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.DEPTH;
  
  import org.logicng.formulas.Formula;
  import org.logicng.formulas.FormulaFunction;
  
  /**
   * A function that computes the depth of a formula. The depth of an atomic formula
   * is defined as 0, all other operators increase the depth by 1.
   * @version 2.3.0
   * @since 2.0
   */
  public final class FormulaDepthFunction implements FormulaFunction<Integer> {
  
      private static final FormulaDepthFunction INSTANCE = new FormulaDepthFunction();
  
      /**
       * @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 FormulaDepthFunction() {
          // Intentionally left empty
      }
  
      /**
       * Returns the singleton instance of this function.
       * @return an instance of this function
       */
      public static FormulaDepthFunction get() {
          return INSTANCE;
      }
  
      @Override
      public Integer apply(final Formula formula, final boolean cache) {
          final Object cached = formula.functionCacheEntry(DEPTH);
          if (cached != null) {
              return (Integer) cached;
          }
          final int result;
          if (formula.isAtomicFormula()) {
              result = 0;
          } else {
              int maxDepth = 0;
              for (final Formula op : formula) {
                  maxDepth = Math.max(maxDepth, apply(op, cache));
              }
              result = maxDepth + 1;
          }
          if (cache) {
              formula.setFunctionCacheEntry(DEPTH, result);
          }
          return result;
      }
  }
  