/*******************************************************************************
    * 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.tools.encoding;
  
  import org.sat4j.core.ConstrGroup;
  import org.sat4j.core.VecInt;
  import org.sat4j.specs.ContradictionException;
  import org.sat4j.specs.IConstr;
  import org.sat4j.specs.ISolver;
  import org.sat4j.specs.IVecInt;
  
  /**
   * Binary encoding for the "at most one" and "at most k" cases.
   * 
   * For the case "at most one", we can use the binary encoding (also called
   * birwise encoding) first described in A. M. Frisch, T. J. Peugniez, A. J.
   * Dogget and P. Nightingale, "Solving Non-Boolean Satisfiability Problems With
   * Stochastic Local Search: A Comparison of Encodings" in Journal of Automated
   * Reasoning, vol. 35, n 1-3, 2005.
   * 
   * The approach is generalized for the "at most k" case in A. M. Frisch and P.
   * A. Giannaros, "SAT Encodings of the At-Most-k Constraint", in International
   * Workshop on Modelling and Reformulating Constraint Satisfaction Problems,
   * 2010
   * 
   * @author sroussel
   * @since 2.3.1
   */
  public class Binary extends EncodingStrategyAdapter {
  
      /**
       * p being the smaller integer greater than log_2(n), this encoding adds p
       * variables and n*p clauses.
       * 
       */
      @Override
      public IConstr addAtMostOne(ISolver solver, IVecInt literals)
              throws ContradictionException {
          ConstrGroup group = new ConstrGroup(false);
  
          final int n = literals.size();
          final int p = (int) Math.ceil(Math.log(n) / Math.log(2));
          final int k = (int) Math.pow(2, p) - n;
  
          int y[] = new int[p];
          for (int i = 0; i < p; i++) {
              y[i] = solver.nextFreeVarId(true);
          }
  
          IVecInt clause = new VecInt();
          String binary = "";
  
          for (int i = 0; i < k; i++) {
              binary = Integer.toBinaryString(i);
              while (binary.length() != p - 1) {
                  binary = "0" + binary;
              }
  
              for (int j = 0; j < p - 1; j++) {
                  clause.push(-literals.get(i));
                  if (binary.charAt(j) == '0') {
                      clause.push(-y[j]);
                  } else {
                      clause.push(y[j]);
                  }
                  group.add(solver.addClause(clause));
                  clause.clear();
  
              }
          }
  
         for (int i = k; i < n; i++) {
             binary = Integer.toBinaryString(2 * k + i - k);
             while (binary.length() != p) {
                 binary = "0" + binary;
             }
             for (int j = 0; j < p; j++) {
                 clause.push(-literals.get(i));
                 if (binary.charAt(j) == '0') {
                     clause.push(-y[j]);
                 } else {
                     clause.push(y[j]);
                 }
                 group.add(solver.addClause(clause));
                 clause.clear();
             }
 
         }
 
         return group;
     }
 
     @Override
     public IConstr addAtMost(ISolver solver, IVecInt literals, int k)
             throws ContradictionException {
 
         final int n = literals.size();
         final int p = (int) Math.ceil(Math.log(n) / Math.log(2));
 
         ConstrGroup group = new ConstrGroup(false);
 
         int[][] b = new int[k][p];
 
         for (int i = 0; i < k; i++) {
             for (int j = 0; j < p; j++) {
                 b[i][j] = solver.nextFreeVarId(true);
             }
         }
 
         int[][] t = new int[k][n];
 
         for (int i = 0; i < k; i++) {
             for (int j = 0; j < n; j++) {
                 t[i][j] = solver.nextFreeVarId(true);
             }
         }
 
         int max, min;
         IVecInt clause1 = new VecInt();
         IVecInt clause2 = new VecInt();
         String binary = "";
         for (int i = 0; i < n; i++) {
             max = Math.max(1, k - n + i + 1);
             min = Math.min(i + 1, k);
             clause1.push(-literals.get(i));
 
             binary = Integer.toBinaryString(i);
             while (binary.length() != p) {
                 binary = "0" + binary;
             }
 
             for (int g = max - 1; g < min; g++) {
                 clause1.push(t[g][i]);
                 for (int j = 0; j < p; j++) {
                     clause2.push(-t[g][i]);
                     if (binary.charAt(j) == '0') {
                         clause2.push(-b[g][j]);
                     } else {
                         clause2.push(b[g][j]);
                     }
                     group.add(solver.addClause(clause2));
                     clause2.clear();
                 }
             }
             group.add(solver.addClause(clause1));
             clause1.clear();
         }
 
         return group;
     }
 
     @Override
     public IConstr addAtLeast(ISolver solver, IVecInt literals, int k)
             throws ContradictionException {
 
         IVecInt newLits = new VecInt();
         for (int i = 0; i < literals.size(); i++) {
             newLits.push(-literals.get(i));
         }
 
         return addAtMost(solver, newLits, literals.size() - k);
     }
 
     @Override
     public IConstr addExactlyOne(ISolver solver, IVecInt literals)
             throws ContradictionException {
         ConstrGroup group = new ConstrGroup();
 
         group.add(addAtLeastOne(solver, literals));
         group.add(addAtMostOne(solver, literals));
 
         return group;
     }
 
     @Override
     public IConstr addExactly(ISolver solver, IVecInt literals, int degree)
             throws ContradictionException {
         ConstrGroup group = new ConstrGroup();
 
         group.add(addAtLeast(solver, literals, degree));
         group.add(addAtMost(solver, literals, degree));
 
         return group;
     }
 }