/*******************************************************************************
    * 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;
  
  /**
   * Commander encoding for "at most one" and "at most k" cases.
   * 
   * The case "at most one" is introduced in W. Klieber and G. Kwon
   * "Efficient CNF encoding for selecting 1 from N objects" in Fourth Workshop on
   * Constraints in Formal Verification, 2007.
   * 
   * The generalization to the "at most k" case is described 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 Commander extends EncodingStrategyAdapter {
  
      /**
       * In this encoding, variables are partitioned in groups. Kwon and Klieber
       * claim that the fewest clauses are produced when the size of the groups is
       * 3, thus leading to 3.5 clauses and introducing n/2 variables.
       */
      @Override
      public IConstr addAtMostOne(ISolver solver, IVecInt literals)
              throws ContradictionException {
  
          return addAtMostOne(solver, literals, 3);
      }
  
      private IConstr addAtMostOne(ISolver solver, IVecInt literals, int groupSize)
              throws ContradictionException {
  
          ConstrGroup constrGroup = new ConstrGroup(false);
  
          IVecInt clause = new VecInt();
          IVecInt clause1 = new VecInt();
  
          final int n = literals.size();
  
          int nbGroup = (int) Math.ceil((double) literals.size()
                  / (double) groupSize);
  
          if (nbGroup == 1) {
              for (int i = 0; i < literals.size() - 1; i++) {
                  for (int j = i + 1; j < literals.size(); j++) {
                      clause.push(-literals.get(i));
                      clause.push(-literals.get(j));
                      constrGroup.add(solver.addClause(clause));
                      clause.clear();
                  }
              }
              return constrGroup;
          }
  
          int[] c = new int[nbGroup];
  
          for (int i = 0; i < nbGroup; i++) {
              c[i] = solver.nextFreeVarId(true);
          }
  
         int nbVarLastGroup = n - (nbGroup - 1) * groupSize;
 
         // Encoding <=1 for each group of groupLitterals
         for (int i = 0; i < nbGroup; i++) {
             int size = 0;
             if (i == nbGroup - 1) {
                 size = nbVarLastGroup;
             } else {
                 size = groupSize;
             }
             // Encoding <=1 for each group of groupLitterals
             for (int j = 0; j < size - 1; j++) {
                 for (int k = j + 1; k < size; k++) {
                     clause.push(-literals.get(i * groupSize + j));
                     clause.push(-literals.get(i * groupSize + k));
                     constrGroup.add(solver.addClause(clause));
                     clause.clear();
                 }
             }
 
             // If a commander variable is true then some variable in its
             // corresponding group must be true (clause1)
             // If a commander variable is false then no variable in its group
             // can be true (clause)
             clause1.push(-c[i]);
             for (int j = 0; j < size; j++) {
                 clause1.push(literals.get(i * groupSize + j));
                 clause.push(c[i]);
                 clause.push(-literals.get(i * groupSize + j));
                 constrGroup.add(solver.addClause(clause));
                 clause.clear();
             }
             constrGroup.add(solver.addClause(clause1));
             clause1.clear();
         }
 
         // encode <=1 on commander variables
 
         constrGroup.add(addAtMostOne(solver, new VecInt(c), groupSize));
         return constrGroup;
     }
 
     @Override
     public IConstr addAtMost(ISolver solver, IVecInt literals, int degree)
             throws ContradictionException {
         return super.addAtMost(solver, literals, degree);
         // return addAtMost(solver, literals, degree, degree * 2);
     }
 
     private IConstr addAtMost(ISolver solver, IVecInt literals, int k,
             int groupSize) throws ContradictionException {
         ConstrGroup constrGroup = new ConstrGroup(false);
 
         IVecInt clause = new VecInt();
 
         final int n = literals.size();
 
         int nbGroup = (int) Math.ceil((double) n / (double) groupSize);
 
         if (nbGroup == 1) {
             for (IVecInt vec : literals.subset(k + 1)) {
                 for (int i = 0; i < vec.size(); i++) {
                     clause.push(-vec.get(i));
                 }
                 constrGroup.add(solver.addClause(clause));
                 clause.clear();
             }
             return constrGroup;
         }
 
         int[][] c = new int[nbGroup][k];
         VecInt vecC = new VecInt();
 
         for (int i = 0; i < nbGroup - 1; i++) {
             for (int j = 0; j < k; j++) {
                 c[i][j] = solver.nextFreeVarId(true);
                 vecC.push(c[i][j]);
             }
         }
 
         int nbVarLastGroup = n - (nbGroup - 1) * groupSize;
         int nbCForLastGroup;
         // nbCForLastGroup = Math.min(k, nbVarLastGroup);
         nbCForLastGroup = k;
 
         for (int j = 0; j < nbCForLastGroup; j++) {
             c[nbGroup - 1][j] = solver.nextFreeVarId(true);
             vecC.push(c[nbGroup - 1][j]);
         }
 
         VecInt[] groupTab = new VecInt[nbGroup];
 
         // Every literal x is in a group Gi
         // For every group Gi, we construct the group every {Gi \cup {c[i][j], j
         // =0,...k-1}}
         for (int i = 0; i < nbGroup - 1; i++) {
             groupTab[i] = new VecInt();
 
             int size = 0;
             if (i == nbGroup - 1) {
                 size = nbVarLastGroup;
             } else {
                 size = groupSize;
             }
 
             for (int j = 0; j < size; j++) {
                 groupTab[i].push(literals.get(i * groupSize + j));
             }
             for (int j = 0; j < k; j++) {
                 groupTab[i].push(-c[i][j]);
             }
         }
 
         int size = nbVarLastGroup;
         groupTab[nbGroup - 1] = new VecInt();
         for (int j = 0; j < size; j++) {
             groupTab[nbGroup - 1].push(literals.get((nbGroup - 1) * groupSize
                     + j));
         }
         for (int j = 0; j < nbCForLastGroup; j++) {
             groupTab[nbGroup - 1].push(-c[nbGroup - 1][j]);
         }
 
         Binomial bin = new Binomial();
 
         // Encode <=k for every Gi \cup {c[i][j], j=0,...k-1}} with Binomial
         // encoding
         for (int i = 0; i < nbGroup; i++) {
             constrGroup.add(bin.addAtMost(solver, groupTab[i], k));
             System.out.println(constrGroup.getConstr(i).size());
         }
 
         // Encode >=k for every Gi \cup {c[i][j], j=0,...k-1}} with Binomial
         // encoding
         for (int i = 0; i < nbGroup; i++) {
             constrGroup.add(bin.addAtLeast(solver, groupTab[i], k));
             System.out.println(constrGroup.getConstr(i + nbGroup).size());
         }
 
         for (int i = 0; i < nbGroup; i++) {
             for (int j = 0; j < k - 1; j++) {
                 clause.push(-c[i][j]);
                 clause.push(c[i][j + 1]);
                 constrGroup.add(solver.addClause(clause));
                 clause.clear();
             }
         }
 
         constrGroup.add(addAtMost(solver, vecC, k));
 
         return constrGroup;
     }
 
     @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;
     }
 }