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.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  /*
   * 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.collections.LNGVector;
  import org.logicng.datastructures.EncodingResult;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.Variable;
  
  /**
   * Encodes that at most one variable is assigned value true.  Uses the bimander encoding due to Hölldobler and Nguyen.
   * @version 2.0.0
   * @since 1.1
   */
  public final class CCAMOBimander implements CCAtMostOne {
  
      private final LNGVector<LNGVector<Literal>> groups;
      private final LNGVector<Literal> bits;
      private final int m;
      private EncodingResult result;
      private int numberOfBits;
      private int twoPowNBits;
      private int k;
  
      /**
       * Constructs the bimander AMO encoder with a given number of groups.
       */
      CCAMOBimander(final int m) {
          this.m = m;
          this.groups = new LNGVector<>();
          this.bits = new LNGVector<>();
      }
  
      @Override
      public void build(final EncodingResult result, final Variable... vars) {
          result.reset();
          this.result = result;
          this.encodeIntern(new LNGVector<>(vars));
      }
  
      /**
       * Internal encoding.
       * @param vars the variables of the constraint
       */
      private void encodeIntern(final LNGVector<Literal> vars) {
          this.initializeGroups(vars);
          this.initializeBits();
          int grayCode;
          int nextGray;
          int i = 0;
          int index = -1;
          for (; i < this.k; i++) {
              index++;
              grayCode = i ^ (i >> 1);
              i++;
              nextGray = i ^ (i >> 1);
              for (int j = 0; j < this.numberOfBits; j++) {
                  if ((grayCode & (1 << j)) == (nextGray & (1 << j))) {
                      handleGrayCode(grayCode, index, j);
                  }
              }
          }
          for (; i < this.twoPowNBits; i++) {
              index++;
              grayCode = i ^ (i >> 1);
              for (int j = 0; j < this.numberOfBits; j++) {
                  handleGrayCode(grayCode, index, j);
              }
          }
      }
  
      private void handleGrayCode(final int grayCode, final int index, final int j) {
          if ((grayCode & (1 << j)) != 0) {
              for (int p = 0; p < this.groups.get(index).size(); ++p) {
                  this.result.addClause(this.groups.get(index).get(p).negate(), this.bits.get(j));
              }
          } else {
              for (int p = 0; p < this.groups.get(index).size(); ++p) {
                  this.result.addClause(this.groups.get(index).get(p).negate(), this.bits.get(j).negate());
              }
          }
      }
  
      /**
       * Initializes the groups
       * @param vars the variables of the constraint
       */
      private void initializeGroups(final LNGVector<Literal> vars) {
          final int n = vars.size();
          this.groups.clear();
          for (int i = 0; i < this.m; i++) {
              this.groups.push(new LNGVector<>());
          }
  
          int g = (int) Math.ceil((double) n / this.m);
          int ig = 0;
          for (int i = 0; i < vars.size(); ) {
              while (i < g) {
                  this.groups.get(ig).push(vars.get(i));
                  i++;
              }
              ig++;
              g = g + (int) Math.ceil((double) (n - i) / (this.m - ig));
          }
  
          for (int i = 0; i < this.groups.size(); i++) {
              this.encodeNaive(this.groups.get(i));
          }
      }
  
      /**
       * Initializes the bits.
       */
      private void initializeBits() {
          this.bits.clear();
          this.numberOfBits = (int) Math.ceil(Math.log(this.m) / Math.log(2));
          this.twoPowNBits = (int) Math.pow(2, this.numberOfBits);
          this.k = (this.twoPowNBits - this.m) * 2;
          for (int i = 0; i < this.numberOfBits; ++i) {
              this.bits.push(this.result.newVariable());
          }
      }
  
      /**
       * Naive encoding of a cardinality constraint.
       * @param vars the variables of the constraint
       */
      private void encodeNaive(final LNGVector<Literal> vars) {
          if (vars.size() > 1) {
              for (int i = 0; i < vars.size(); i++) {
                  for (int j = i + 1; j < vars.size(); j++) {
                      this.result.addClause(vars.get(i).negate(), vars.get(j).negate());
                  }
              }
          }
      }
  
      @Override
      public String toString() {
          return this.getClass().getSimpleName();
      }
  }
  