lemon/bucket_heap.h
changeset 681 532697c9fa53
child 682 bb8c4cd57900
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/lemon/bucket_heap.h	Thu Jun 11 22:11:29 2009 +0200
     1.3 @@ -0,0 +1,831 @@
     1.4 +/* -*- mode: C++; indent-tabs-mode: nil; -*-
     1.5 + *
     1.6 + * This file is a part of LEMON, a generic C++ optimization library.
     1.7 + *
     1.8 + * Copyright (C) 2003-2009
     1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
    1.11 + *
    1.12 + * Permission to use, modify and distribute this software is granted
    1.13 + * provided that this copyright notice appears in all copies. For
    1.14 + * precise terms see the accompanying LICENSE file.
    1.15 + *
    1.16 + * This software is provided "AS IS" with no warranty of any kind,
    1.17 + * express or implied, and with no claim as to its suitability for any
    1.18 + * purpose.
    1.19 + *
    1.20 + */
    1.21 +
    1.22 +#ifndef LEMON_BUCKET_HEAP_H
    1.23 +#define LEMON_BUCKET_HEAP_H
    1.24 +
    1.25 +///\ingroup auxdat
    1.26 +///\file
    1.27 +///\brief Bucket Heap implementation.
    1.28 +
    1.29 +#include <vector>
    1.30 +#include <utility>
    1.31 +#include <functional>
    1.32 +
    1.33 +namespace lemon {
    1.34 +
    1.35 +  /// \ingroup auxdat
    1.36 +  ///
    1.37 +  /// \brief A Bucket Heap implementation.
    1.38 +  ///
    1.39 +  /// This class implements the \e bucket \e heap data structure. A \e heap
    1.40 +  /// is a data structure for storing items with specified values called \e
    1.41 +  /// priorities in such a way that finding the item with minimum priority is
    1.42 +  /// efficient. The bucket heap is very simple implementation, it can store
    1.43 +  /// only integer priorities and it stores for each priority in the
    1.44 +  /// \f$ [0..C) \f$ range a list of items. So it should be used only when
    1.45 +  /// the priorities are small. It is not intended to use as dijkstra heap.
    1.46 +  ///
    1.47 +  /// \param _ItemIntMap A read and writable Item int map, used internally
    1.48 +  /// to handle the cross references.
    1.49 +  /// \param minimize If the given parameter is true then the heap gives back
    1.50 +  /// the lowest priority.
    1.51 +  template <typename _ItemIntMap, bool minimize = true >
    1.52 +  class BucketHeap {
    1.53 +
    1.54 +  public:
    1.55 +    /// \e
    1.56 +    typedef typename _ItemIntMap::Key Item;
    1.57 +    /// \e
    1.58 +    typedef int Prio;
    1.59 +    /// \e
    1.60 +    typedef std::pair<Item, Prio> Pair;
    1.61 +    /// \e
    1.62 +    typedef _ItemIntMap ItemIntMap;
    1.63 +
    1.64 +    /// \brief Type to represent the items states.
    1.65 +    ///
    1.66 +    /// Each Item element have a state associated to it. It may be "in heap",
    1.67 +    /// "pre heap" or "post heap". The latter two are indifferent from the
    1.68 +    /// heap's point of view, but may be useful to the user.
    1.69 +    ///
    1.70 +    /// The ItemIntMap \e should be initialized in such way that it maps
    1.71 +    /// PRE_HEAP (-1) to any element to be put in the heap...
    1.72 +    enum State {
    1.73 +      IN_HEAP = 0,
    1.74 +      PRE_HEAP = -1,
    1.75 +      POST_HEAP = -2
    1.76 +    };
    1.77 +
    1.78 +  public:
    1.79 +    /// \brief The constructor.
    1.80 +    ///
    1.81 +    /// The constructor.
    1.82 +    /// \param _index should be given to the constructor, since it is used
    1.83 +    /// internally to handle the cross references. The value of the map
    1.84 +    /// should be PRE_HEAP (-1) for each element.
    1.85 +    explicit BucketHeap(ItemIntMap &_index) : index(_index), minimal(0) {}
    1.86 +
    1.87 +    /// The number of items stored in the heap.
    1.88 +    ///
    1.89 +    /// \brief Returns the number of items stored in the heap.
    1.90 +    int size() const { return data.size(); }
    1.91 +
    1.92 +    /// \brief Checks if the heap stores no items.
    1.93 +    ///
    1.94 +    /// Returns \c true if and only if the heap stores no items.
    1.95 +    bool empty() const { return data.empty(); }
    1.96 +
    1.97 +    /// \brief Make empty this heap.
    1.98 +    ///
    1.99 +    /// Make empty this heap. It does not change the cross reference
   1.100 +    /// map.  If you want to reuse a heap what is not surely empty you
   1.101 +    /// should first clear the heap and after that you should set the
   1.102 +    /// cross reference map for each item to \c PRE_HEAP.
   1.103 +    void clear() {
   1.104 +      data.clear(); first.clear(); minimal = 0;
   1.105 +    }
   1.106 +
   1.107 +  private:
   1.108 +
   1.109 +    void relocate_last(int idx) {
   1.110 +      if (idx + 1 < int(data.size())) {
   1.111 +        data[idx] = data.back();
   1.112 +        if (data[idx].prev != -1) {
   1.113 +          data[data[idx].prev].next = idx;
   1.114 +        } else {
   1.115 +          first[data[idx].value] = idx;
   1.116 +        }
   1.117 +        if (data[idx].next != -1) {
   1.118 +          data[data[idx].next].prev = idx;
   1.119 +        }
   1.120 +        index[data[idx].item] = idx;
   1.121 +      }
   1.122 +      data.pop_back();
   1.123 +    }
   1.124 +
   1.125 +    void unlace(int idx) {
   1.126 +      if (data[idx].prev != -1) {
   1.127 +        data[data[idx].prev].next = data[idx].next;
   1.128 +      } else {
   1.129 +        first[data[idx].value] = data[idx].next;
   1.130 +      }
   1.131 +      if (data[idx].next != -1) {
   1.132 +        data[data[idx].next].prev = data[idx].prev;
   1.133 +      }
   1.134 +    }
   1.135 +
   1.136 +    void lace(int idx) {
   1.137 +      if (int(first.size()) <= data[idx].value) {
   1.138 +        first.resize(data[idx].value + 1, -1);
   1.139 +      }
   1.140 +      data[idx].next = first[data[idx].value];
   1.141 +      if (data[idx].next != -1) {
   1.142 +        data[data[idx].next].prev = idx;
   1.143 +      }
   1.144 +      first[data[idx].value] = idx;
   1.145 +      data[idx].prev = -1;
   1.146 +    }
   1.147 +
   1.148 +  public:
   1.149 +    /// \brief Insert a pair of item and priority into the heap.
   1.150 +    ///
   1.151 +    /// Adds \c p.first to the heap with priority \c p.second.
   1.152 +    /// \param p The pair to insert.
   1.153 +    void push(const Pair& p) {
   1.154 +      push(p.first, p.second);
   1.155 +    }
   1.156 +
   1.157 +    /// \brief Insert an item into the heap with the given priority.
   1.158 +    ///
   1.159 +    /// Adds \c i to the heap with priority \c p.
   1.160 +    /// \param i The item to insert.
   1.161 +    /// \param p The priority of the item.
   1.162 +    void push(const Item &i, const Prio &p) {
   1.163 +      int idx = data.size();
   1.164 +      index[i] = idx;
   1.165 +      data.push_back(BucketItem(i, p));
   1.166 +      lace(idx);
   1.167 +      if (p < minimal) {
   1.168 +        minimal = p;
   1.169 +      }
   1.170 +    }
   1.171 +
   1.172 +    /// \brief Returns the item with minimum priority.
   1.173 +    ///
   1.174 +    /// This method returns the item with minimum priority.
   1.175 +    /// \pre The heap must be nonempty.
   1.176 +    Item top() const {
   1.177 +      while (first[minimal] == -1) {
   1.178 +        ++minimal;
   1.179 +      }
   1.180 +      return data[first[minimal]].item;
   1.181 +    }
   1.182 +
   1.183 +    /// \brief Returns the minimum priority.
   1.184 +    ///
   1.185 +    /// It returns the minimum priority.
   1.186 +    /// \pre The heap must be nonempty.
   1.187 +    Prio prio() const {
   1.188 +      while (first[minimal] == -1) {
   1.189 +        ++minimal;
   1.190 +      }
   1.191 +      return minimal;
   1.192 +    }
   1.193 +
   1.194 +    /// \brief Deletes the item with minimum priority.
   1.195 +    ///
   1.196 +    /// This method deletes the item with minimum priority from the heap.
   1.197 +    /// \pre The heap must be non-empty.
   1.198 +    void pop() {
   1.199 +      while (first[minimal] == -1) {
   1.200 +        ++minimal;
   1.201 +      }
   1.202 +      int idx = first[minimal];
   1.203 +      index[data[idx].item] = -2;
   1.204 +      unlace(idx);
   1.205 +      relocate_last(idx);
   1.206 +    }
   1.207 +
   1.208 +    /// \brief Deletes \c i from the heap.
   1.209 +    ///
   1.210 +    /// This method deletes item \c i from the heap, if \c i was
   1.211 +    /// already stored in the heap.
   1.212 +    /// \param i The item to erase.
   1.213 +    void erase(const Item &i) {
   1.214 +      int idx = index[i];
   1.215 +      index[data[idx].item] = -2;
   1.216 +      unlace(idx);
   1.217 +      relocate_last(idx);
   1.218 +    }
   1.219 +
   1.220 +
   1.221 +    /// \brief Returns the priority of \c i.
   1.222 +    ///
   1.223 +    /// This function returns the priority of item \c i.
   1.224 +    /// \pre \c i must be in the heap.
   1.225 +    /// \param i The item.
   1.226 +    Prio operator[](const Item &i) const {
   1.227 +      int idx = index[i];
   1.228 +      return data[idx].value;
   1.229 +    }
   1.230 +
   1.231 +    /// \brief \c i gets to the heap with priority \c p independently
   1.232 +    /// if \c i was already there.
   1.233 +    ///
   1.234 +    /// This method calls \ref push(\c i, \c p) if \c i is not stored
   1.235 +    /// in the heap and sets the priority of \c i to \c p otherwise.
   1.236 +    /// \param i The item.
   1.237 +    /// \param p The priority.
   1.238 +    void set(const Item &i, const Prio &p) {
   1.239 +      int idx = index[i];
   1.240 +      if (idx < 0) {
   1.241 +        push(i,p);
   1.242 +      } else if (p > data[idx].value) {
   1.243 +        increase(i, p);
   1.244 +      } else {
   1.245 +        decrease(i, p);
   1.246 +      }
   1.247 +    }
   1.248 +
   1.249 +    /// \brief Decreases the priority of \c i to \c p.
   1.250 +    ///
   1.251 +    /// This method decreases the priority of item \c i to \c p.
   1.252 +    /// \pre \c i must be stored in the heap with priority at least \c
   1.253 +    /// p relative to \c Compare.
   1.254 +    /// \param i The item.
   1.255 +    /// \param p The priority.
   1.256 +    void decrease(const Item &i, const Prio &p) {
   1.257 +      int idx = index[i];
   1.258 +      unlace(idx);
   1.259 +      data[idx].value = p;
   1.260 +      if (p < minimal) {
   1.261 +        minimal = p;
   1.262 +      }
   1.263 +      lace(idx);
   1.264 +    }
   1.265 +
   1.266 +    /// \brief Increases the priority of \c i to \c p.
   1.267 +    ///
   1.268 +    /// This method sets the priority of item \c i to \c p.
   1.269 +    /// \pre \c i must be stored in the heap with priority at most \c
   1.270 +    /// p relative to \c Compare.
   1.271 +    /// \param i The item.
   1.272 +    /// \param p The priority.
   1.273 +    void increase(const Item &i, const Prio &p) {
   1.274 +      int idx = index[i];
   1.275 +      unlace(idx);
   1.276 +      data[idx].value = p;
   1.277 +      lace(idx);
   1.278 +    }
   1.279 +
   1.280 +    /// \brief Returns if \c item is in, has already been in, or has
   1.281 +    /// never been in the heap.
   1.282 +    ///
   1.283 +    /// This method returns PRE_HEAP if \c item has never been in the
   1.284 +    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   1.285 +    /// otherwise. In the latter case it is possible that \c item will
   1.286 +    /// get back to the heap again.
   1.287 +    /// \param i The item.
   1.288 +    State state(const Item &i) const {
   1.289 +      int idx = index[i];
   1.290 +      if (idx >= 0) idx = 0;
   1.291 +      return State(idx);
   1.292 +    }
   1.293 +
   1.294 +    /// \brief Sets the state of the \c item in the heap.
   1.295 +    ///
   1.296 +    /// Sets the state of the \c item in the heap. It can be used to
   1.297 +    /// manually clear the heap when it is important to achive the
   1.298 +    /// better time complexity.
   1.299 +    /// \param i The item.
   1.300 +    /// \param st The state. It should not be \c IN_HEAP.
   1.301 +    void state(const Item& i, State st) {
   1.302 +      switch (st) {
   1.303 +      case POST_HEAP:
   1.304 +      case PRE_HEAP:
   1.305 +        if (state(i) == IN_HEAP) {
   1.306 +          erase(i);
   1.307 +        }
   1.308 +        index[i] = st;
   1.309 +        break;
   1.310 +      case IN_HEAP:
   1.311 +        break;
   1.312 +      }
   1.313 +    }
   1.314 +
   1.315 +  private:
   1.316 +
   1.317 +    struct BucketItem {
   1.318 +      BucketItem(const Item& _item, int _value)
   1.319 +        : item(_item), value(_value) {}
   1.320 +
   1.321 +      Item item;
   1.322 +      int value;
   1.323 +
   1.324 +      int prev, next;
   1.325 +    };
   1.326 +
   1.327 +    ItemIntMap& index;
   1.328 +    std::vector<int> first;
   1.329 +    std::vector<BucketItem> data;
   1.330 +    mutable int minimal;
   1.331 +
   1.332 +  }; // class BucketHeap
   1.333 +
   1.334 +
   1.335 +  template <typename _ItemIntMap>
   1.336 +  class BucketHeap<_ItemIntMap, false> {
   1.337 +
   1.338 +  public:
   1.339 +    typedef typename _ItemIntMap::Key Item;
   1.340 +    typedef int Prio;
   1.341 +    typedef std::pair<Item, Prio> Pair;
   1.342 +    typedef _ItemIntMap ItemIntMap;
   1.343 +
   1.344 +    enum State {
   1.345 +      IN_HEAP = 0,
   1.346 +      PRE_HEAP = -1,
   1.347 +      POST_HEAP = -2
   1.348 +    };
   1.349 +
   1.350 +  public:
   1.351 +
   1.352 +    explicit BucketHeap(ItemIntMap &_index) : index(_index), maximal(-1) {}
   1.353 +
   1.354 +    int size() const { return data.size(); }
   1.355 +    bool empty() const { return data.empty(); }
   1.356 +
   1.357 +    void clear() {
   1.358 +      data.clear(); first.clear(); maximal = -1;
   1.359 +    }
   1.360 +
   1.361 +  private:
   1.362 +
   1.363 +    void relocate_last(int idx) {
   1.364 +      if (idx + 1 != int(data.size())) {
   1.365 +        data[idx] = data.back();
   1.366 +        if (data[idx].prev != -1) {
   1.367 +          data[data[idx].prev].next = idx;
   1.368 +        } else {
   1.369 +          first[data[idx].value] = idx;
   1.370 +        }
   1.371 +        if (data[idx].next != -1) {
   1.372 +          data[data[idx].next].prev = idx;
   1.373 +        }
   1.374 +        index[data[idx].item] = idx;
   1.375 +      }
   1.376 +      data.pop_back();
   1.377 +    }
   1.378 +
   1.379 +    void unlace(int idx) {
   1.380 +      if (data[idx].prev != -1) {
   1.381 +        data[data[idx].prev].next = data[idx].next;
   1.382 +      } else {
   1.383 +        first[data[idx].value] = data[idx].next;
   1.384 +      }
   1.385 +      if (data[idx].next != -1) {
   1.386 +        data[data[idx].next].prev = data[idx].prev;
   1.387 +      }
   1.388 +    }
   1.389 +
   1.390 +    void lace(int idx) {
   1.391 +      if (int(first.size()) <= data[idx].value) {
   1.392 +        first.resize(data[idx].value + 1, -1);
   1.393 +      }
   1.394 +      data[idx].next = first[data[idx].value];
   1.395 +      if (data[idx].next != -1) {
   1.396 +        data[data[idx].next].prev = idx;
   1.397 +      }
   1.398 +      first[data[idx].value] = idx;
   1.399 +      data[idx].prev = -1;
   1.400 +    }
   1.401 +
   1.402 +  public:
   1.403 +
   1.404 +    void push(const Pair& p) {
   1.405 +      push(p.first, p.second);
   1.406 +    }
   1.407 +
   1.408 +    void push(const Item &i, const Prio &p) {
   1.409 +      int idx = data.size();
   1.410 +      index[i] = idx;
   1.411 +      data.push_back(BucketItem(i, p));
   1.412 +      lace(idx);
   1.413 +      if (data[idx].value > maximal) {
   1.414 +        maximal = data[idx].value;
   1.415 +      }
   1.416 +    }
   1.417 +
   1.418 +    Item top() const {
   1.419 +      while (first[maximal] == -1) {
   1.420 +        --maximal;
   1.421 +      }
   1.422 +      return data[first[maximal]].item;
   1.423 +    }
   1.424 +
   1.425 +    Prio prio() const {
   1.426 +      while (first[maximal] == -1) {
   1.427 +        --maximal;
   1.428 +      }
   1.429 +      return maximal;
   1.430 +    }
   1.431 +
   1.432 +    void pop() {
   1.433 +      while (first[maximal] == -1) {
   1.434 +        --maximal;
   1.435 +      }
   1.436 +      int idx = first[maximal];
   1.437 +      index[data[idx].item] = -2;
   1.438 +      unlace(idx);
   1.439 +      relocate_last(idx);
   1.440 +    }
   1.441 +
   1.442 +    void erase(const Item &i) {
   1.443 +      int idx = index[i];
   1.444 +      index[data[idx].item] = -2;
   1.445 +      unlace(idx);
   1.446 +      relocate_last(idx);
   1.447 +    }
   1.448 +
   1.449 +    Prio operator[](const Item &i) const {
   1.450 +      int idx = index[i];
   1.451 +      return data[idx].value;
   1.452 +    }
   1.453 +
   1.454 +    void set(const Item &i, const Prio &p) {
   1.455 +      int idx = index[i];
   1.456 +      if (idx < 0) {
   1.457 +        push(i,p);
   1.458 +      } else if (p > data[idx].value) {
   1.459 +        decrease(i, p);
   1.460 +      } else {
   1.461 +        increase(i, p);
   1.462 +      }
   1.463 +    }
   1.464 +
   1.465 +    void decrease(const Item &i, const Prio &p) {
   1.466 +      int idx = index[i];
   1.467 +      unlace(idx);
   1.468 +      data[idx].value = p;
   1.469 +      if (p > maximal) {
   1.470 +        maximal = p;
   1.471 +      }
   1.472 +      lace(idx);
   1.473 +    }
   1.474 +
   1.475 +    void increase(const Item &i, const Prio &p) {
   1.476 +      int idx = index[i];
   1.477 +      unlace(idx);
   1.478 +      data[idx].value = p;
   1.479 +      lace(idx);
   1.480 +    }
   1.481 +
   1.482 +    State state(const Item &i) const {
   1.483 +      int idx = index[i];
   1.484 +      if (idx >= 0) idx = 0;
   1.485 +      return State(idx);
   1.486 +    }
   1.487 +
   1.488 +    void state(const Item& i, State st) {
   1.489 +      switch (st) {
   1.490 +      case POST_HEAP:
   1.491 +      case PRE_HEAP:
   1.492 +        if (state(i) == IN_HEAP) {
   1.493 +          erase(i);
   1.494 +        }
   1.495 +        index[i] = st;
   1.496 +        break;
   1.497 +      case IN_HEAP:
   1.498 +        break;
   1.499 +      }
   1.500 +    }
   1.501 +
   1.502 +  private:
   1.503 +
   1.504 +    struct BucketItem {
   1.505 +      BucketItem(const Item& _item, int _value)
   1.506 +        : item(_item), value(_value) {}
   1.507 +
   1.508 +      Item item;
   1.509 +      int value;
   1.510 +
   1.511 +      int prev, next;
   1.512 +    };
   1.513 +
   1.514 +    ItemIntMap& index;
   1.515 +    std::vector<int> first;
   1.516 +    std::vector<BucketItem> data;
   1.517 +    mutable int maximal;
   1.518 +
   1.519 +  }; // class BucketHeap
   1.520 +
   1.521 +  /// \ingroup auxdat
   1.522 +  ///
   1.523 +  /// \brief A Simplified Bucket Heap implementation.
   1.524 +  ///
   1.525 +  /// This class implements a simplified \e bucket \e heap data
   1.526 +  /// structure.  It does not provide some functionality but it faster
   1.527 +  /// and simplier data structure than the BucketHeap. The main
   1.528 +  /// difference is that the BucketHeap stores for every key a double
   1.529 +  /// linked list while this class stores just simple lists. In the
   1.530 +  /// other way it does not supports erasing each elements just the
   1.531 +  /// minimal and it does not supports key increasing, decreasing.
   1.532 +  ///
   1.533 +  /// \param _ItemIntMap A read and writable Item int map, used internally
   1.534 +  /// to handle the cross references.
   1.535 +  /// \param minimize If the given parameter is true then the heap gives back
   1.536 +  /// the lowest priority.
   1.537 +  ///
   1.538 +  /// \sa BucketHeap
   1.539 +  template <typename _ItemIntMap, bool minimize = true >
   1.540 +  class SimpleBucketHeap {
   1.541 +
   1.542 +  public:
   1.543 +    typedef typename _ItemIntMap::Key Item;
   1.544 +    typedef int Prio;
   1.545 +    typedef std::pair<Item, Prio> Pair;
   1.546 +    typedef _ItemIntMap ItemIntMap;
   1.547 +
   1.548 +    /// \brief Type to represent the items states.
   1.549 +    ///
   1.550 +    /// Each Item element have a state associated to it. It may be "in heap",
   1.551 +    /// "pre heap" or "post heap". The latter two are indifferent from the
   1.552 +    /// heap's point of view, but may be useful to the user.
   1.553 +    ///
   1.554 +    /// The ItemIntMap \e should be initialized in such way that it maps
   1.555 +    /// PRE_HEAP (-1) to any element to be put in the heap...
   1.556 +    enum State {
   1.557 +      IN_HEAP = 0,
   1.558 +      PRE_HEAP = -1,
   1.559 +      POST_HEAP = -2
   1.560 +    };
   1.561 +
   1.562 +  public:
   1.563 +
   1.564 +    /// \brief The constructor.
   1.565 +    ///
   1.566 +    /// The constructor.
   1.567 +    /// \param _index should be given to the constructor, since it is used
   1.568 +    /// internally to handle the cross references. The value of the map
   1.569 +    /// should be PRE_HEAP (-1) for each element.
   1.570 +    explicit SimpleBucketHeap(ItemIntMap &_index)
   1.571 +      : index(_index), free(-1), num(0), minimal(0) {}
   1.572 +
   1.573 +    /// \brief Returns the number of items stored in the heap.
   1.574 +    ///
   1.575 +    /// The number of items stored in the heap.
   1.576 +    int size() const { return num; }
   1.577 +
   1.578 +    /// \brief Checks if the heap stores no items.
   1.579 +    ///
   1.580 +    /// Returns \c true if and only if the heap stores no items.
   1.581 +    bool empty() const { return num == 0; }
   1.582 +
   1.583 +    /// \brief Make empty this heap.
   1.584 +    ///
   1.585 +    /// Make empty this heap. It does not change the cross reference
   1.586 +    /// map.  If you want to reuse a heap what is not surely empty you
   1.587 +    /// should first clear the heap and after that you should set the
   1.588 +    /// cross reference map for each item to \c PRE_HEAP.
   1.589 +    void clear() {
   1.590 +      data.clear(); first.clear(); free = -1; num = 0; minimal = 0;
   1.591 +    }
   1.592 +
   1.593 +    /// \brief Insert a pair of item and priority into the heap.
   1.594 +    ///
   1.595 +    /// Adds \c p.first to the heap with priority \c p.second.
   1.596 +    /// \param p The pair to insert.
   1.597 +    void push(const Pair& p) {
   1.598 +      push(p.first, p.second);
   1.599 +    }
   1.600 +
   1.601 +    /// \brief Insert an item into the heap with the given priority.
   1.602 +    ///
   1.603 +    /// Adds \c i to the heap with priority \c p.
   1.604 +    /// \param i The item to insert.
   1.605 +    /// \param p The priority of the item.
   1.606 +    void push(const Item &i, const Prio &p) {
   1.607 +      int idx;
   1.608 +      if (free == -1) {
   1.609 +        idx = data.size();
   1.610 +        data.push_back(BucketItem(i));
   1.611 +      } else {
   1.612 +        idx = free;
   1.613 +        free = data[idx].next;
   1.614 +        data[idx].item = i;
   1.615 +      }
   1.616 +      index[i] = idx;
   1.617 +      if (p >= int(first.size())) first.resize(p + 1, -1);
   1.618 +      data[idx].next = first[p];
   1.619 +      first[p] = idx;
   1.620 +      if (p < minimal) {
   1.621 +        minimal = p;
   1.622 +      }
   1.623 +      ++num;
   1.624 +    }
   1.625 +
   1.626 +    /// \brief Returns the item with minimum priority.
   1.627 +    ///
   1.628 +    /// This method returns the item with minimum priority.
   1.629 +    /// \pre The heap must be nonempty.
   1.630 +    Item top() const {
   1.631 +      while (first[minimal] == -1) {
   1.632 +        ++minimal;
   1.633 +      }
   1.634 +      return data[first[minimal]].item;
   1.635 +    }
   1.636 +
   1.637 +    /// \brief Returns the minimum priority.
   1.638 +    ///
   1.639 +    /// It returns the minimum priority.
   1.640 +    /// \pre The heap must be nonempty.
   1.641 +    Prio prio() const {
   1.642 +      while (first[minimal] == -1) {
   1.643 +        ++minimal;
   1.644 +      }
   1.645 +      return minimal;
   1.646 +    }
   1.647 +
   1.648 +    /// \brief Deletes the item with minimum priority.
   1.649 +    ///
   1.650 +    /// This method deletes the item with minimum priority from the heap.
   1.651 +    /// \pre The heap must be non-empty.
   1.652 +    void pop() {
   1.653 +      while (first[minimal] == -1) {
   1.654 +        ++minimal;
   1.655 +      }
   1.656 +      int idx = first[minimal];
   1.657 +      index[data[idx].item] = -2;
   1.658 +      first[minimal] = data[idx].next;
   1.659 +      data[idx].next = free;
   1.660 +      free = idx;
   1.661 +      --num;
   1.662 +    }
   1.663 +
   1.664 +    /// \brief Returns the priority of \c i.
   1.665 +    ///
   1.666 +    /// This function returns the priority of item \c i.
   1.667 +    /// \warning This operator is not a constant time function
   1.668 +    /// because it scans the whole data structure to find the proper
   1.669 +    /// value.
   1.670 +    /// \pre \c i must be in the heap.
   1.671 +    /// \param i The item.
   1.672 +    Prio operator[](const Item &i) const {
   1.673 +      for (int k = 0; k < first.size(); ++k) {
   1.674 +        int idx = first[k];
   1.675 +        while (idx != -1) {
   1.676 +          if (data[idx].item == i) {
   1.677 +            return k;
   1.678 +          }
   1.679 +          idx = data[idx].next;
   1.680 +        }
   1.681 +      }
   1.682 +      return -1;
   1.683 +    }
   1.684 +
   1.685 +    /// \brief Returns if \c item is in, has already been in, or has
   1.686 +    /// never been in the heap.
   1.687 +    ///
   1.688 +    /// This method returns PRE_HEAP if \c item has never been in the
   1.689 +    /// heap, IN_HEAP if it is in the heap at the moment, and POST_HEAP
   1.690 +    /// otherwise. In the latter case it is possible that \c item will
   1.691 +    /// get back to the heap again.
   1.692 +    /// \param i The item.
   1.693 +    State state(const Item &i) const {
   1.694 +      int idx = index[i];
   1.695 +      if (idx >= 0) idx = 0;
   1.696 +      return State(idx);
   1.697 +    }
   1.698 +
   1.699 +  private:
   1.700 +
   1.701 +    struct BucketItem {
   1.702 +      BucketItem(const Item& _item)
   1.703 +        : item(_item) {}
   1.704 +
   1.705 +      Item item;
   1.706 +      int next;
   1.707 +    };
   1.708 +
   1.709 +    ItemIntMap& index;
   1.710 +    std::vector<int> first;
   1.711 +    std::vector<BucketItem> data;
   1.712 +    int free, num;
   1.713 +    mutable int minimal;
   1.714 +
   1.715 +  }; // class SimpleBucketHeap
   1.716 +
   1.717 +  template <typename _ItemIntMap>
   1.718 +  class SimpleBucketHeap<_ItemIntMap, false> {
   1.719 +
   1.720 +  public:
   1.721 +    typedef typename _ItemIntMap::Key Item;
   1.722 +    typedef int Prio;
   1.723 +    typedef std::pair<Item, Prio> Pair;
   1.724 +    typedef _ItemIntMap ItemIntMap;
   1.725 +
   1.726 +    enum State {
   1.727 +      IN_HEAP = 0,
   1.728 +      PRE_HEAP = -1,
   1.729 +      POST_HEAP = -2
   1.730 +    };
   1.731 +
   1.732 +  public:
   1.733 +
   1.734 +    explicit SimpleBucketHeap(ItemIntMap &_index)
   1.735 +      : index(_index), free(-1), num(0), maximal(0) {}
   1.736 +
   1.737 +    int size() const { return num; }
   1.738 +
   1.739 +    bool empty() const { return num == 0; }
   1.740 +
   1.741 +    void clear() {
   1.742 +      data.clear(); first.clear(); free = -1; num = 0; maximal = 0;
   1.743 +    }
   1.744 +
   1.745 +    void push(const Pair& p) {
   1.746 +      push(p.first, p.second);
   1.747 +    }
   1.748 +
   1.749 +    void push(const Item &i, const Prio &p) {
   1.750 +      int idx;
   1.751 +      if (free == -1) {
   1.752 +        idx = data.size();
   1.753 +        data.push_back(BucketItem(i));
   1.754 +      } else {
   1.755 +        idx = free;
   1.756 +        free = data[idx].next;
   1.757 +        data[idx].item = i;
   1.758 +      }
   1.759 +      index[i] = idx;
   1.760 +      if (p >= int(first.size())) first.resize(p + 1, -1);
   1.761 +      data[idx].next = first[p];
   1.762 +      first[p] = idx;
   1.763 +      if (p > maximal) {
   1.764 +        maximal = p;
   1.765 +      }
   1.766 +      ++num;
   1.767 +    }
   1.768 +
   1.769 +    Item top() const {
   1.770 +      while (first[maximal] == -1) {
   1.771 +        --maximal;
   1.772 +      }
   1.773 +      return data[first[maximal]].item;
   1.774 +    }
   1.775 +
   1.776 +    Prio prio() const {
   1.777 +      while (first[maximal] == -1) {
   1.778 +        --maximal;
   1.779 +      }
   1.780 +      return maximal;
   1.781 +    }
   1.782 +
   1.783 +    void pop() {
   1.784 +      while (first[maximal] == -1) {
   1.785 +        --maximal;
   1.786 +      }
   1.787 +      int idx = first[maximal];
   1.788 +      index[data[idx].item] = -2;
   1.789 +      first[maximal] = data[idx].next;
   1.790 +      data[idx].next = free;
   1.791 +      free = idx;
   1.792 +      --num;
   1.793 +    }
   1.794 +
   1.795 +    Prio operator[](const Item &i) const {
   1.796 +      for (int k = 0; k < first.size(); ++k) {
   1.797 +        int idx = first[k];
   1.798 +        while (idx != -1) {
   1.799 +          if (data[idx].item == i) {
   1.800 +            return k;
   1.801 +          }
   1.802 +          idx = data[idx].next;
   1.803 +        }
   1.804 +      }
   1.805 +      return -1;
   1.806 +    }
   1.807 +
   1.808 +    State state(const Item &i) const {
   1.809 +      int idx = index[i];
   1.810 +      if (idx >= 0) idx = 0;
   1.811 +      return State(idx);
   1.812 +    }
   1.813 +
   1.814 +  private:
   1.815 +
   1.816 +    struct BucketItem {
   1.817 +      BucketItem(const Item& _item) : item(_item) {}
   1.818 +
   1.819 +      Item item;
   1.820 +
   1.821 +      int next;
   1.822 +    };
   1.823 +
   1.824 +    ItemIntMap& index;
   1.825 +    std::vector<int> first;
   1.826 +    std::vector<BucketItem> data;
   1.827 +    int free, num;
   1.828 +    mutable int maximal;
   1.829 +
   1.830 +  };
   1.831 +
   1.832 +}
   1.833 +
   1.834 +#endif