code: ///////////////////////////////////////////////////////////////////////////
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  //                                                                       //
  //               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.                       //
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  ///////////////////////////////////////////////////////////////////////////
  
  package org.logicng.knowledgecompilation.dnnf.datastructures.dtree;
  
  import org.logicng.formulas.FType;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.Variable;
  
  import java.util.ArrayList;
  import java.util.Iterator;
  import java.util.List;
  
  /**
   * A generator for a DTree from an arbitrary eliminating order of variables as described in
   * A. Darwiche "Decomposable Negation Normal Form" (algorithm "el2dt").
   * @version 2.0.0
   * @since 2.0.0
   */
  public abstract class EliminatingOrderDTreeGenerator implements DTreeGenerator {
  
      /**
       * Generates the DTree
       * @param cnf      the CNF input formula
       * @param ordering the variable ordering
       * @return the DTree
       */
      public final DTree generateWithEliminatingOrder(final Formula cnf, final List<Variable> ordering) {
          assert cnf.variables().size() == ordering.size();
  
          if (!cnf.isCNF() || cnf.isAtomicFormula()) {
              throw new IllegalArgumentException("Cannot generate DTree from a non-cnf formula or atomic formula");
          } else if (cnf.type() != FType.AND) {
              return new DTreeLeaf(0, cnf);
          }
  
          final List<DTree> sigma = new ArrayList<>();
          int id = 0;
          for (final Formula clause : cnf) {
              sigma.add(new DTreeLeaf(id++, clause));
          }
  
          for (final Variable variable : ordering) {
              final List<DTree> gamma = new ArrayList<>();
              final Iterator<DTree> sigmaIterator = sigma.iterator();
              while (sigmaIterator.hasNext()) {
                  final DTree tree = sigmaIterator.next();
                  if (tree.staticVariableSet().contains(variable)) {
                      gamma.add(tree);
                      sigmaIterator.remove();
                  }
              }
              if (!gamma.isEmpty()) {
                  sigma.add(compose(gamma));
              }
          }
  
          return compose(sigma);
      }
  
      protected DTree compose(final List<DTree> trees) {
          assert !trees.isEmpty();
  
          if (trees.size() == 1) {
              return trees.get(0);
          } else {
              final DTree left = compose(trees.subList(0, trees.size() / 2));
              final DTree right = compose(trees.subList(trees.size() / 2, trees.size()));
              return new DTreeNode(left, right);
          }
      }
  }
  