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.formulas;
  
  import org.logicng.datastructures.Assignment;
  import org.logicng.datastructures.Substitution;
  
  import java.util.ArrayList;
  import java.util.Collection;
  import java.util.Iterator;
  import java.util.LinkedHashSet;
  import java.util.List;
  import java.util.NoSuchElementException;
  import java.util.stream.Stream;
  
  /**
   * Super class for Boolean n-ary operators.
   * @version 2.2.0
   * @since 1.0
   */
  public abstract class NAryOperator extends Formula {
  
      protected final Formula[] operands;
      private volatile int hashCode;
  
      /**
       * Constructor.
       * @param type     the operator's type
       * @param operands the list of operands
       * @param f        the factory which created this instance
       */
      NAryOperator(final FType type, final Collection<? extends Formula> operands, final FormulaFactory f) {
          super(type, f);
          this.operands = operands.toArray(new Formula[0]);
          this.hashCode = 0;
      }
  
      @Override
      public int numberOfOperands() {
          return this.operands.length;
      }
  
      @Override
      public boolean isConstantFormula() {
          return false;
      }
  
      @Override
      public boolean isAtomicFormula() {
          return false;
      }
  
      @Override
      public boolean containsVariable(final Variable variable) {
          for (final Formula op : this.operands) {
              if (op.containsVariable(variable)) {
                  return true;
              }
          }
          return false;
      }
  
      @Override
      public Formula restrict(final Assignment assignment) {
          final LinkedHashSet<Formula> nops = new LinkedHashSet<>();
          for (final Formula op : this.operands) {
              nops.add(op.restrict(assignment));
          }
          return this.f.naryOperator(this.type, nops);
      }
  
      @Override
      public boolean containsNode(final Formula formula) {
          if (this.equals(formula)) {
              return true;
          }
          if (this.type != formula.type) {
              for (final Formula op : this.operands) {
                  if (op.containsNode(formula)) {
                      return true;
                  }
              }
              return false;
          }
          final List<Formula> fOps = new ArrayList<>(formula.numberOfOperands());
          for (final Formula op : formula) {
              fOps.add(op);
          }
          for (final Formula op : this.operands) {
              fOps.remove(op);
              if (op.containsNode(formula)) {
                  return true;
              }
          }
          return fOps.isEmpty();
      }
  
      @Override
      public Formula substitute(final Substitution substitution) {
          final LinkedHashSet<Formula> nops = new LinkedHashSet<>();
          for (final Formula op : this.operands) {
              nops.add(op.substitute(substitution));
          }
          return this.f.naryOperator(this.type, nops);
      }
  
      @Override
      public Formula negate() {
          return this.f.not(this);
      }
  
      /**
       * Helper method for generating the hashcode.
       * @param shift shift value
       * @return hashcode
       */
      protected int hashCode(final int shift) {
          if (this.hashCode == 0) {
              int temp = 1;
              for (final Formula formula : this.operands) {
                  temp += formula.hashCode();
              }
              temp *= shift;
              this.hashCode = temp;
          }
          return this.hashCode;
      }
  
      protected boolean compareOperands(final Formula[] other) {
          if (this.operands.length != other.length) {
              return false;
          }
          for (final Formula op1 : this.operands) {
              boolean found = false;
              for (final Formula op2 : other) {
                  if (op1.equals(op2)) {
                      found = true;
                      break;
                  }
              }
              if (!found) {
                  return false;
              }
          }
          return true;
      }
  
      @Override
      public Iterator<Formula> iterator() {
          return new Iterator<Formula>() {
              private int i;
  
              @Override
              public boolean hasNext() {
                  return this.i < NAryOperator.this.operands.length;
              }
  
              @Override
              public Formula next() {
                  if (this.i == NAryOperator.this.operands.length) {
                      throw new NoSuchElementException();
                  }
                  return NAryOperator.this.operands[this.i++];
              }
  
              @Override
              public void remove() {
                  throw new UnsupportedOperationException();
              }
          };
      }
  
      @Override
      public Stream<Formula> stream() {
          return Stream.of(this.operands);
      }
  }
  