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.                       //
  //                                                                       //
  ///////////////////////////////////////////////////////////////////////////
  
  /*
   * Copyright (C) 2012 - 2014 Armin Biere JKU Linz
   * <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.collections;
  
  /**
   * A simple priority queue implementation for elements with long priorities taken from CleaneLing.
   * @version 1.3
   * @since 1.0
   */
  public final class LNGLongPriorityQueue {
  
      private final LNGIntVector heap;
      private final LNGLongVector prior;
      private final LNGIntVector pos;
  
      /**
       * Creates a new priority queue.
       */
      public LNGLongPriorityQueue() {
          this.heap = new LNGIntVector();
          this.prior = new LNGLongVector();
          this.pos = new LNGIntVector();
      }
  
      /**
       * Returns the left position on the heap for a given position.
       * @param position the position
       * @return the left position
       */
      private static int left(final int position) {
          return 2 * position + 1;
      }
  
      /**
       * Returns the right position on the heap for a given position.
       * @param position the position
       * @return the right position
       */
      private static int right(final int position) {
          return 2 * position + 2;
      }
  
      /**
       * Returns the parent position on the heap for a given position.
       * @param position the position
       * @return the parent position
       */
      private static int parent(final int position) {
          assert position > 0;
          return (position - 1) / 2;
      }
  
      /**
       * Returns whether the queue is empty or not.
       * @return {@code true} if the queue is empty, {@code false} otherwise
       */
      public boolean empty() {
          return this.heap.empty();
      }
  
      /**
       * Returns the size of the queue.
       * @return the size of the queue
       */
      public int size() {
          return this.heap.size();
      }
  
      /**
       * Returns whether a given element is already imported and present in the queue or not.
       * @param element the element
       * @return {@code true} if the element is already imported and present in the queue, {@code false otherwise}.
       */
      public boolean contains(final int element) {
          return element >= 0 && this.imported(element) && this.pos.get(Math.abs(element)) >= 0;
      }
  
      /**
       * Returns the priority for a given element.
       * @param element the element
       * @return the priority of the element
       */
      public long priority(final int element) {
          assert this.imported(element);
          return this.prior.get(Math.abs(element));
      }
  
      /**
       * Returns the top element of the priority queue (= the element with the largest priority).
       * @return the top element of the priority queue
       */
      public int top() {
          return this.heap.get(0);
      }
  
      /**
       * Pushes a new element to the queue.
       * @param element the element
       * @throws IllegalArgumentException if the element to add is negative
       */
      public void push(final int element) {
          if (element < 0) {
              throw new IllegalArgumentException("Cannot add negative integers to the priority queue");
          }
          assert !this.contains(element);
          this.doImport(element);
          this.pos.set(element, this.heap.size());
          this.heap.push(element);
          assert this.heap.get(this.pos.get(element)) == element;
          this.up(element);
      }
  
      /**
       * Updated the priority of a given element.
       * @param element  the element
       * @param priority the new priority
       */
      public void update(final int element, final long priority) {
          this.doImport(element);
          final long q = this.prior.get(element);
          if (q == priority) {
              return;
          }
          this.prior.set(element, priority);
          if (this.pos.get(element) < 0) {
              return;
          }
          if (priority < q) {
              this.down(element);
          }
          if (q < priority) {
              this.up(element);
          }
      }
  
      /**
       * Removes a given element from the priority queue.  Its priority is kept as is.
       * @param element the element
       */
      public void pop(final int element) {
          assert this.contains(element);
          final int i = this.pos.get(element);
          this.pos.set(element, -1);
          final int last = this.heap.back();
          this.heap.pop();
          final int j = this.heap.size();
          if (i == j) {
              return;
          }
          assert i < j;
          this.pos.set(last, i);
          this.heap.set(i, last);
          this.up(last);
          this.down(last);
      }
  
      /**
       * Removes the top element from the priority queue.
       */
      public void pop() {
          this.pop(this.top());
      }
  
      /**
       * Compares two elements by their priority and returns whether the first element's priority is less than the second
       * element's priority.
       * @param e1 the first element
       * @param e2 the second element
       * @return {@code true} if the priority of the first element is less than the priority of the second element
       */
      private boolean less(final int e1, final int e2) {
          return this.prior.get(e1) < this.prior.get(e2);
      }
  
      /**
       * Bubbles a given element up.
       * @param element the element
       */
      private void up(final int element) {
          int epos = this.pos.get(element);
          while (epos > 0) {
              final int ppos = parent(epos);
              final int p = this.heap.get(ppos);
              if (!this.less(p, element)) {
                  break;
              }
              this.heap.set(epos, p);
              this.heap.set(ppos, element);
              this.pos.set(p, epos);
              epos = ppos;
          }
          this.pos.set(element, epos);
      }
  
      /**
       * Bubbles a given element down.
       * @param element the element
       */
      private void down(final int element) {
          assert this.contains(element);
          int epos = this.pos.get(element);
          final int size = this.heap.size();
          while (true) {
              int cpos = left(epos);
              if (cpos >= size) {
                  break;
              }
              int c = this.heap.get(cpos);
              final int o;
              final int opos = right(epos);
              if (!this.less(element, c)) {
                  if (opos >= size) {
                      break;
                  }
                  o = this.heap.get(opos);
                  if (!this.less(element, o)) {
                      break;
                  }
                  cpos = opos;
                  c = o;
              } else if (opos < size) {
                  o = this.heap.get(opos);
                  if (!this.less(o, c)) {
                      cpos = opos;
                      c = o;
                  }
              }
              this.heap.set(cpos, element);
              this.heap.set(epos, c);
              this.pos.set(c, epos);
              epos = cpos;
          }
          this.pos.set(element, epos);
      }
  
      /**
       * Returns whether a given element is already imported.
       * @param element the element
       * @return {@code true} if the element is imported, {@code false} otherwise
       */
      private boolean imported(final int element) {
          assert 0 <= element;
          return element < this.pos.size();
      }
  
      /**
       * Imports a given element.
       * @param element the element
       */
      private void doImport(final int element) {
          while (!this.imported(element)) {
              this.pos.push(-1);
              this.prior.push(0);
          }
      }
  
      @Override
      public String toString() {
          final StringBuilder sb = new StringBuilder("LNGLongPriorityQueue{");
          for (int i = 0; i < this.heap.size(); i++) {
              sb.append(String.format("<elem=%d, pos=%d, prio=%d>", this.heap.get(i), this.pos.get(i), this.prior.get(i)));
              if (i != this.heap.size() - 1) {
                  sb.append(", ");
              }
          }
          sb.append("}");
          return sb.toString();
      }
  }
  
  