code: ///////////////////////////////////////////////////////////////////////////
  //                   __                _      _   ________               //
  //                  / /   ____  ____ _(_)____/ | / / ____/               //
  //                 / /   / __ \/ __ `/ / ___/  |/ / / __                 //
  //                / /___/ /_/ / /_/ / / /__/ /|  / /_/ /                 //
  //               /_____/\____/\__, /_/\___/_/ |_/\____/                  //
  //                           /____/                                      //
  //                                                                       //
  //               The Next Generation Logic Library                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  //                                                                       //
  //  Copyright 2015-20xx Christoph Zengler                                //
  //                                                                       //
  //  Licensed under the Apache License, Version 2.0 (the "License");      //
  //  you may not use this file except in compliance with the License.     //
  //  You may obtain a copy of the License at                              //
  //                                                                       //
  //  http://www.apache.org/licenses/LICENSE-2.0                           //
  //                                                                       //
  //  Unless required by applicable law or agreed to in writing, software  //
  //  distributed under the License is distributed on an "AS IS" BASIS,    //
  //  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or      //
  //  implied.  See the License for the specific language governing        //
  //  permissions and limitations under the License.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.transformations.simplification;
  
  import static org.logicng.formulas.FType.dual;
  
  import org.logicng.formulas.Equivalence;
  import org.logicng.formulas.FType;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.FormulaTransformation;
  import org.logicng.formulas.Implication;
  import org.logicng.formulas.Not;
  import org.logicng.formulas.cache.TransformationCacheEntry;
  
  import java.util.LinkedHashMap;
  import java.util.LinkedHashSet;
  import java.util.Map;
  import java.util.Set;
  
  /**
   * A formula transformation which performs simplifications by applying the distributive laws.
   * @version 2.3.0
   * @since 1.3
   */
  public final class DistributiveSimplifier implements FormulaTransformation {
  
      private static final DistributiveSimplifier INSTANCE = new DistributiveSimplifier();
  
      /**
       * @deprecated In the next version, the standard constructor will be replaced by a private constructor.
       * In order to instantiate an object of this class, use the {@link #get()} method.
       */
      @Deprecated
      public DistributiveSimplifier() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static DistributiveSimplifier get() {
          return INSTANCE;
      }
  
      @Override
      public Formula apply(final Formula formula, final boolean cache) {
          final FormulaFactory f = formula.factory();
          final Formula result;
          switch (formula.type()) {
              case FALSE:
              case TRUE:
              case LITERAL:
              case PBC:
                  result = formula;
                  break;
              case EQUIV:
                  final Equivalence equiv = (Equivalence) formula;
                  result = f.equivalence(this.apply(equiv.left(), cache), this.apply(equiv.right(), cache));
                  break;
              case IMPL:
                  final Implication impl = (Implication) formula;
                  result = f.implication(this.apply(impl.left(), cache), this.apply(impl.right(), cache));
                  break;
              case NOT:
                  final Not not = (Not) formula;
                  result = f.not(this.apply(not.operand(), cache));
                  break;
              case OR:
              case AND:
                  result = distributeNAry(formula, cache, f);
                  break;
              default:
                  throw new IllegalStateException("Unknown formula type: " + formula.type());
          }
          if (cache) {
              formula.setTransformationCacheEntry(TransformationCacheEntry.DISTRIBUTIVE_SIMPLIFICATION, result);
          }
          return result;
      }
  
      private Formula distributeNAry(final Formula formula, final boolean cache, final FormulaFactory f) {
          final Formula result;
          final FType outerType = formula.type();
          final FType innerType = dual(outerType);
          final Set<Formula> operands = new LinkedHashSet<>();
          for (final Formula op : formula) {
              operands.add(this.apply(op, cache));
          }
          final Map<Formula, Set<Formula>> part2Operands = new LinkedHashMap<>();
          Formula mostCommon = null;
          int mostCommonAmount = 0;
          for (final Formula op : operands) {
              if (op.type() == innerType) {
                  for (final Formula part : op) {
                      final Set<Formula> partOperands = part2Operands.computeIfAbsent(part, k -> new LinkedHashSet<>());
                      partOperands.add(op);
                      if (partOperands.size() > mostCommonAmount) {
                          mostCommon = part;
                          mostCommonAmount = partOperands.size();
                      }
                  }
              }
          }
          if (mostCommon == null || mostCommonAmount == 1) {
              result = f.naryOperator(outerType, operands);
              return result;
          }
          operands.removeAll(part2Operands.get(mostCommon));
          final Set<Formula> relevantFormulas = new LinkedHashSet<>();
          for (final Formula preRelevantFormula : part2Operands.get(mostCommon)) {
              final Set<Formula> relevantParts = new LinkedHashSet<>();
              for (final Formula part : preRelevantFormula) {
                  if (!part.equals(mostCommon)) {
                      relevantParts.add(part);
                  }
              }
              relevantFormulas.add(f.naryOperator(innerType, relevantParts));
          }
          operands.add(f.naryOperator(innerType, mostCommon, f.naryOperator(outerType, relevantFormulas)));
          result = f.naryOperator(outerType, operands);
          return result;
      }
  }
  