priorityQueue_tpl.h

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#include <agrum/tools/core/priorityQueue.h>

namespace gum {

  // ===========================================================================
  // ===             GENERAL IMPLEMENTATIION OF PRIORITY QUEUES              ===
  // ===========================================================================

  // basic constructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     PriorityQueueImplementation(Cmp compare, Size capacity) :
      __indices(capacity >> 1, true, true),
      __cmp(compare) {
    __heap.reserve(capacity);

    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueueImplementation);
  }

  // initializer list constructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     PriorityQueueImplementation(
        std::initializer_list< std::pair< Val, Priority > > list) :
      __indices(Size(list.size()) / 2, true, true) {
    // fill the queue
    __heap.reserve(list.size());
    for (const auto& elt: list) {
      insert(elt.first, elt.second);
    }

    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueueImplementation);
  }

  // copy constructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     PriorityQueueImplementation(
        const PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&
           from) :
      __heap(from.__heap),
      __indices(from.__indices), __nb_elements(from.__nb_elements),
      __cmp(from.__cmp) {
    // fill the heap structure
    for (const auto& elt: __indices) {
      __heap[elt.second].second = &(elt.first);
    }

    // for debugging purposes
    GUM_CONS_CPY(PriorityQueueImplementation);
  }

  // generalized copy constructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  template < typename OtherAlloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     PriorityQueueImplementation(
        const PriorityQueueImplementation< Val, Priority, Cmp, OtherAlloc, Gen >&
           from) :
      __indices(from.__indices),
      __nb_elements(from.__nb_elements), __cmp(from.__cmp) {
    // fill the heap structure
    if (__nb_elements) {
      __heap.reserve(from.__heap.size());
      for (const auto& elt: from.__heap) {
        __heap.push_back(elt);
      }
      for (const auto& elt: __indices) {
        __heap[elt.second].second = &(elt.first);
      }
    }

    // for debugging purposes
    GUM_CONS_CPY(PriorityQueueImplementation);
  }

  // move constructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     PriorityQueueImplementation(
        PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&& from) :
      __heap(std::move(from.__heap)),
      __indices(std::move(from.__indices)),
      __nb_elements(std::move(from.__nb_elements)), __cmp(std::move(from.__cmp)) {
    // for debugging purposes
    GUM_CONS_MOV(PriorityQueueImplementation);
  }

  // destructor
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     ~PriorityQueueImplementation() {
    // for debugging purposes
    GUM_DESTRUCTOR(PriorityQueueImplementation);
  }

  // copy operator
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::operator=(
        const PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&
           from) {
    // avoid self assignment
    if (this != &from) {
      // for debugging purposes
      GUM_OP_CPY(PriorityQueueImplementation);

      try {
        // set the comparison function
        __cmp = from.__cmp;

        // copy the indices and the heap
        __indices = from.__indices;
        __heap = from.__heap;
        __nb_elements = from.__nb_elements;

        // restore the link between __indices and __heap
        for (const auto& elt: __indices) {
          __heap[elt.second].second = &(elt.first);
        }
      } catch (...) {
        __heap.clear();
        __indices.clear();
        __nb_elements = 0;

        throw;
      }
    }

    return *this;
  }

  // generalized copy operator
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  template < typename OtherAlloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::operator=(
        const PriorityQueueImplementation< Val, Priority, Cmp, OtherAlloc, Gen >&
           from) {
    // for debugging purposes
    GUM_OP_CPY(PriorityQueueImplementation);

    try {
      // set the comprison function
      __cmp = from.__cmp;

      // copy the indices and the heap
      __indices = from.__indices;
      __nb_elements = from.__nb_elements;

      __heap.clear();
      if (__nb_elements) {
        __heap.reserve(from.__heap.size());
        for (const auto& elt: from.__heap) {
          __heap.push_back(elt);
        }
        for (const auto& elt: __indices) {
          __heap[elt.second].second = &(elt.first);
        }
      }
    } catch (...) {
      __heap.clear();
      __indices.clear();
      __nb_elements = 0;

      throw;
    }

    return *this;
  }

  // move operator
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::operator=(
        PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >&& from) {
    // avoid self assignment
    if (this != &from) {
      // for debugging purposes
      GUM_OP_MOV(PriorityQueueImplementation);

      __indices = std::move(from.__indices);
      __heap = std::move(from.__heap);
      __cmp = std::move(from.__cmp);
      __nb_elements = std::move(from.__nb_elements);
    }

    return *this;
  }

  // returns the element at the top of the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const Val&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::top() const {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    return *(__heap[0].second);
  }

  // returns the priority of the top element
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::topPriority()
        const {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    return __heap[0].first;
  }

  // returns the number of elements in the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::size() const
     noexcept {
    return __nb_elements;
  }

  // return the size of the array storing the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::capacity()
        const noexcept {
    return Size(__heap.capacity());
  }

  // changes the size of the array storing the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::resize(
        Size new_size) {
    if (new_size < __nb_elements) return;

    __heap.reserve(new_size);
    __indices.resize(new_size / 2);
  }

  // removes all the elements from the queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::clear() {
    __nb_elements = 0;
    __heap.clear();
    __indices.clear();
  }

  // removes the element at index elt from the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::eraseByPos(
     Size index) {
    if (index >= __nb_elements) return;

    // remove the element from the hashtable
    __indices.erase(*(__heap[index].second));

    // put the last element at the "index" location
    std::pair< Priority, const Val* > last = std::move(__heap[__nb_elements - 1]);
    __heap.pop_back();
    --__nb_elements;

    if (!__nb_elements || (index == __nb_elements)) return;

    // restore the heap property
    Size i = index;

    for (Size j = (index << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "last" is lower than heap[j], "last" must be stored at index i
      if (__cmp(last.first, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // put "last" back into the heap
    __heap[i] = std::move(last);
    __indices[*(__heap[i].second)] = i;
  }

  // removes a given element from the priority queue (but does not return it)
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::erase(
     const Val& val) {
    try {
      eraseByPos(__indices[val]);
    } catch (NotFound&) {}
  }

  // removes the top of the priority queue (but does not return it)
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::eraseTop() {
    eraseByPos(0);
  }

  // removes the top element from the priority queue and return it
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE Val PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::pop() {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    Val v = *(__heap[0].second);
    eraseByPos(0);

    return v;
  }

  // returns a hashtable the keys of which are the values stored in the queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const HashTable< Val, Size >&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::allValues()
        const noexcept {
    return reinterpret_cast< const HashTable< Val, Size >& >(__indices);
  }

  // inserts a new (a copy) element in the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::insert(
        const Val& val, const Priority& priority) {
    // create the entry in the indices hashtable (if the element already exists,
    // __indices.insert will raise a Duplicateelement exception)
    typename HashTable< Val, Size, IndexAllocator >::value_type& new_elt =
       __indices.insert(val, 0);

    try {
      __heap.push_back(
         std::pair< Priority, const Val* >(priority, &new_elt.first));
    } catch (...) {
      __indices.erase(val);
      throw;
    }

    std::pair< Priority, const Val* > new_heap_val =
       std::move(__heap[__nb_elements]);
    ++__nb_elements;

    // restore the heap property
    Size i = __nb_elements - 1;

    for (Size j = (i - 1) >> 1; i && __cmp(new_heap_val.first, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // put the new bucket into the heap
    __heap[i].first = std::move(new_heap_val.first);
    __heap[i].second = &(new_elt.first);
    new_elt.second = i;

    return i;
  }

  // inserts by move a new element in the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::insert(
        Val&& val, Priority&& priority) {
    // create the entry in the indices hashtable (if the element already exists,
    // __indices.insert will raise a Duplicateelement exception)
    typename HashTable< Val, Size, IndexAllocator >::value_type& new_elt =
       __indices.insert(std::move(val), 0);

    try {
      __heap.push_back(
         std::pair< Priority, const Val* >(std::move(priority), &(new_elt.first)));
    } catch (...) {
      __indices.erase(new_elt.first);
      throw;
    }

    std::pair< Priority, const Val* > new_heap_val =
       std::move(__heap[__nb_elements]);
    ++__nb_elements;

    // restore the heap property
    Size i = __nb_elements - 1;

    for (Size j = (i - 1) >> 1; i && __cmp(new_heap_val.first, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // put the new bucket into the heap
    __heap[i].first = std::move(new_heap_val.first);
    __heap[i].second = &(new_elt.first);
    new_elt.second = i;

    return i;
  }

  // emplace a new element into the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  template < typename... Args >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::emplace(
        Args&&... args) {
    std::pair< Val, Priority > new_elt =
       std::make_pair< Val, Priority >(std::forward< Args >(args)...);
    return insert(std::move(new_elt.first), std::move(new_elt.second));
  }

  // indicates whether the priority queue is empty
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE bool
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::empty() const
     noexcept {
    return (__nb_elements == 0);
  }

  // indicates whether the priority queue contains a given value
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE bool
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::contains(
        const Val& val) const {
    return __indices.exists(val);
  }

  // returns the element at position "index" in the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const Val&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::operator[](
        Size index) const {
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    return *(__heap[index].second);
  }

  // displays the content of the queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  std::string
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::toString()
        const {
    bool              deja = false;
    std::stringstream stream;
    stream << "[";

    for (Size i = 0; i != __nb_elements; ++i, deja = true) {
      if (deja) stream << " , ";

      stream << "(" << __heap[i].first << " , " << *(__heap[i].second) << ")";
    }

    stream << "]";

    return stream.str();
  }

  // changes the size of the internal structure storing the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  Size PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     setPriorityByPos(Size index, const Priority& new_priority) {
    // check whether the element the priority of which should be changed exists
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    // get the element itself
    const Val* val = __heap[index].second;

    // restore the heap property
    Size i = index;

    // move val upward if needed
    for (Size j = (i - 1) >> 1; i && __cmp(new_priority, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // move val downward if needed
    for (Size j = (i << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "val" is lower than heap[j], "val" must be stored at index i
      if (__cmp(new_priority, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // update the index of val
    __heap[i].first = new_priority;
    __heap[i].second = val;
    __indices[*val] = i;

    return i;
  }

  // changes the size of the internal structure storing the priority queue
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  Size PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::
     setPriorityByPos(Size index, Priority&& new_priority) {
    // check whether the element the priority of which should be changed exists
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    // get the element itself
    const Val* val = __heap[index].second;

    // restore the heap property
    Size i = index;

    // move val upward if needed
    for (Size j = (i - 1) >> 1; i && __cmp(new_priority, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // move val downward if needed
    for (Size j = (i << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "val" is lower than heap[j], "val" must be stored at index i
      if (__cmp(new_priority, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[*(__heap[i].second)] = i;
    }

    // update the index of val
    __heap[i].first = std::move(new_priority);
    __heap[i].second = val;
    __indices[*val] = i;

    return i;
  }

  // modifies the priority of a given element
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::setPriority(
     const Val& elt, const Priority& new_priority) {
    setPriorityByPos(__indices[elt], new_priority);
  }

  // modifies the priority of a given element
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::setPriority(
     const Val& elt, Priority&& new_priority) {
    setPriorityByPos(__indices[elt], std::move(new_priority));
  }

  // returns the priority of a given element
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::priority(
        const Val& elt) const {
    return __heap[__indices[elt]].first;
  }

  // returns the priority of a given element
  template < typename Val,
             typename Priority,
             typename Cmp,
             typename Alloc,
             bool Gen >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, Gen >::priorityByPos(
        Size index) const {
    if (index > __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }
    return __heap[index].first;
  }

  // ===========================================================================
  // ===          SCALAR OPTIMIZED IMPLEMENTATION OF PRIORITY QUEUES         ===
  // ===========================================================================

  // basic constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     PriorityQueueImplementation(Cmp compare, Size capacity) :
      __indices(capacity >> 1, true, true),
      __cmp(compare) {
    __heap.reserve(capacity);

    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueueImplementation);
  }

  // initializer list constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     PriorityQueueImplementation(
        std::initializer_list< std::pair< Val, Priority > > list) :
      __indices(Size(list.size()) / 2, true, true) {
    // fill the queue
    __heap.reserve(list.size());
    for (const auto& elt: list) {
      insert(elt.first, elt.second);
    }

    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueueImplementation);
  }

  // copy constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     PriorityQueueImplementation(
        const PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&
           from) :
      __heap(from.__heap),
      __indices(from.__indices), __nb_elements(from.__nb_elements),
      __cmp(from.__cmp) {
    // for debugging purposes
    GUM_CONS_CPY(PriorityQueueImplementation);
  }

  // generalized copy constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  template < typename OtherAlloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     PriorityQueueImplementation(
        const PriorityQueueImplementation< Val, Priority, Cmp, OtherAlloc, true >&
           from) :
      __indices(from.__indices),
      __nb_elements(from.__nb_elements), __cmp(from.__cmp) {
    // fill the heap structure
    if (__nb_elements) {
      __heap.reserve(from.__heap.size());
      for (const auto& elt: from.__heap) {
        __heap.push_back(elt);
      }
    }

    // for debugging purposes
    GUM_CONS_CPY(PriorityQueueImplementation);
  }

  // move constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     PriorityQueueImplementation(
        PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&& from) :
      __heap(std::move(from.__heap)),
      __indices(std::move(from.__indices)),
      __nb_elements(std::move(from.__nb_elements)), __cmp(std::move(from.__cmp)) {
    // for debugging purposes
    GUM_CONS_MOV(PriorityQueueImplementation);
  }

  // destructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     ~PriorityQueueImplementation() {
    // for debugging purposes
    GUM_DESTRUCTOR(PriorityQueueImplementation);
  }

  // copy operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::operator=(
        const PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&
           from) {
    // avoid self assignment
    if (this != &from) {
      // for debugging purposes
      GUM_OP_CPY(PriorityQueueImplementation);

      try {
        // set the comparison function
        __cmp = from.__cmp;

        // copy the indices and the heap
        __indices = from.__indices;
        __heap = from.__heap;
        __nb_elements = from.__nb_elements;
      } catch (...) {
        __heap.clear();
        __indices.clear();
        __nb_elements = 0;

        throw;
      }
    }

    return *this;
  }

  // generalized copy operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  template < typename OtherAlloc >
  PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::operator=(
        const PriorityQueueImplementation< Val, Priority, Cmp, OtherAlloc, true >&
           from) {
    // for debugging purposes
    GUM_OP_CPY(PriorityQueueImplementation);

    try {
      // set the comprison function
      __cmp = from.__cmp;

      // copy the indices and the heap
      __indices = from.__indices;
      __nb_elements = from.__nb_elements;

      __heap.clear();
      if (__nb_elements) {
        __heap.reserve(from.__heap.size());
        for (const auto& elt: from.__heap) {
          __heap.push_back(elt);
        }
      }
    } catch (...) {
      __heap.clear();
      __indices.clear();
      __nb_elements = 0;

      throw;
    }

    return *this;
  }

  // move operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::operator=(
        PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >&& from) {
    // avoid self assignment
    if (this != &from) {
      // for debugging purposes
      GUM_OP_MOV(PriorityQueueImplementation);

      __indices = std::move(from.__indices);
      __heap = std::move(from.__heap);
      __cmp = std::move(from.__cmp);
      __nb_elements = std::move(from.__nb_elements);
    }

    return *this;
  }

  // returns the element at the top of the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const Val&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::top() const {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    return __heap[0].second;
  }

  // returns the priority of the top element
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::topPriority()
        const {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    return __heap[0].first;
  }

  // returns the number of elements in the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::size() const
     noexcept {
    return __nb_elements;
  }

  // return the size of the array storing the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::capacity()
        const noexcept {
    return Size(__heap.capacity());
  }

  // changes the size of the array storing the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::resize(
        Size new_size) {
    if (new_size < __nb_elements) return;

    __heap.reserve(new_size);
    __indices.resize(new_size / 2);
  }

  // removes all the elements from the queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::clear() {
    __nb_elements = 0;
    __heap.clear();
    __indices.clear();
  }

  // removes the element at index elt from the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::eraseByPos(
     Size index) {
    if (index >= __nb_elements) return;

    // remove the element from the hashtable
    __indices.erase(__heap[index].second);

    // put the last element at the "index" location
    std::pair< Priority, Val > last = std::move(__heap[__nb_elements - 1]);
    __heap.pop_back();
    --__nb_elements;

    if (!__nb_elements || (index == __nb_elements)) return;

    // restore the heap property
    Size i = index;

    for (Size j = (index << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "last" is lower than heap[j], "last" must be stored at index i
      if (__cmp(last.first, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // put "last" back into the heap
    __heap[i] = std::move(last);
    __indices[__heap[i].second] = i;
  }

  // removes a given element from the priority queue (but does not return it)
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::erase(
        Val val) {
    try {
      eraseByPos(__indices[val]);
    } catch (NotFound&) {}
  }

  // removes the top of the priority queue (but does not return it)
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE void
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::eraseTop() {
    eraseByPos(0);
  }

  // removes the top element from the priority queue and return it
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE Val
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::pop() {
    if (!__nb_elements) { GUM_ERROR(NotFound, "empty priority queue"); }

    Val v = __heap[0].second;
    eraseByPos(0);

    return v;
  }

  // returns a hashtable the keys of which are the values stored in the queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const HashTable< Val, Size >&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::allValues()
        const noexcept {
    return reinterpret_cast< const HashTable< Val, Size >& >(__indices);
  }

  // inserts a new (a copy) element in the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::insert(
        Val val, const Priority& priority) {
    // create the entry in the indices hashtable (if the element already exists,
    // __indices.insert will raise a Duplicateelement exception)
    typename HashTable< Val, Size, IndexAllocator >::value_type& new_elt =
       __indices.insert(val, 0);

    try {
      __heap.push_back(std::pair< Priority, Val >(priority, val));
    } catch (...) {
      __indices.erase(val);
      throw;
    }

    std::pair< Priority, Val > new_heap_val = std::move(__heap[__nb_elements]);
    ++__nb_elements;

    // restore the heap property
    Size i = __nb_elements - 1;

    for (Size j = (i - 1) >> 1; i && __cmp(new_heap_val.first, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // put the new bucket into the heap
    __heap[i].first = std::move(new_heap_val.first);
    __heap[i].second = val;
    new_elt.second = i;

    return i;
  }

  // inserts by move a new element in the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::insert(
        Val val, Priority&& priority) {
    // create the entry in the indices hashtable (if the element already exists,
    // __indices.insert will raise a Duplicateelement exception)
    typename HashTable< Val, Size, IndexAllocator >::value_type& new_elt =
       __indices.insert(val, 0);

    try {
      __heap.push_back(std::pair< Priority, Val >(std::move(priority), val));
    } catch (...) {
      __indices.erase(val);
      throw;
    }

    std::pair< Priority, Val > new_heap_val = std::move(__heap[__nb_elements]);
    ++__nb_elements;

    // restore the heap property
    Size i = __nb_elements - 1;

    for (Size j = (i - 1) >> 1; i && __cmp(new_heap_val.first, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // put the new bucket into the heap
    __heap[i].first = std::move(new_heap_val.first);
    __heap[i].second = val;
    new_elt.second = i;

    return i;
  }

  // emplace a new element into the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  template < typename... Args >
  INLINE Size
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::emplace(
        Args&&... args) {
    std::pair< Val, Priority > new_elt =
       std::make_pair< Val, Priority >(std::forward< Args >(args)...);
    return insert(new_elt.first, std::move(new_elt.second));
  }

  // indicates whether the priority queue is empty
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE bool
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::empty() const
     noexcept {
    return (__nb_elements == 0);
  }

  // indicates whether the priority queue contains a given value
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE bool
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::contains(
        Val val) const {
    return __indices.exists(val);
  }

  // returns the element at position "index" in the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const Val&
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::operator[](
        Size index) const {
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    return __heap[index].second;
  }

  // displays the content of the queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  std::string
     PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::toString()
        const {
    bool              deja = false;
    std::stringstream stream;
    stream << "[";

    for (Size i = 0; i != __nb_elements; ++i, deja = true) {
      if (deja) stream << " , ";

      stream << "(" << __heap[i].first << " , " << __heap[i].second << ")";
    }

    stream << "]";

    return stream.str();
  }

  // changes the size of the internal structure storing the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  Size PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     setPriorityByPos(Size index, const Priority& new_priority) {
    // check whether the element the priority of which should be changed exists
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    // get the element itself
    Val val = __heap[index].second;

    // restore the heap property
    Size i = index;

    // move val upward if needed
    for (Size j = (i - 1) >> 1; i && __cmp(new_priority, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // move val downward if needed
    for (Size j = (i << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "val" is lower than heap[j], "val" must be stored at index i
      if (__cmp(new_priority, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // update the index of val
    __heap[i].first = new_priority;
    __heap[i].second = val;
    __indices[val] = i;

    return i;
  }

  // changes the size of the internal structure storing the priority queue
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  Size PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::
     setPriorityByPos(Size index, Priority&& new_priority) {
    // check whether the element the priority of which should be changed exists
    if (index >= __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }

    // get the element itself
    Val val = __heap[index].second;

    // restore the heap property
    Size i = index;

    // move val upward if needed
    for (Size j = (i - 1) >> 1; i && __cmp(new_priority, __heap[j].first);
         i = j, j = (j - 1) >> 1) {
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // move val downward if needed
    for (Size j = (i << 1) + 1; j < __nb_elements; i = j, j = (j << 1) + 1) {
      // let j be the max child
      if ((j + 1 < __nb_elements) && __cmp(__heap[j + 1].first, __heap[j].first))
        ++j;

      // if "val" is lower than heap[j], "val" must be stored at index i
      if (__cmp(new_priority, __heap[j].first)) break;

      // else pull up the jth node
      __heap[i] = std::move(__heap[j]);
      __indices[__heap[i].second] = i;
    }

    // update the index of val
    __heap[i].first = std::move(new_priority);
    __heap[i].second = val;
    __indices[val] = i;

    return i;
  }

  // modifies the priority of a given element
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::setPriority(
     Val elt, const Priority& new_priority) {
    setPriorityByPos(__indices[elt], new_priority);
  }

  // modifies the priority of a given element
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  void PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::setPriority(
     Val elt, Priority&& new_priority) {
    setPriorityByPos(__indices[elt], std::move(new_priority));
  }

  // returns the priority of a given element
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::priority(
        Val elt) const {
    return __heap[__indices[elt]].first;
  }

  // returns the priority of a given element
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE const Priority&
               PriorityQueueImplementation< Val, Priority, Cmp, Alloc, true >::priorityByPos(
        Size index) const {
    if (index > __nb_elements) {
      GUM_ERROR(NotFound,
                "not enough elements in the PriorityQueueImplementation");
    }
    return __heap[index].first;
  }

  // ===========================================================================
  // ===                           PRIORITY QUEUES                           ===
  // ===========================================================================

  // basic constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::PriorityQueue(Cmp  cmp,
                                                                   Size capacity) :
      PriorityQueue< Val, Priority, Cmp, Alloc >::Implementation(cmp, capacity) {
    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueue);
  }

  // initializer list constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::PriorityQueue(
     std::initializer_list< std::pair< Val, Priority > > list) :
      PriorityQueue< Val, Priority, Cmp, Alloc >::Implementation{list} {
    // for debugging purposes
    GUM_CONSTRUCTOR(PriorityQueue);
  }

  // copy constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::PriorityQueue(
     const PriorityQueue< Val, Priority, Cmp, Alloc >& from) :
      PriorityQueue< Val, Priority, Cmp, Alloc >::Implementation(from) {
    // for debugging purposes
    GUM_CONS_CPY(PriorityQueue);
  }

  // generalized copy constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  template < typename OtherAlloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::PriorityQueue(
     const PriorityQueue< Val, Priority, Cmp, OtherAlloc >& from) :
      PriorityQueue< Val, Priority, Cmp, Alloc >::Implementation(from) {
    // for debugging purposes
    GUM_CONS_CPY(PriorityQueue);
  }

  // move constructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::PriorityQueue(
     PriorityQueue< Val, Priority, Cmp, Alloc >&& from) :
      PriorityQueue< Val, Priority, Cmp, Alloc >::Implementation(std::move(from)) {
    // for debugging purposes
    GUM_CONS_MOV(PriorityQueue);
  }

  // destructor
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >::~PriorityQueue() {
    // for debugging purposes
    GUM_DESTRUCTOR(PriorityQueue);
  }

  // copy operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >&
     PriorityQueue< Val, Priority, Cmp, Alloc >::operator=(
        const PriorityQueue< Val, Priority, Cmp, Alloc >& from) {
    Implementation::operator=(from);
    return *this;
  }

  // generalized copy operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  template < typename OtherAlloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >&
     PriorityQueue< Val, Priority, Cmp, Alloc >::operator=(
        const PriorityQueue< Val, Priority, Cmp, OtherAlloc >& from) {
    Implementation::operator=(from);
    return *this;
  }

  // move operator
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE PriorityQueue< Val, Priority, Cmp, Alloc >&
     PriorityQueue< Val, Priority, Cmp, Alloc >::operator=(
        PriorityQueue< Val, Priority, Cmp, Alloc >&& from) {
    Implementation::operator=(std::move(from));
    return *this;
  }

  // A \c << operator for priority queues
  template < typename Val, typename Priority, typename Cmp, typename Alloc >
  INLINE std::ostream&
         operator<<(std::ostream&                                     stream,
                const PriorityQueue< Val, Priority, Cmp, Alloc >& queue) {
    stream << queue.toString();
    return stream;
  }

} /* namespace gum */