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.knowledgecompilation.bdds.orderings;
  
  import org.logicng.formulas.BinaryOperator;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.Not;
  import org.logicng.formulas.PBConstraint;
  import org.logicng.formulas.Variable;
  
  import java.util.ArrayList;
  import java.util.LinkedHashSet;
  import java.util.LinkedList;
  import java.util.List;
  import java.util.Queue;
  
  /**
   * A breadth-first-search BDD variable ordering.  Traverses the formula in a BFS manner
   * and gathers all variables in the occurrence.
   * @version 2.0.0
   * @since 1.4.0
   */
  public final class BFSOrdering implements VariableOrderingProvider {
  
      @Override
      public List<Variable> getOrder(final Formula formula) {
          return new ArrayList<>(bfs(formula));
      }
  
      private LinkedHashSet<Variable> bfs(final Formula formula) {
          final LinkedHashSet<Variable> variables = new LinkedHashSet<>();
          final Queue<Formula> queue = new LinkedList<>();
          queue.add(formula);
          while (!queue.isEmpty()) {
              final Formula current = queue.remove();
              switch (current.type()) {
                  case LITERAL:
                      final Literal lit = (Literal) current;
                      if (lit.phase()) {
                          variables.add(lit.variable());
                      } else {
                          queue.add(lit.variable());
                      }
                      break;
                  case NOT:
                      queue.add(((Not) current).operand());
                      break;
                  case IMPL:
                  case EQUIV:
                      final BinaryOperator op = (BinaryOperator) current;
                      queue.add(op.left());
                      queue.add(op.right());
                      break;
                  case AND:
                  case OR:
                      for (final Formula operand : current) {
                          queue.add(operand);
                      }
                      break;
                  case PBC:
                      final PBConstraint pbc = (PBConstraint) current;
                      for (final Literal literal : pbc.operands()) {
                          variables.add(literal.variable());
                      }
                      break;
              }
          }
          return variables;
      }
  }
  