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.cardinalityconstraints;
  
  import org.logicng.datastructures.EncodingResult;
  import org.logicng.formulas.Variable;
  
  /**
   * Encodes that at most one variable is assigned value true.  Uses the 2-product method due to Chen.
   * @version 2.0.0
   * @since 1.0
   */
  public final class CCAMOProduct implements CCAtMostOne {
      private final int recursiveBound;
      private EncodingResult result;
  
      /**
       * Constructs the naive AMO encoder.
       */
      CCAMOProduct(final int recursiveBound) {
          this.recursiveBound = recursiveBound;
      }
  
      @Override
      public void build(final EncodingResult result, final Variable... vars) {
          result.reset();
          this.result = result;
          this.productRec(vars);
      }
  
      private void productRec(final Variable... vars) {
          final int n = vars.length;
          final int p = (int) Math.ceil(Math.sqrt(n));
          final int q = (int) Math.ceil((double) n / (double) p);
          final Variable[] us = new Variable[p];
          for (int i = 0; i < us.length; i++) {
              us[i] = this.result.newVariable();
          }
          final Variable[] vs = new Variable[q];
          for (int i = 0; i < vs.length; i++) {
              vs[i] = this.result.newVariable();
          }
          if (us.length <= this.recursiveBound) {
              buildPure(us);
          } else {
              this.productRec(us);
          }
          if (vs.length <= this.recursiveBound) {
              buildPure(vs);
          } else {
              this.productRec(vs);
          }
          for (int i = 0; i < p; i++) {
              for (int j = 0; j < q; j++) {
                  final int k = i * q + j;
                  if (k >= 0 && k < n) {
                      this.result.addClause(vars[k].negate(), us[i]);
                      this.result.addClause(vars[k].negate(), vs[j]);
                  }
              }
          }
      }
  
      private void buildPure(final Variable... vars) {
          for (int i = 0; i < vars.length; i++) {
              for (int j = i + 1; j < vars.length; j++) {
                  this.result.addClause(vars[i].negate(), vars[j].negate());
              }
          }
      }
  
      @Override
      public String toString() {
          return this.getClass().getSimpleName();
      }
  }
  