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.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  /*
   * PBLib       -- Copyright (c) 2012-2013  Peter Steinke
   * <p>
   * Permission is hereby granted, free of charge, to any person obtaining a
   * copy of this software and associated documentation files (the
   * "Software"), to deal in the Software without restriction, including
   * without limitation the rights to use, copy, modify, merge, publish,
   * distribute, sublicense, and/or sell copies of the Software, and to
   * permit persons to whom the Software is furnished to do so, subject to
   * the following conditions:
   * <p>
   * The above copyright notice and this permission notice shall be included
   * in all copies or substantial portions of the Software.
   * <p>
   * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
   * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
   * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
   * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
   * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
   * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
   * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
   */
  
  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 binary encoding due to Doggett, Frisch, Peugniez,
   * and Nightingale.
   * @version 2.0.0
   * @since 1.1
   */
  public final class CCAMOBinary implements CCAtMostOne {
  
      /**
       * Constructs the binary AMO encoder.
       */
      CCAMOBinary() {
          //intentionally left empty
      }
  
      @Override
      public void build(final EncodingResult result, final Variable... vars) {
          result.reset();
          final int numberOfBits = (int) Math.ceil(Math.log(vars.length) / Math.log(2));
          final int twoPowNBits = (int) Math.pow(2, numberOfBits);
          final int k = (twoPowNBits - vars.length) * 2;
          final Variable[] bits = new Variable[numberOfBits];
          for (int i = 0; i < numberOfBits; i++) {
              bits[i] = result.newVariable();
          }
          int grayCode;
          int nextGray;
          int i = 0;
          int index = -1;
          while (i < k) {
              index++;
              grayCode = i ^ (i >> 1);
              i++;
              nextGray = i ^ (i >> 1);
              for (int j = 0; j < numberOfBits; ++j) {
                  if ((grayCode & (1 << j)) == (nextGray & (1 << j))) {
                      if ((grayCode & (1 << j)) != 0) {
                          result.addClause(vars[index].negate(), bits[j]);
                      } else {
                          result.addClause(vars[index].negate(), bits[j].negate());
                      }
                  }
              }
              i++;
          }
          while (i < twoPowNBits) {
              index++;
              grayCode = i ^ (i >> 1);
              for (int j = 0; j < numberOfBits; ++j) {
                  if ((grayCode & (1 << j)) != 0) {
                      result.addClause(vars[index].negate(), bits[j]);
                  } else {
                      result.addClause(vars[index].negate(), bits[j].negate());
                  }
              }
              i++;
          }
      }
  
      @Override
      public String toString() {
          return this.getClass().getSimpleName();
      }
  }
  