hand side of the implication.
 	 */
 	public ImplicationRHS<T, C> implication(T... lhs) {
 		IVecInt clause = new VecInt();
 		for (T t : lhs) {
 			clause.push(-getIntValue(t));
 		}
 		return new ImplicationRHS<T, C>(this, clause);
 	}
 
 	public DisjunctionRHS<T, C> disjunction(T... lhs) {
 		IVecInt literals = new VecInt();
 		for (T t : lhs) {
 			literals.push(-getIntValue(t));
 		}
 		return new DisjunctionRHS<T, C>(this, literals);
 	}
 
 	/**
 	 * Create a constraint stating that at most i domain object should be set to
 	 * true.
 	 * 
 	 * @param i
 	 *            the maximum number of domain object to set to true.
 	 * @param things
 	 *            the domain objects.
 	 * @return an object used to name the constraint. The constraint MUST BE
 	 *         NAMED.
 	 * @throws ContradictionException
 	 */
 	public void atLeast(C name, int i, T... things)
 			throws ContradictionException {
 		IVecInt literals = new VecInt();
 		for (T t : things) {
 			literals.push(getIntValue(t));
 		}
 		this.descs.put(this.solver.addAtLeast(literals, i), name);
 	}
 
 	/**
 	 * Create a constraint stating that at most i domain object should be set to
 	 * true.
 	 * 
 	 * @param i
 	 *            the maximum number of domain object to set to true.
 	 * @param things
 	 *            the domain objects.
 	 * @return an object used to name the constraint. The constraint MUST BE
 	 *         NAMED.
 	 * @throws ContradictionException
 	 */
 	public ImplicationNamer<T, C> atMost(int i, T... things)
 			throws ContradictionException {
 		IVec<IConstr> toName = new Vec<IConstr>();
 		IVecInt literals = new VecInt();
 		for (T t : things) {
 			literals.push(getIntValue(t));
 		}
 		toName.push(this.solver.addAtMost(literals, i));
 		return new ImplicationNamer<T, C>(this, toName);
 	}
 
 	/**
 	 * Create a constraint stating that at most i domain object should be set to
 	 * true.
 	 * 
 	 * @param i
 	 *            the maximum number of domain object to set to true.
 	 * @param things
 	 *            the domain objects.
 	 * @return an object used to name the constraint. The constraint MUST BE
 	 *         NAMED.
 	 * @throws ContradictionException
 	 */
 	public void atMost(C name, int i, T... things)
 			throws ContradictionException {
 		IVecInt literals = new VecInt();
 		for (T t : things) {
 			literals.push(getIntValue(t));
 		}
 		this.descs.put(this.solver.addAtMost(literals, i), name);
 	}
 
 	/**
 	 * Create a clause (thing1 or thing 2 ... or thingn)
 	 * 
 	 * @param name
 	 * @param things
 	 * 
 	 * @throws ContradictionException
 	 */
 	public void clause(C name, T... things) throws ContradictionException {
 		IVecInt literals = new VecInt(things.length);
 		for (T t : things) {
 			literals.push(getIntValue(t));
 		}
 		IConstr constr = this.gator.addClause(literals);
 		// constr can be null if duplicated clauses are detected.
 		if (constr != null) {
 			this.descs.put(constr, name);
 		}
 
 	}
 
 	/**
 	 * Create a constraint using equivalency chains thing <=> (thing1 <=> thing2
 	 * <=> ... <=> thingn)
 	 * 
 	 * @param thing
 	 *            a domain object
 	 * @param things
 	 *            other domain objects.
 	 * @throws ContradictionException
 	 */
 	public void iff(C name, T thing, T... otherThings)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(otherThings.length);
 		for (T t : otherThings) {
 			literals.push(getIntValue(t));
 		}
 		IConstr[] constrs = this.gator.iff(getIntValue(thing), literals);
 		for (IConstr constr : constrs) {
 			if (constr != null) {
 				this.descs.put(constr, name);
 			}
 		}
 	}
 
 	/**
 	 * Create a constraint of the form thing <=> (thing1 and thing 2 ... and
 	 * thingn)
 	 * 
 	 * @param name
 	 * @param thing
 	 * @param otherThings
 	 * @throws ContradictionException
 	 */
 	public void and(C name, T thing, T... otherThings)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(otherThings.length);
 		for (T t : otherThings) {
 			literals.push(getIntValue(t));
 		}
 		IConstr[] constrs = this.gator.and(getIntValue(thing), literals);
 		for (IConstr constr : constrs) {
 			if (constr != null) {
 				this.descs.put(constr, name);
 			}
 		}
 	}
 
 	/**
 	 * Create a constraint of the form thing <=> (thing1 or thing 2 ... or
 	 * thingn)
 	 * 
 	 * @param name
 	 * @param thing
 	 * @param otherThings
 	 * @throws ContradictionException
 	 */
 	public void or(C name, T thing, T... otherThings)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(otherThings.length);
 		for (T t : otherThings) {
 			literals.push(getIntValue(t));
 		}
 		IConstr[] constrs = this.gator.or(getIntValue(thing), literals);
 		for (IConstr constr : constrs) {
 			if (constr != null) {
 				this.descs.put(constr, name);
 			}
 		}
 	}
 
 	/**
 	 * Create a constraint of the form thing <= (thing1 or thing 2 ... or
 	 * thingn)
 	 * 
 	 * @param name
 	 * @param thing
 	 * @param otherThings
 	 * @throws ContradictionException
 	 */
 	public void halfOr(C name, T thing, T... otherThings)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(otherThings.length);
 		for (T t : otherThings) {
 			literals.push(getIntValue(t));
 		}
 		IConstr[] constrs = this.gator.halfOr(getIntValue(thing), literals);
 		for (IConstr constr : constrs) {
 			if (constr != null) {
 				this.descs.put(constr, name);
 			}
 		}
 	}
 
 	/**
 	 * Create a constraint of the form thing <=> (if conditionThing then
 	 * thenThing else elseThing)
 	 * 
 	 * @param name
 	 * @param thing
 	 * @param otherThings
 	 * @throws ContradictionException
 	 */
 	public void ifThenElse(C name, T thing, T conditionThing, T thenThing,
 			T elseThing) throws ContradictionException {
 		IConstr[] constrs = this.gator.ite(getIntValue(thing),
 				getIntValue(conditionThing), getIntValue(thenThing),
 				getIntValue(elseThing));
 		for (IConstr constr : constrs) {
 			if (constr != null) {
 				this.descs.put(constr, name);
 			}
 		}
 	}
 
 	/**
 	 * Add an objective function to ask for a solution that minimize the
 	 * objective function.
 	 * 
 	 * @param wobj
 	 *            a set of weighted objects (pairs of domain object and
 	 *            BigInteger).
 	 */
 	public void setObjectiveFunction(WeightedObject<T>... wobj) {
 		createObjectivetiveFunctionIfNeeded(wobj.length);
 		for (WeightedObject<T> wo : wobj) {
 			addProperly(wo.thing, wo.getWeight());
 		}
 
 	}
 
 	private void addProperly(T thing, BigInteger weight) {
 		int lit = getIntValue(thing);
 		int index;
 		if (this.canonicalOptFunction
 				&& (index = this.objLiterals.indexOf(lit)) != -1) {
 			this.objCoefs.set(index, this.objCoefs.get(index).add(weight));
 			if (this.objCoefs.get(index).equals(BigInteger.ZERO)) {
 				this.objLiterals.delete(index);
 				this.objCoefs.delete(index);
 			}
 		} else {
 			this.objLiterals.push(lit);
 			this.objCoefs.push(weight);
 		}
 	}
 
 	private void createObjectivetiveFunctionIfNeeded(int n) {
 		if (this.objFunction == null) {
 			this.objLiterals = new VecInt(n);
 			this.objCoefs = new Vec<BigInteger>(n);
 			this.objFunction = new ObjectiveFunction(this.objLiterals,
 					this.objCoefs);
 			this.solver.setObjectiveFunction(this.objFunction);
 		}
 	}
 
 	/**
 	 * Add a weighted literal to the objective function.
 	 * 
 	 * @param thing
 	 * @param weight
 	 */
 	public void addToObjectiveFunction(T thing, int weight) {
 		addToObjectiveFunction(thing, BigInteger.valueOf(weight));
 	}
 
 	/**
 	 * Add a weighted literal to the objective function.
 	 * 
 	 * @param thing
 	 * @param weight
 	 */
 	public void addToObjectiveFunction(T thing, BigInteger weight) {
 		createObjectivetiveFunctionIfNeeded(20);
 		addProperly(thing, weight);
 	}
 
 	/**
 	 * Create a PB constraint of the form <code>
 	 * w1.l1 + w2.l2 + ... wn.ln >= degree
 	 * </code> where wi are position integers and li are domain objects.
 	 * 
 	 * @param degree
 	 * @param wobj
 	 * @throws ContradictionException
 	 */
 	public void atLeast(C name, BigInteger degree, WeightedObject<T>... wobj)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(wobj.length);
 		IVec<BigInteger> coeffs = new Vec<BigInteger>(wobj.length);
 		for (WeightedObject<T> wo : wobj) {
 			literals.push(getIntValue(wo.thing));
 			coeffs.push(wo.getWeight());
 		}
 		this.descs.put(
 				this.solver.addPseudoBoolean(literals, coeffs, true, degree),
 				name);
 	}
 
 	/**
 	 * Create a PB constraint of the form <code>
 	 * w1.l1 + w2.l2 + ... wn.ln <= degree
 	 * </code> where wi are position integers and li are domain objects.
 	 * 
 	 * @param degree
 	 * @param wobj
 	 * @throws ContradictionException
 	 */
 	public void atMost(C name, BigInteger degree, WeightedObject<T>... wobj)
 			throws ContradictionException {
 		IVecInt literals = new VecInt(wobj.length);
 		IVec<BigInteger> coeffs = new Vec<BigInteger>(wobj.length);
 		for (WeightedObject<T> wo : wobj) {
 			literals.push(getIntValue(wo.thing));
 			coeffs.push(wo.getWeight());
 		}
 		this.descs.put(
 				this.solver.addPseudoBoolean(literals, coeffs, false, degree),
 				name);
 	}
 
 	public void atMost(C name, int degree, WeightedObject<T>... wobj)
 			throws ContradictionException {
 		atMost(name, BigInteger.valueOf(degree), wobj);
 	}
 
 	/**
 	 * Stop the SAT solver that is looking for a solution. The solver will throw
 	 * a TimeoutException.
 	 */
 	public void stopSolver() {
 		this.solver.expireTimeout();
 	}
 
 	/**
 	 * Stop the explanation computation. A TimeoutException will be thrown by
 	 * the explanation algorithm.
 	 */
 	public void stopExplanation() {
 		if (!this.explanationEnabled) {
 			throw new UnsupportedOperationException("Explanation not enabled!");
 		}
 		this.xplain.cancelExplanation();
 	}
 
 	public void discard(IVec<T> things) throws ContradictionException {
 		IVecInt literals = new VecInt(things.size());
 		for (Iterator<T> it = things.iterator(); it.hasNext();) {
 			literals.push(-getIntValue(it.next()));
 		}
 		this.solver.addBlockingClause(literals);
 	}
 
 	public void discardSolutionsWithObjectiveValueGreaterThan(long value)
 			throws ContradictionException {
 		ObjectiveFunction obj = this.solver.getObjectiveFunction();
 		IVecInt literals = new VecInt(obj.getVars().size());
 		obj.getVars().copyTo(literals);
 		IVec<BigInteger> coeffs = new Vec<BigInteger>(obj.getCoeffs().size());
 		obj.getCoeffs().copyTo(coeffs);
 		this.solver.addPseudoBoolean(literals, coeffs, false,
 				BigInteger.valueOf(value));
 	}
 
 	public String getObjectiveFunction() {
 		ObjectiveFunction obj = this.solver.getObjectiveFunction();
 		StringBuffer stb = new StringBuffer();
 		for (int i = 0; i < obj.getVars().size(); i++) {
 			stb.append(obj.getCoeffs().get(i)
 					+ (obj.getVars().get(i) > 0 ? " " : "~")
 					+ this.mapToDomain.get(Math.abs(obj.getVars().get(i)))
 					+ " ");
 		}
 		return stb.toString();
 	}
 
 	public int getNumberOfVariables() {
 		return this.mapToDimacs.size();
 	}
 
 	public int getNumberOfConstraints() {
 		return this.descs.size();
 	}
 
 	public Map<Integer, T> getMappingToDomain() {
 		return this.mapToDomain;
 	}
 
 	public Object not(T thing) {
 		return new Negation(thing);
 	}
 
 	/**
 	 * @since 2.2
 	 * @return the IPBSolver enclosed in the helper.
 	 */
 	public IPBSolver getSolver() {
 		if (this.explanationEnabled) {
 			return this.xplain.decorated();
 		}
 		return this.solver;
 	}
 
 	/**
 	 * Reset the state of the helper (mapping, objective function, etc).
 	 * 
 	 * @since 2.3.1
 	 */
 	public void reset() {
 		this.mapToDimacs.clear();
 		this.mapToDomain.clear();
 		this.descs.clear();
 		this.solver.reset();
 		if (this.objLiterals != null) {
 			this.objLiterals.clear();
 			this.objCoefs.clear();
 		}
 	}
 
 	/**
 	 * Compute the objects implied by the assumptions.
 	 * 
 	 * @param assumptions
 	 *            already satisfied objects (e.g. user choices)
 	 * @param satisfied
 	 *            the objects that are always satisfied under assumptions
 	 *            (includes the objects from assumptions)
 	 * @param falsified
 	 *            the objects that are always falsified under assumptions.
 	 * @return the set of objects fixed
 	 * @throws TimeoutException
 	 * @since 2.3.3
 	 */
 	public void impliedBy(Collection<T> assumptions, Collection<T> satisfied,
 			Collection<T> falsified) throws TimeoutException {
 		IVecInt assump = new VecInt(assumptions.size());
 		for (T thing : assumptions) {
 			assump.push(getIntValue(thing));
 		}
 		IVecInt implied = Backbone.compute(solver, assump);
 		int p;
 		for (IteratorInt it = implied.iterator(); it.hasNext();) {
 			p = it.next();
 			if (p > 0) {
 				satisfied.add(mapToDomain.get(p));
 			} else {
 				falsified.add(mapToDomain.get(-p));
 			}
 		}
 	}
 }