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.functions;
  
  import static org.logicng.formulas.cache.FunctionCacheEntry.VARPROFILE;
  
  import org.logicng.formulas.FType;
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFunction;
  import org.logicng.formulas.Literal;
  import org.logicng.formulas.Variable;
  
  import java.util.HashMap;
  import java.util.Map;
  import java.util.SortedMap;
  import java.util.TreeMap;
  
  /**
   * A function that computes the variable profile for a given formula, i.e. it counts the number of occurrences for
   * each variable.
   * <p>
   * For this function, the non-caching version is preferred since it usually performs better.  The non-caching version
   * of this function generates the result mapping only once and fills it recursively whereas the caching version has to
   * construct a new mapping for each sub-formula.
   * @version 2.3.0
   * @since 1.0
   */
  public final class VariableProfileFunction implements FormulaFunction<Map<Variable, Integer>> {
  
      private static final VariableProfileFunction INSTANCE = new VariableProfileFunction();
  
      /**
       * @deprecated In the next version, the standard constructor will be replaced by a private constructor.
       * In order to instantiate an object of this class, use the {@link #get()} method.
       */
      @Deprecated
      public VariableProfileFunction() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static VariableProfileFunction get() {
          return INSTANCE;
      }
  
      /**
       * The non-caching implementation of the variable profile computation.  In this case the result map is only
       * constructed once and results are just added to it.
       * @param formula the formula
       * @return the variable profile
       */
      private static Map<Variable, Integer> nonCachingVariableProfile(final Formula formula) {
          final SortedMap<Variable, Integer> map = new TreeMap<>();
          nonCachingRecursion(formula, map);
          return map;
      }
  
      /**
       * Recursive function for the non-caching variable profile computation.
       * @param formula the formula
       * @param map     the variable profile
       */
      private static void nonCachingRecursion(final Formula formula, final Map<Variable, Integer> map) {
          if (formula.type() == FType.LITERAL) {
              final Literal lit = (Literal) formula;
              map.merge(lit.variable(), 1, Integer::sum);
          } else if (formula.type() == FType.PBC) {
              for (final Literal l : formula.literals()) {
                  nonCachingRecursion(l.variable(), map);
              }
          } else {
              for (final Formula op : formula) {
                  nonCachingRecursion(op, map);
              }
          }
      }
  
      /**
       * The caching implementation of the variable profile computation.  In this case a result map is constructed for
       * each sub-formula.
       * @param formula the formula
       * @return the variable profile
       */
      @SuppressWarnings("unchecked")
      private static Map<Variable, Integer> cachingVariableProfile(final Formula formula) {
          final Object cached = formula.functionCacheEntry(VARPROFILE);
          if (cached != null) {
              return (Map<Variable, Integer>) cached;
          }
          final Map<Variable, Integer> result = new HashMap<>();
          if (formula.type() == FType.LITERAL) {
              result.put(((Literal) formula).variable(), 1);
          } else if (formula.type() == FType.PBC) {
              for (final Literal l : formula.literals()) {
                  result.put(l.variable(), 1);
              }
          } else {
              for (final Formula op : formula) {
                  final Map<Variable, Integer> temp = cachingVariableProfile(op);
                  for (final Map.Entry<Variable, Integer> entry : temp.entrySet()) {
                      result.merge(entry.getKey(), entry.getValue(), Integer::sum);
                  }
              }
          }
          formula.setFunctionCacheEntry(VARPROFILE, result);
          return result;
      }
  
      @Override
      public Map<Variable, Integer> apply(final Formula formula, final boolean cache) {
          return cache ? cachingVariableProfile(formula) : nonCachingVariableProfile(formula);
      }
  }
  