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.transformations.qmc;
  
  import org.logicng.datastructures.Tristate;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFactory;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.Variable;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.List;
  
  /**
   * A term in the Quine–McCluskey algorithm.  A term represents a set of
   * minterms of a canonical DNF and has its own representation as a vector
   * of tristates.  Two minterms are considered equals if their bit representation
   * is equals (independent of their associated minterms)
   * @version 2.0.0
   * @since 1.4.0
   */
  public class Term {
  
      protected final Tristate[] bits;
      protected final List<Formula> minterms;
      protected final int termClass;
      protected boolean used;
      protected final long undefNum;
  
      /**
       * Constructs a new term with a given set of bits and the related minterms.
       * @param bits     the bits
       * @param minterms the minterms
       */
      Term(final Tristate[] bits, final List<Formula> minterms) {
          this.bits = bits;
          this.minterms = minterms;
          this.termClass = countNonNegativeBits(bits);
          this.undefNum = computeUndefNum(bits);
      }
  
      /**
       * Counts the number of non-negative bits of a given tristate vector.
       * @param bits the tristate vector
       * @return the number of non-negative bits
       */
      protected int countNonNegativeBits(final Tristate[] bits) {
          int result = 0;
          for (final Tristate bit : bits) {
              if (bit != Tristate.FALSE) {
                  result++;
              }
          }
          return result;
      }
  
      /**
       * Computes a number representing the number and position of the UNDEF states in the bit array.
       * @param bits the bit array
       * @return the computed number
       */
      protected long computeUndefNum(final Tristate[] bits) {
          long sum = 0;
          for (int i = bits.length - 1; i >= 0; i--) {
              if (bits[i] == Tristate.UNDEF) {
                  sum += Math.pow(2, bits.length - 1 - i);
              }
          }
          return sum;
      }
  
      /**
       * Returns the bit array of this term.
       * @return the bit array of this term
       */
      Tristate[] bits() {
          return this.bits;
      }
  
      /**
       * Returns the associated minterms for this term.
       * @return the associated minterms for this term
       */
      List<Formula> minterms() {
          return this.minterms;
      }
  
      /**
       * Returns the term class of this term.  The term class is the number of non-negative bits in the bit array.
       * @return the term class of this term
       */
      int termClass() {
          return this.termClass;
      }
  
      /**
       * Returns whether this term was used in the combination step of QMC or not.
       * @return whether this term was used
       */
      boolean isUsed() {
          return this.used;
      }
  
      /**
       * Sets whether this term was used in the combination step of QMC or not.
       * @param used whether this term was used
       */
      void setUsed(final boolean used) {
          this.used = used;
      }
  
      /**
       * Combines this term with another term if possible.  This is only possible if their bit vectors
       * differ in exactly one position.  In this case a new term with the new bit vector and the
       * combined minterms is returned.  If no union is possible, {@code null} is returned.
       * @param other the other term
       * @return a new combined term or {@code null} if not possible
       */
      Term combine(final Term other) {
          if (this.bits.length != other.bits.length) {
              return null;
          }
          if (this.undefNum != other.undefNum) {
              return null;
          }
          int diffPosition = -1;
          for (int i = 0; i < this.bits.length; i++) {
              if (this.bits[i] != other.bits[i]) {
                  if (diffPosition != -1) {
                      return null;
                  } else {
                      diffPosition = i;
                  }
              }
          }
          if (diffPosition == -1) {
              return null;
          }
          final Tristate[] newBits = Arrays.copyOf(this.bits, this.bits.length);
          newBits[diffPosition] = Tristate.UNDEF;
          final List<Formula> newMinterms = new ArrayList<>(this.minterms);
          newMinterms.addAll(other.minterms);
          return new Term(newBits, newMinterms);
      }
  
      /**
       * Translates this term to a formula for a given variable ordering
       * @param varOrder the variable ordering
       * @return the translation of this term to a formula
       */
      Formula translateToFormula(final List<Variable> varOrder) {
          final FormulaFactory f = varOrder.get(0).factory();
          assert this.bits.length == varOrder.size();
          final List<Literal> operands = new ArrayList<>(varOrder.size());
          for (int i = 0; i < this.bits.length; i++) {
              if (this.bits[i] != Tristate.UNDEF) {
                  operands.add(this.bits[i] == Tristate.TRUE ? varOrder.get(i) : varOrder.get(i).negate());
              }
          }
          return f.and(operands);
      }
  
      @Override
      public boolean equals(final Object o) {
          if (this == o) {
              return true;
          }
          if (o == null || getClass() != o.getClass()) {
              return false;
          }
          final Term term = (Term) o;
          return Arrays.equals(this.bits, term.bits);
      }
  
      @Override
      public int hashCode() {
          return Arrays.hashCode(this.bits);
      }
  
      @Override
      public String toString() {
          return "Term{" +
                  "bits=" + Arrays.toString(this.bits) +
                  ", minterms=" + this.minterms +
                  ", termClass=" + this.termClass +
                  '}';
      }
  }
  