/*******************************************************************************
    * SAT4J: a SATisfiability library for Java Copyright (C) 2004-2008 Daniel Le Berre
    *
    * 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++.
   * 
   *******************************************************************************/
  package org.sat4j.tools;
  
  import java.math.BigInteger;
  
  import org.sat4j.core.Vec;
  import org.sat4j.core.VecInt;
  import org.sat4j.specs.ContradictionException;
  import org.sat4j.specs.IConstr;
  import org.sat4j.specs.ISolver;
  import org.sat4j.specs.IVec;
  import org.sat4j.specs.IVecInt;
  
  /**
   * Utility class to easily feed a SAT solver using logical gates.
   * 
   * @author leberre
   * 
   */
  public class GateTranslator extends SolverDecorator<ISolver> {
  
  	/**
       * 
       */
  	private static final long serialVersionUID = 1L;
  
  	public GateTranslator(ISolver solver) {
  		super(solver);
  	}
  
  	/**
  	 * translate y <=> FALSE into a clause.
  	 * 
  	 * @param y
  	 *            a variable to falsify
  	 * @throws ContradictionException
  	 *             iff a trivial inconsistency is found.
  	 * @since 2.1
  	 */
  	public IConstr gateFalse(int y) throws ContradictionException {
  		IVecInt clause = new VecInt(2);
  		clause.push(-y);
  		return processClause(clause);
  	}
  
  	/**
  	 * translate y <=> TRUE into a clause.
  	 * 
  	 * @param y
  	 *            a variable to verify
  	 * @throws ContradictionException
  	 * @since 2.1
  	 */
  	public IConstr gateTrue(int y) throws ContradictionException {
  		IVecInt clause = new VecInt(2);
  		clause.push(y);
  		return processClause(clause);
  	}
  
  	/**
  	 * translate y <=> if x1 then x2 else x3 into clauses.
  	 * 
  	 * @param y
  	 * @param x1
  	 *            the selector variable
  	 * @param x2
  	 * @param x3
  	 * @throws ContradictionException
  	 * @since 2.1
  	 */
  	public IConstr[] ite(int y, int x1, int x2, int x3)
  			throws ContradictionException {
  		IConstr[] constrs = new IConstr[6];
 		IVecInt clause = new VecInt(5);
 		// y <=> (x1 -> x2) and (not x1 -> x3)
 		// y -> (x1 -> x2) and (not x1 -> x3)
 		clause.push(-y).push(-x1).push(x2);
 		constrs[0] = processClause(clause);
 		clause.clear();
 		clause.push(-y).push(x1).push(x3);
 		constrs[1] = processClause(clause);
 		// y <- (x1 -> x2) and (not x1 -> x3)
 		// not(x1 -> x2) or not(not x1 -> x3) or y
 		// x1 and not x2 or not x1 and not x3 or y
 		// (x1 and not x2) or ((not x1 or y) and (not x3 or y))
 		// (x1 or not x1 or y) and (not x2 or not x1 or y) and (x1 or not x3 or
 		// y) and (not x2 or not x3 or y)
 		// not x1 or not x2 or y and x1 or not x3 or y and not x2 or not x3 or y
 		clause.clear();
 		clause.push(-x1).push(-x2).push(y);
 		constrs[2] = processClause(clause);
 		clause.clear();
 		clause.push(x1).push(-x3).push(y);
 		constrs[3] = processClause(clause);
 		clause.clear();
 		clause.push(-x2).push(-x3).push(y);
 		constrs[4] = processClause(clause);
 		// taken from Niklas Een et al SAT 2007 paper
 		// Adding the following redundant clause will improve unit propagation
 		// y -> x2 or x3
 		clause.clear();
 		clause.push(-y).push(x2).push(x3);
 		constrs[5] = processClause(clause);
 		return constrs;
 	}
 
 	/**
 	 * Translate y <=> x1 /\ x2 /\ ... /\ xn into clauses.
 	 * 
 	 * @param y
 	 * @param literals
 	 *            the x1 ... xn literals.
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] and(int y, IVecInt literals) throws ContradictionException {
 		// y <=> AND x1 ... xn
 		IConstr[] constrs = new IConstr[literals.size() + 1];
 		// y <= x1 .. xn
 		IVecInt clause = new VecInt(literals.size() + 2);
 		clause.push(y);
 		for (int i = 0; i < literals.size(); i++) {
 			clause.push(-literals.get(i));
 		}
 		constrs[0] = processClause(clause);
 		clause.clear();
 		for (int i = 0; i < literals.size(); i++) {
 			// y => xi
 			clause.clear();
 			clause.push(-y);
 			clause.push(literals.get(i));
 			constrs[i + 1] = processClause(clause);
 		}
 		return constrs;
 	}
 
 	/**
 	 * Translate y <=> x1 /\ x2
 	 * 
 	 * @param y
 	 * @param x1
 	 * @param x2
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] and(int y, int x1, int x2) throws ContradictionException {
 		IVecInt clause = new VecInt(4);
 		IConstr[] constrs = new IConstr[3];
 		clause.push(-y);
 		clause.push(x1);
 		constrs[0] = addClause(clause);
 		clause.clear();
 		clause.push(-y);
 		clause.push(x2);
 		constrs[1] = addClause(clause);
 		clause.clear();
 		clause.push(y);
 		clause.push(-x1);
 		clause.push(-x2);
 		constrs[2] = addClause(clause);
 		return constrs;
 	}
 
 	/**
 	 * translate y <=> x1 \/ x2 \/ ... \/ xn into clauses.
 	 * 
 	 * @param y
 	 * @param literals
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] or(int y, IVecInt literals) throws ContradictionException {
 		// y <=> OR x1 x2 ...xn
 		// y => x1 x2 ... xn
 		IConstr[] constrs = new IConstr[literals.size() + 1];
 		IVecInt clause = new VecInt(literals.size() + 2);
 		literals.copyTo(clause);
 		clause.push(-y);
 		constrs[0] = processClause(clause);
 		clause.clear();
 		for (int i = 0; i < literals.size(); i++) {
 			// xi => y
 			clause.clear();
 			clause.push(y);
 			clause.push(-literals.get(i));
 			constrs[i + 1] = processClause(clause);
 		}
 		return constrs;
 	}
 
 	private IConstr processClause(IVecInt clause) throws ContradictionException {
 		return addClause(clause);
 	}
 
 	/**
 	 * Translate y <=> not x into clauses.
 	 * 
 	 * @param y
 	 * @param x
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] not(int y, int x) throws ContradictionException {
 		IConstr[] constrs = new IConstr[2];
 		IVecInt clause = new VecInt(3);
 		// y <=> not x
 		// y => not x = not y or not x
 		clause.push(-y).push(-x);
 		constrs[0] = processClause(clause);
 		// y <= not x = y or x
 		clause.clear();
 		clause.push(y).push(x);
 		constrs[1] = processClause(clause);
 		return constrs;
 	}
 
 	/**
 	 * translate y <=> x1 xor x2 xor ... xor xn into clauses.
 	 * 
 	 * @param y
 	 * @param literals
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] xor(int y, IVecInt literals) throws ContradictionException {
 		literals.push(-y);
 		int[] f = new int[literals.size()];
 		literals.copyTo(f);
 		IVec<IConstr> vconstrs = new Vec<IConstr>();
 		xor2Clause(f, 0, false, vconstrs);
 		IConstr[] constrs = new IConstr[vconstrs.size()];
 		vconstrs.copyTo(constrs);
 		return constrs;
 	}
 
 	/**
 	 * translate y <=> (x1 <=> x2 <=> ... <=> xn) into clauses.
 	 * 
 	 * @param y
 	 * @param literals
 	 * @throws ContradictionException
 	 * @since 2.1
 	 */
 	public IConstr[] iff(int y, IVecInt literals) throws ContradictionException {
 		literals.push(y);
 		int[] f = new int[literals.size()];
 		literals.copyTo(f);
 		IVec<IConstr> vconstrs = new Vec<IConstr>();
 		iff2Clause(f, 0, false, vconstrs);
 		IConstr[] constrs = new IConstr[vconstrs.size()];
 		vconstrs.copyTo(constrs);
 		return constrs;
 	}
 
 	/**
 	 * @since 2.2
 	 */
 	public void xor(int x, int a, int b) throws ContradictionException {
 		IVecInt clause = new VecInt(3);
 		clause.push(-a).push(b).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(-b).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(-b).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(b).push(-x);
 		processClause(clause);
 		clause.clear();
 	}
 
 	private void xor2Clause(int[] f, int prefix, boolean negation,
 			IVec<IConstr> constrs) throws ContradictionException {
 		if (prefix == f.length - 1) {
 			IVecInt clause = new VecInt(f.length + 1);
 			for (int i = 0; i < f.length - 1; ++i) {
 				clause.push(f[i]);
 			}
 			clause.push(f[f.length - 1] * (negation ? -1 : 1));
 			constrs.push(processClause(clause));
 			return;
 		}
 
 		if (negation) {
 			f[prefix] = -f[prefix];
 			xor2Clause(f, prefix + 1, false, constrs);
 			f[prefix] = -f[prefix];
 
 			xor2Clause(f, prefix + 1, true, constrs);
 		} else {
 			xor2Clause(f, prefix + 1, false, constrs);
 
 			f[prefix] = -f[prefix];
 			xor2Clause(f, prefix + 1, true, constrs);
 			f[prefix] = -f[prefix];
 		}
 	}
 
 	private void iff2Clause(int[] f, int prefix, boolean negation,
 			IVec<IConstr> constrs) throws ContradictionException {
 		if (prefix == f.length - 1) {
 			IVecInt clause = new VecInt(f.length + 1);
 			for (int i = 0; i < f.length - 1; ++i) {
 				clause.push(f[i]);
 			}
 			clause.push(f[f.length - 1] * (negation ? -1 : 1));
 			processClause(clause);
 			return;
 		}
 
 		if (negation) {
 			iff2Clause(f, prefix + 1, false, constrs);
 			f[prefix] = -f[prefix];
 			iff2Clause(f, prefix + 1, true, constrs);
 			f[prefix] = -f[prefix];
 		} else {
 			f[prefix] = -f[prefix];
 			iff2Clause(f, prefix + 1, false, constrs);
 			f[prefix] = -f[prefix];
 			iff2Clause(f, prefix + 1, true, constrs);
 		}
 	}
 
 	// From Een and Sorensson JSAT 2006 paper
 
 	/**
 	 * @since 2.2
 	 */
 	public void fullAdderSum(int x, int a, int b, int c)
 			throws ContradictionException {
 		IVecInt clause = new VecInt(4);
 		// -a /\ -b /\ -c -> -x
 		clause.push(a).push(b).push(c).push(-x);
 		processClause(clause);
 		clause.clear();
 		// -a /\ b /\ c -> -x
 		clause.push(a).push(-b).push(-c).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(b).push(-c).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(-b).push(c).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(-b).push(-c).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(b).push(c).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(-b).push(c).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(b).push(-c).push(x);
 		processClause(clause);
 		clause.clear();
 	}
 
 	/**
 	 * @since 2.2
 	 */
 	public void fullAdderCarry(int x, int a, int b, int c)
 			throws ContradictionException {
 		IVecInt clause = new VecInt(3);
 		clause.push(-b).push(-c).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(-c).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(-a).push(-b).push(x);
 		processClause(clause);
 		clause.clear();
 		clause.push(b).push(c).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(c).push(-x);
 		processClause(clause);
 		clause.clear();
 		clause.push(a).push(b).push(-x);
 		processClause(clause);
 		clause.clear();
 	}
 
 	/**
 	 * @since 2.2
 	 */
 	public void additionalFullAdderConstraints(int xcarry, int xsum, int a,
 			int b, int c) throws ContradictionException {
 		IVecInt clause = new VecInt(3);
 		clause.push(-xcarry).push(-xsum).push(a);
 		processClause(clause);
 		clause.push(-xcarry).push(-xsum).push(b);
 		processClause(clause);
 		clause.push(-xcarry).push(-xsum).push(c);
 		processClause(clause);
 		clause.push(xcarry).push(xsum).push(-a);
 		processClause(clause);
 		clause.push(xcarry).push(xsum).push(-b);
 		processClause(clause);
 		clause.push(xcarry).push(xsum).push(-c);
 		processClause(clause);
 	}
 
 	/**
 	 * @since 2.2
 	 */
 	public void halfAdderSum(int x, int a, int b) throws ContradictionException {
 		xor(x, a, b);
 	}
 
 	/**
 	 * @since 2.2
 	 */
 	public void halfAdderCarry(int x, int a, int b)
 			throws ContradictionException {
 		and(x, a, b);
 	}
 
 	/**
 	 * Translate an optimization function into constraints and provides the
 	 * binary literals in results. Works only when the value of the objective
 	 * function is positive.
 	 * 
 	 * @since 2.2
 	 */
 	public void optimisationFunction(IVecInt literals, IVec<BigInteger> coefs,
 			IVecInt result) throws ContradictionException {
 		IVec<IVecInt> buckets = new Vec<IVecInt>();
 		IVecInt bucket;
 		// filling the buckets
 		for (int i = 0; i < literals.size(); i++) {
 			int p = literals.get(i);
 			BigInteger a = coefs.get(i);
 			for (int j = 0; j < a.bitLength(); j++) {
 				bucket = createIfNull(buckets, j);
 				if (a.testBit(j)) {
 					bucket.push(p);
 				}
 			}
 		}
 		// creating the adder
 		int x, y, z;
 		int sum, carry;
 		for (int i = 0; i < buckets.size(); i++) {
 			bucket = buckets.get(i);
 			while (bucket.size() >= 3) {
 				x = bucket.get(0);
 				y = bucket.get(1);
 				z = bucket.get(2);
 				bucket.remove(x);
 				bucket.remove(y);
 				bucket.remove(z);
 				sum = nextFreeVarId(true);
 				carry = nextFreeVarId(true);
 				fullAdderSum(sum, x, y, z);
 				fullAdderCarry(carry, x, y, z);
 				additionalFullAdderConstraints(carry, sum, x, y, z);
 				bucket.push(sum);
 				createIfNull(buckets, i + 1).push(carry);
 			}
 			while (bucket.size() == 2) {
 				x = bucket.get(0);
 				y = bucket.get(1);
 				bucket.remove(x);
 				bucket.remove(y);
 				sum = nextFreeVarId(true);
 				carry = nextFreeVarId(true);
 				halfAdderSum(sum, x, y);
 				halfAdderCarry(carry, x, y);
 				bucket.push(sum);
 				createIfNull(buckets, i + 1).push(carry);
 			}
 			assert bucket.size() == 1;
 			result.push(bucket.last());
 			bucket.pop();
 			assert bucket.isEmpty();
 		}
 	}
 
 	/**
 	 * Create a new bucket if it does not exists. Works only because the buckets
 	 * are explored in increasing order.
 	 * 
 	 * @param buckets
 	 * @param i
 	 * @return
 	 */
 	private IVecInt createIfNull(IVec<IVecInt> buckets, int i) {
 		IVecInt bucket = buckets.get(i);
 		if (bucket == null) {
 			bucket = new VecInt();
 			buckets.push(bucket);
 			assert buckets.get(i) == bucket;
 		}
 		return bucket;
 
 	}
 }