--- milena/ChangeLog | 4 + milena/mln/util/fibonacci_heap.hh | 2126 ++++++++++++++++++------------------ 2 files changed, 1067 insertions(+), 1063 deletions(-) diff --git a/milena/ChangeLog b/milena/ChangeLog index 306a838..f8bdc57 100644 --- a/milena/ChangeLog +++ b/milena/ChangeLog @@ -1,5 +1,9 @@ 2009-04-06 Roland Levillain <roland@lrde.epita.fr> + * mln/util/fibonacci_heap.hh: Convert to Unix line terminators. + +2009-04-06 Roland Levillain <roland@lrde.epita.fr> + * mln/util/ord_pair.hh: Remove outdated FIXME. 2009-04-06 Roland Levillain <roland@lrde.epita.fr> diff --git a/milena/mln/util/fibonacci_heap.hh b/milena/mln/util/fibonacci_heap.hh index ef85508..597d87a 100644 --- a/milena/mln/util/fibonacci_heap.hh +++ b/milena/mln/util/fibonacci_heap.hh @@ -1,1063 +1,1063 @@ -// Copyright (C) 2009 EPITA Research and Development Laboratory -// (LRDE) -// -// This file is part of the Olena Library. This library is free -// software; you can redistribute it and/or modify it under the terms -// of the GNU General Public License version 2 as published by the -// Free Software Foundation. -// -// This library is distributed in the hope that it will be useful, -// but WITHOUT ANY WARRANTY; without even the implied warranty of -// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU -// General Public License for more details. -// -// You should have received a copy of the GNU General Public License -// along with this library; see the file COPYING. If not, write to -// the Free Software Foundation, 51 Franklin Street, Fifth Floor, -// Boston, MA 02111-1307, USA. -// -// As a special exception, you may use this file as part of a free -// software library without restriction. Specifically, if other files -// instantiate templates or use macros or inline functions from this -// file, or you compile this file and link it with other files to -// produce an executable, this file does not by itself cause the -// resulting executable to be covered by the GNU General Public -// License. This exception does not however invalidate any other -// reasons why the executable file might be covered by the GNU General -// Public License. -// -//*************************************************************************** -// The Fibonacci heap implementation is Copyright (c) 1996 by John Boyer -// -// Once this Fibonacci heap implementation (the software) has been published -// by Dr. Dobb's Journal, permission to use and distribute the software is -// granted provided that this copyright notice remains in the source and -// and the author (John Boyer) is acknowledged in works that use this program. -// -// Every effort has been made to ensure that this implementation is free of -// errors. Nonetheless, the author (John Boyer) assumes no liability regarding -// your use of this software. -// -// The author would also be very glad to hear from anyone who uses the -// software or has any feedback about it. -// Email: jboyer@gulf.csc.uvic.ca -//*************************************************************************** - - -#ifndef MLN_UTIL_FIBONACCI_HEAP_HH -# define MLN_UTIL_FIBONACCI_HEAP_HH - - -# include <iostream> -# include <mln/core/concept/object.hh> -# include <mln/util/ord.hh> - - - -namespace mln -{ - - namespace util - { - - - namespace internal - { - - /*--------------------------\ - | Fibonacci Heap node Class | - `--------------------------*/ - - template <typename P, typename T> - class fibonacci_heap_node - { - - public: - /// Default constructor. - fibonacci_heap_node(); - - /// Construct a new node with \p value as value. - fibonacci_heap_node(const P& priority, const T& value); - - ~fibonacci_heap_node(); - - /// Return the node value. - const T& value() const; - - const P& priority() const; - - fibonacci_heap_node<P,T> *left() const; - fibonacci_heap_node<P,T> *right() const; - fibonacci_heap_node<P,T> *parent() const; - fibonacci_heap_node<P,T> *child() const; - - short degree() const; - - short mark() const; - - - void set_value(const T&); - void set_left(fibonacci_heap_node<P,T> *node); - void set_right(fibonacci_heap_node<P,T> *node); - void set_parent(fibonacci_heap_node<P,T> *node); - void set_child(fibonacci_heap_node<P,T> *node); - void set_degree(short degree); - void set_mark(short mark); - - void operator=(fibonacci_heap_node<P,T>& rhs); - bool operator==(fibonacci_heap_node<P,T>& rhs); - bool operator<(fibonacci_heap_node<P,T>& rhs); - - void print_() const; - - - private: - - fibonacci_heap_node<P,T> *left_; - fibonacci_heap_node<P,T> *right_; - fibonacci_heap_node<P,T> *parent_; - fibonacci_heap_node<P,T> *child_; - short degree_; - short mark_; - P priority_; - T value_; - }; - - } // end of namespace mln::util::internal - - - - /*---------------------\ - | Fibonacci Heap Class | - `---------------------*/ - - template <typename P, typename T> - class fibonacci_heap : public Object< fibonacci_heap<P,T> > - { - public: - - typedef T element; - - /// Default constructor - fibonacci_heap(); - - /// Copy constructor - /// Be ware that once this heap is constructed, the argument \p node - /// is cleared and all its elements are part of this new heap. - fibonacci_heap(const fibonacci_heap<P,T>& node); - - ~fibonacci_heap(); - - /// Push a new element in the heap. - /// \sa insert - void push(const P& priority, const T& value); - - /// Take \p other_heap's elements and insert them in this heap. - /// After this call \p other_heap is cleared. - void push(fibonacci_heap<P,T>& other_heap); - - /// Return the minimum value in the heap. - const T& front() const; - - /// Return and remove the minimum value in the heap. - T pop_front(); - - /// Is it empty? - bool is_empty() const; - - /// return false if it is empty. - bool is_valid() const; - - /// Return the number of elements. - unsigned nelements() const; - - /// Clear all elements in the heap and make the heap empty. - void clear(); - - /// Assignment operator. - /// Be ware that this operator do *not* copy the data from \p rhs to this heap. - /// It moves all elements which means that afterwards, \p rhs is - /// is cleared and all its elements are part of this new heap. - fibonacci_heap<P,T>& operator=(fibonacci_heap<P,T>& rhs); - - - - std::ostream& print_(std::ostream& cout, - internal::fibonacci_heap_node<P,T> *tree = 0, - internal::fibonacci_heap_node<P,T> *parent = 0) const; - - private: - - // Internal functions that help to implement the Standard Operations - - - /// Allow to change a node value. - /// FIXME: cannot use that function efficiently except by passing the - /// node pointer. Any idea? - /// FIXME: may be part of the public interface. - int decrease_key(internal::fibonacci_heap_node<P,T> *node, - internal::fibonacci_heap_node<P,T>& key); - - /// Remove node \p node from the child list of its parent node. - /// FIXME: cannot use that function efficiently except by passing the - /// node pointer. Any idea? - /// FIXME: may be part of the public interface. - int remove(internal::fibonacci_heap_node<P,T> *node); - - /// Insert a new node \p node in the heap. - void insert(internal::fibonacci_heap_node<P,T> *node); - - /// Swap the two given nodes. - void exchange(internal::fibonacci_heap_node<P,T>*& lhs, - internal::fibonacci_heap_node<P,T>*& rhs); - - /// Internal function that reorganizes heap as part of an pop_front(). - /// We must find new minimum in heap, which could be anywhere along the - /// root list. The search could be O(n) since all nodes could be on - /// the root list. So, we reorganize the tree into more of a binomial - /// forest structure, and then find the new minimum on the consolidated - /// O(lg n) sized root list, and in the process set each Parent pointer - /// to 0, and count the number of resulting subtrees. - /// - /// Note that after a list of n inserts, there will be n nodes on the - /// root list, so the first pop_front() will be O(n) regardless of - /// whether or not we consolidate. However, the consolidation causes - /// subsequent pop_front() operations to be O(lg n). Furthermore, - /// the extra cost of the first pop_front() is covered by the higher - /// amortized cost of insert(), which is the real governing factor in - /// how costly the first pop_front() will be. - void consolidate(); - - /// The node \p lhs is removed from the root list and becomes a subtree - /// of node \p rhs. - void link(internal::fibonacci_heap_node<P,T> *lhs, - internal::fibonacci_heap_node<P,T> *rhs); - - void add_to_root_list(internal::fibonacci_heap_node<P,T> *); - - /// Remove node \p lhs from the child list of its parent node \p rhs. - void cut(internal::fibonacci_heap_node<P,T> *lhs, - internal::fibonacci_heap_node<P,T> *rhs); - - /// Cuts each node in parent list, putting successive ancestor nodes on - /// the root list until we either arrive at the root list or until we - /// find an ancestor that is unmarked. When a mark is set (which only - /// happens during a cascading cut), it means that one child subtree has - /// been lost; if a second subtree is lost later during another - /// cascading cut, then we move the node to the root list so that it - /// can be re-balanced on the next consolidate. - void cascading_cut(internal::fibonacci_heap_node<P,T> *); - - /// Clear the heap but do *NOT* delete elements. - void soft_clear_(); - - /// FIXME: ugly but we need to be able to soft_clear() the heap in the - /// copy constructor... Any idea how to do without that? - mutable internal::fibonacci_heap_node<P,T> *min_root; - mutable long num_nodes; - mutable long num_trees; - mutable long num_marked_nodes; - - }; - - - template <typename P, typename T> - std::ostream& - operator<<(std::ostream& cout, const fibonacci_heap<P,T>& heap); - - - -# ifndef MLN_INCLUDE_ONLY - - - namespace internal - { - - - /*--------------------\ - | fibonacci_heap_node | - `--------------------*/ - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T>::fibonacci_heap_node() - : left_(0), right_(0), parent_(0), child_(0), - degree_(0), mark_(0), priority_(0) - // FIXME: don't we want to initialize priority with literal::zero? - { - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T>::fibonacci_heap_node(const P& priority, - const T& new_value) - : left_(0), right_(0), parent_(0), child_(0), - degree_(0), mark_(0), priority_(priority), value_(new_value) - { - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T>::~fibonacci_heap_node() - { - } - - - template <typename P, typename T> - inline - const T& - fibonacci_heap_node<P,T>::value() const - { - return value_; - } - - - template <typename P, typename T> - inline - const P& - fibonacci_heap_node<P,T>::priority() const - { - return priority_; - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T> * - fibonacci_heap_node<P,T>::left() const - { - return left_; - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T> * - fibonacci_heap_node<P,T>::right() const - { - return right_; - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T> * - fibonacci_heap_node<P,T>::parent() const - { - return parent_; - } - - - template <typename P, typename T> - inline - fibonacci_heap_node<P,T> * - fibonacci_heap_node<P,T>::child() const - { - return child_; - } - - - template <typename P, typename T> - inline - short - fibonacci_heap_node<P,T>::degree() const - { - return degree_; - } - - - template <typename P, typename T> - inline - short - fibonacci_heap_node<P,T>::mark() const - { - return mark_; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_value(const T& value) - { - value_ = value; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_left(fibonacci_heap_node<P,T> *node) - { - left_ = node; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_right(fibonacci_heap_node<P,T> *node) - { - right_ = node; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_parent(fibonacci_heap_node<P,T> *node) - { - parent_ = node; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_child(fibonacci_heap_node<P,T> *node) - { - child_ = node; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_degree(short degree) - { - degree_ = degree; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap_node<P,T>::set_mark(short mark) - { - mark_ = mark; - } - - - template <typename P, typename T> - inline - void fibonacci_heap_node<P,T>::operator=(fibonacci_heap_node<P,T>& rhs) - { - priority_ = rhs.priority(); - value_ = rhs.value(); - } - - - template <typename P, typename T> - inline - bool - fibonacci_heap_node<P,T>::operator==(fibonacci_heap_node<P,T>& rhs) - { - return priority_ == rhs.priority() && value_ == rhs.value(); - } - - - template <typename P, typename T> - inline - bool - fibonacci_heap_node<P,T>::operator<(fibonacci_heap_node<P,T>& rhs) - { - return util::ord_strict(priority_, rhs.priority()) - || (priority_ == rhs.priority() && util::ord_strict(value_, rhs.value())); - } - - - template <typename P, typename T> - inline - void fibonacci_heap_node<P,T>::print_() const - { - std::cout << value_ << " (" << priority_ << ")"; - } - - - } // end of namespace mln::util::internal - - - - /*---------------\ - | fibonacci_heap | - `---------------*/ - - template <typename P, typename T> - inline - fibonacci_heap<P,T>::fibonacci_heap() - { - soft_clear_(); - } - - - template <typename P, typename T> - inline - fibonacci_heap<P,T>::fibonacci_heap(const fibonacci_heap<P,T>& rhs) - : Object< fibonacci_heap<P,T> >() - { - min_root = rhs.min_root; - num_nodes = rhs.num_nodes; - num_trees = rhs.num_trees; - num_marked_nodes = rhs.num_marked_nodes; - -// rhs is const, we cannot call that method. -// rhs.soft_clear_(); - rhs.min_root = 0; - rhs.num_nodes = 0; - rhs.num_trees = 0; - rhs.num_marked_nodes = 0; - } - - - template <typename P, typename T> - inline - fibonacci_heap<P,T>::~fibonacci_heap() - { - clear(); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::push(const P& priority, const T& value) - { - typedef internal::fibonacci_heap_node<P,T> node_t; - node_t *new_node = new node_t(priority, value); - - insert(new_node); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::push(fibonacci_heap<P,T>& other_heap) - { - if (other_heap.is_empty() || &other_heap == this) - return; - - if (min_root != 0) - { - internal::fibonacci_heap_node<P,T> *min1, *min2, *next1, *next2; - - // We join the two circular lists by cutting each list between its - // min node and the node after the min. This code just pulls those - // nodes into temporary variables so we don't get lost as changes - // are made. - min1 = min_root; - min2 = other_heap.min_root; - next1 = min1->right(); - next2 = min2->right(); - - // To join the two circles, we join the minimum nodes to the next - // nodes on the opposite chains. Conceptually, it looks like the way - // two bubbles join to form one larger bubble. They meet at one point - // of contact, then expand out to make the bigger circle. - min1->set_right(next2); - next2->set_left(min1); - min2->set_right(next1); - next1->set_left(min2); - - // Choose the new minimum for the heap - if (*min2 < *min1) - min_root = min2; - } - else - min_root = other_heap.min_root; - - // Set the amortized analysis statistics and size of the new heap - num_nodes += other_heap.num_nodes; - num_marked_nodes += other_heap.num_marked_nodes; - num_trees += other_heap.num_trees; - - // Complete the union by setting the other heap to emptiness - other_heap.soft_clear_(); - - mln_postcondition(other_heap.is_empty()); - } - - - template <typename P, typename T> - inline - const T& - fibonacci_heap<P,T>::front() const - { - return min_root->value(); - } - - - template <typename P, typename T> - inline - T - fibonacci_heap<P,T>::pop_front() - { - mln_precondition(is_valid()); - mln_precondition(!is_empty()); - - internal::fibonacci_heap_node<P,T> *result = min_root; - fibonacci_heap<P,T> *child_heap = 0; - - // Remove minimum node and set min_root to next node - min_root = result->right(); - result->right()->set_left(result->left()); - result->left()->set_right(result->right()); - result->set_left(0); - result->set_right(0); - - --num_nodes; - if (result->mark()) - { - --num_marked_nodes; - result->set_mark(0); - } - result->set_degree(0); - - // Attach child list of minimum node to the root list of the heap - // If there is no child list, then do no work - if (result->child() == 0) - { - if (min_root == result) - min_root = 0; - } - - // If min_root==result then there was only one root tree, so the - // root list is simply the child list of that node (which is - // 0 if this is the last node in the list) - else if (min_root == result) - min_root = result->child(); - - // If min_root is different, then the child list is pushed into a - // new temporary heap, which is then merged by union() onto the - // root list of this heap. - else - { - child_heap = new fibonacci_heap<P,T>(); - child_heap->min_root = result->child(); - } - - // Complete the disassociation of the result node from the heap - if (result->child() != 0) - result->child()->set_parent(0); - result->set_child(0); - result->set_parent(0); - - // If there was a child list, then we now merge it with the - // rest of the root list - if (child_heap) - { - push(*child_heap); - delete child_heap; - } - - // Consolidate heap to find new minimum and do reorganize work - if (min_root != 0) - consolidate(); - - // Return the minimum node, which is now disassociated with the heap - // It has left, right, parent, child, mark and degree cleared. - T val = result->value(); - delete result; - - return val; - } - - - template <typename P, typename T> - inline - int - fibonacci_heap<P,T>::decrease_key(internal::fibonacci_heap_node<P,T> *node, - internal::fibonacci_heap_node<P,T>& key) - { - internal::fibonacci_heap_node<P,T> *parent; - - if (node == 0 || *node < key) - return -1; - - *node = key; - - parent = node->parent(); - if (parent != 0 && *node < *parent) - { - cut(node, parent); - cascading_cut(parent); - } - - if (*node < *min_root) - min_root = node; - - return 0; - } - - - template <typename P, typename T> - inline - int - fibonacci_heap<P,T>::remove(internal::fibonacci_heap_node<P,T> *node) - { - internal::fibonacci_heap_node<P,T> temp; - int result; - - if (node == 0) - return -1; - - result = decrease_key(node, temp); - - if (result == 0) - if (pop_front() == 0) - result = -1; - - if (result == 0) - delete node; - - return result; - } - - - template <typename P, typename T> - inline - bool - fibonacci_heap<P,T>::is_empty() const - { - return min_root == 0; - } - - - template <typename P, typename T> - inline - bool - fibonacci_heap<P,T>::is_valid() const - { - return min_root != 0; - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::clear() - { - while (min_root != 0) - pop_front(); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::soft_clear_() - { - min_root = 0; - num_nodes = 0; - num_trees = 0; - num_marked_nodes = 0; - } - - - template <typename P, typename T> - inline - unsigned - fibonacci_heap<P,T>::nelements() const - { - return num_nodes; - }; - - - template <typename P, typename T> - inline - fibonacci_heap<P,T>& - fibonacci_heap<P,T>::operator=(fibonacci_heap<P,T>& rhs) - { - if (&rhs != this) - { - min_root = rhs.min_root; - num_nodes = rhs.num_nodes; - num_trees = rhs.num_trees; - num_marked_nodes = rhs.num_marked_nodes; - rhs.soft_clear_(); - } - return *this; - } - - - template <typename P, typename T> - std::ostream& - fibonacci_heap<P,T>::print_(std::ostream& cout, - internal::fibonacci_heap_node<P,T> *tree, - internal::fibonacci_heap_node<P,T> *parent) const - { - internal::fibonacci_heap_node<P,T>* temp = 0; - - if (tree == 0) - tree = min_root; - - temp = tree; - if (temp != 0) - { - do { - if (temp->left() == 0) - cout << "(left is 0)"; - temp->print_(); - if (temp->parent() != parent) - cout << "(parent is incorrect)"; - if (temp->right() == 0) - cout << "(right is 0)"; - else if (temp->right()->left() != temp) - cout << "(Error in left link left) ->"; - else - cout << " <-> "; - - temp = temp->right(); - - } while (temp != 0 && temp != tree); - } - else - cout << " <empty>" << std::endl; - cout << std::endl; - - temp = tree; - if (temp != 0) - { - do { - cout << "children of " << temp->value() << ": "; - if (temp->child() == 0) - cout << "NONE" << std::endl; - else print_(cout, temp->child(), temp); - temp = temp->right(); - } while (temp!=0 && temp != tree); - } - - return cout; - } - - - template <typename P, typename T> - inline - void fibonacci_heap<P,T>::consolidate() - { - internal::fibonacci_heap_node<P,T> *x, *y, *w; - internal::fibonacci_heap_node<P,T> *a[1 + 8 * sizeof (long)]; // 1+lg(n) - short dn = 1 + 8 * sizeof (long); - - // Initialize the consolidation detection array - for (int i = 0; i < dn; ++i) - a[i] = 0; - - // We need to loop through all elements on root list. - // When a collision of degree is found, the two trees - // are consolidated in favor of the one with the lesser - // element key value. We first need to break the circle - // so that we can have a stopping condition (we can't go - // around until we reach the tree we started with - // because all root trees are subject to becoming a - // child during the consolidation). - min_root->left()->set_right(0); - min_root->set_left(0); - w = min_root; - - short d; - do { - x = w; - d = x->degree(); - w = w->right(); - - // We need another loop here because the consolidated result - // may collide with another large tree on the root list. - while (a[d] != 0) - { - y = a[d]; - if (*y < *x) - exchange(x, y); - if (w == y) w = y->right(); - link(y, x); - a[d] = 0; - ++d; - } - a[d] = x; - - } while (w != 0); - - // Now we rebuild the root list, find the new minimum, - // set all root list nodes' parent pointers to 0 and - // count the number of subtrees. - min_root = 0; - num_trees = 0; - for (int i = 0; i < dn; ++i) - if (a[i] != 0) - add_to_root_list(a[i]); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::link(internal::fibonacci_heap_node<P,T> *y, - internal::fibonacci_heap_node<P,T> *x) - { - // Remove node y from root list - if (y->right() != 0) - y->right()->set_left(y->left()); - if (y->left() != 0) - y->left()->set_right(y->right()); - --num_trees; - - // Make node y a singleton circular list with a parent of x - y->set_left(y); - y->set_right(y); - y->set_parent(x); - - // If node x has no children, then list y is its new child list - if (x->child() == 0) - x->set_child(y); - - // Otherwise, node y must be added to node x's child list - else - { - y->set_left(x->child()); - y->set_right(x->child()->right()); - x->child()->set_right(y); - y->right()->set_left(y); - } - - // Increase the degree of node x because it's now a bigger tree - x->set_degree(x->degree() + 1); - - // node y has just been made a child, so clear its mark - if (y->mark()) - --num_marked_nodes; - y->set_mark(0); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::add_to_root_list(internal::fibonacci_heap_node<P,T> *x) - { - if (x->mark()) - --num_marked_nodes; - x->set_mark(0); - - --num_nodes; - insert(x); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::cut(internal::fibonacci_heap_node<P,T> *x, - internal::fibonacci_heap_node<P,T> *y) - { - if (y->child() == x) - y->child() = x->right(); - if (y->child() == x) - y->child() = 0; - - y->set_degree(y->degree() - 1); - - x->left()->right() = x->right(); - x->right()->left() = x->left(); - - add_to_root_list(x); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::cascading_cut(internal::fibonacci_heap_node<P,T> *y) - { - internal::fibonacci_heap_node<P,T> *z = y->parent(); - - while (z != 0) - { - if (y->mark() == 0) - { - y->mark() = 1; - ++num_marked_nodes; - z = 0; - } - else - { - cut(y, z); - y = z; - z = y->parent(); - } - } - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::insert(internal::fibonacci_heap_node<P,T> *node) - { - if (node == 0) - return; - - // If the heap is currently empty, then new node becomes singleton - // circular root list - if (min_root == 0) - { - min_root = node; - node->set_left(node); - node->set_right(node); - } - else - { - // Pointers from node set to insert between min_root and - // min_root->right() - node->set_right(min_root->right()); - node->set_left(min_root); - - // Set Pointers to node - node->left()->set_right(node); - node->right()->set_left(node); - - // The new node becomes new min_root if it is less than current - // min_root - if (*node < *min_root) - min_root = node; - } - - // We have one more node in the heap, and it is a tree on the root list - ++num_nodes; - ++num_trees; - node->set_parent(0); - } - - - template <typename P, typename T> - inline - void - fibonacci_heap<P,T>::exchange(internal::fibonacci_heap_node<P,T>*& n1, - internal::fibonacci_heap_node<P,T>*& n2) - { - internal::fibonacci_heap_node<P,T> *temp; - - temp = n1; - n1 = n2; - n2 = temp; - } - - - template <typename P, typename T> - std::ostream& - operator<<(std::ostream& cout, const fibonacci_heap<P,T>& heap) - { - return heap.print_(cout); - } - -# endif // ! MLN_INCLUDE_ONLY - - - - } // end of namespace mln::util - -} // end of namespace mln - -#endif // ! MLN_UTIL_FIBONACCI_HEAP_HH +// Copyright (C) 2009 EPITA Research and Development Laboratory +// (LRDE) +// +// This file is part of the Olena Library. This library is free +// software; you can redistribute it and/or modify it under the terms +// of the GNU General Public License version 2 as published by the +// Free Software Foundation. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this library; see the file COPYING. If not, write to +// the Free Software Foundation, 51 Franklin Street, Fifth Floor, +// Boston, MA 02111-1307, USA. +// +// As a special exception, you may use this file as part of a free +// software library without restriction. Specifically, if other files +// instantiate templates or use macros or inline functions from this +// file, or you compile this file and link it with other files to +// produce an executable, this file does not by itself cause the +// resulting executable to be covered by the GNU General Public +// License. This exception does not however invalidate any other +// reasons why the executable file might be covered by the GNU General +// Public License. +// +//*************************************************************************** +// The Fibonacci heap implementation is Copyright (c) 1996 by John Boyer +// +// Once this Fibonacci heap implementation (the software) has been published +// by Dr. Dobb's Journal, permission to use and distribute the software is +// granted provided that this copyright notice remains in the source and +// and the author (John Boyer) is acknowledged in works that use this program. +// +// Every effort has been made to ensure that this implementation is free of +// errors. Nonetheless, the author (John Boyer) assumes no liability regarding +// your use of this software. +// +// The author would also be very glad to hear from anyone who uses the +// software or has any feedback about it. +// Email: jboyer@gulf.csc.uvic.ca +//*************************************************************************** + + +#ifndef MLN_UTIL_FIBONACCI_HEAP_HH +# define MLN_UTIL_FIBONACCI_HEAP_HH + + +# include <iostream> +# include <mln/core/concept/object.hh> +# include <mln/util/ord.hh> + + + +namespace mln +{ + + namespace util + { + + + namespace internal + { + + /*--------------------------\ + | Fibonacci Heap node Class | + `--------------------------*/ + + template <typename P, typename T> + class fibonacci_heap_node + { + + public: + /// Default constructor. + fibonacci_heap_node(); + + /// Construct a new node with \p value as value. + fibonacci_heap_node(const P& priority, const T& value); + + ~fibonacci_heap_node(); + + /// Return the node value. + const T& value() const; + + const P& priority() const; + + fibonacci_heap_node<P,T> *left() const; + fibonacci_heap_node<P,T> *right() const; + fibonacci_heap_node<P,T> *parent() const; + fibonacci_heap_node<P,T> *child() const; + + short degree() const; + + short mark() const; + + + void set_value(const T&); + void set_left(fibonacci_heap_node<P,T> *node); + void set_right(fibonacci_heap_node<P,T> *node); + void set_parent(fibonacci_heap_node<P,T> *node); + void set_child(fibonacci_heap_node<P,T> *node); + void set_degree(short degree); + void set_mark(short mark); + + void operator=(fibonacci_heap_node<P,T>& rhs); + bool operator==(fibonacci_heap_node<P,T>& rhs); + bool operator<(fibonacci_heap_node<P,T>& rhs); + + void print_() const; + + + private: + + fibonacci_heap_node<P,T> *left_; + fibonacci_heap_node<P,T> *right_; + fibonacci_heap_node<P,T> *parent_; + fibonacci_heap_node<P,T> *child_; + short degree_; + short mark_; + P priority_; + T value_; + }; + + } // end of namespace mln::util::internal + + + + /*---------------------\ + | Fibonacci Heap Class | + `---------------------*/ + + template <typename P, typename T> + class fibonacci_heap : public Object< fibonacci_heap<P,T> > + { + public: + + typedef T element; + + /// Default constructor + fibonacci_heap(); + + /// Copy constructor + /// Be ware that once this heap is constructed, the argument \p node + /// is cleared and all its elements are part of this new heap. + fibonacci_heap(const fibonacci_heap<P,T>& node); + + ~fibonacci_heap(); + + /// Push a new element in the heap. + /// \sa insert + void push(const P& priority, const T& value); + + /// Take \p other_heap's elements and insert them in this heap. + /// After this call \p other_heap is cleared. + void push(fibonacci_heap<P,T>& other_heap); + + /// Return the minimum value in the heap. + const T& front() const; + + /// Return and remove the minimum value in the heap. + T pop_front(); + + /// Is it empty? + bool is_empty() const; + + /// return false if it is empty. + bool is_valid() const; + + /// Return the number of elements. + unsigned nelements() const; + + /// Clear all elements in the heap and make the heap empty. + void clear(); + + /// Assignment operator. + /// Be ware that this operator do *not* copy the data from \p rhs to this heap. + /// It moves all elements which means that afterwards, \p rhs is + /// is cleared and all its elements are part of this new heap. + fibonacci_heap<P,T>& operator=(fibonacci_heap<P,T>& rhs); + + + + std::ostream& print_(std::ostream& cout, + internal::fibonacci_heap_node<P,T> *tree = 0, + internal::fibonacci_heap_node<P,T> *parent = 0) const; + + private: + + // Internal functions that help to implement the Standard Operations + + + /// Allow to change a node value. + /// FIXME: cannot use that function efficiently except by passing the + /// node pointer. Any idea? + /// FIXME: may be part of the public interface. + int decrease_key(internal::fibonacci_heap_node<P,T> *node, + internal::fibonacci_heap_node<P,T>& key); + + /// Remove node \p node from the child list of its parent node. + /// FIXME: cannot use that function efficiently except by passing the + /// node pointer. Any idea? + /// FIXME: may be part of the public interface. + int remove(internal::fibonacci_heap_node<P,T> *node); + + /// Insert a new node \p node in the heap. + void insert(internal::fibonacci_heap_node<P,T> *node); + + /// Swap the two given nodes. + void exchange(internal::fibonacci_heap_node<P,T>*& lhs, + internal::fibonacci_heap_node<P,T>*& rhs); + + /// Internal function that reorganizes heap as part of an pop_front(). + /// We must find new minimum in heap, which could be anywhere along the + /// root list. The search could be O(n) since all nodes could be on + /// the root list. So, we reorganize the tree into more of a binomial + /// forest structure, and then find the new minimum on the consolidated + /// O(lg n) sized root list, and in the process set each Parent pointer + /// to 0, and count the number of resulting subtrees. + /// + /// Note that after a list of n inserts, there will be n nodes on the + /// root list, so the first pop_front() will be O(n) regardless of + /// whether or not we consolidate. However, the consolidation causes + /// subsequent pop_front() operations to be O(lg n). Furthermore, + /// the extra cost of the first pop_front() is covered by the higher + /// amortized cost of insert(), which is the real governing factor in + /// how costly the first pop_front() will be. + void consolidate(); + + /// The node \p lhs is removed from the root list and becomes a subtree + /// of node \p rhs. + void link(internal::fibonacci_heap_node<P,T> *lhs, + internal::fibonacci_heap_node<P,T> *rhs); + + void add_to_root_list(internal::fibonacci_heap_node<P,T> *); + + /// Remove node \p lhs from the child list of its parent node \p rhs. + void cut(internal::fibonacci_heap_node<P,T> *lhs, + internal::fibonacci_heap_node<P,T> *rhs); + + /// Cuts each node in parent list, putting successive ancestor nodes on + /// the root list until we either arrive at the root list or until we + /// find an ancestor that is unmarked. When a mark is set (which only + /// happens during a cascading cut), it means that one child subtree has + /// been lost; if a second subtree is lost later during another + /// cascading cut, then we move the node to the root list so that it + /// can be re-balanced on the next consolidate. + void cascading_cut(internal::fibonacci_heap_node<P,T> *); + + /// Clear the heap but do *NOT* delete elements. + void soft_clear_(); + + /// FIXME: ugly but we need to be able to soft_clear() the heap in the + /// copy constructor... Any idea how to do without that? + mutable internal::fibonacci_heap_node<P,T> *min_root; + mutable long num_nodes; + mutable long num_trees; + mutable long num_marked_nodes; + + }; + + + template <typename P, typename T> + std::ostream& + operator<<(std::ostream& cout, const fibonacci_heap<P,T>& heap); + + + +# ifndef MLN_INCLUDE_ONLY + + + namespace internal + { + + + /*--------------------\ + | fibonacci_heap_node | + `--------------------*/ + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T>::fibonacci_heap_node() + : left_(0), right_(0), parent_(0), child_(0), + degree_(0), mark_(0), priority_(0) + // FIXME: don't we want to initialize priority with literal::zero? + { + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T>::fibonacci_heap_node(const P& priority, + const T& new_value) + : left_(0), right_(0), parent_(0), child_(0), + degree_(0), mark_(0), priority_(priority), value_(new_value) + { + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T>::~fibonacci_heap_node() + { + } + + + template <typename P, typename T> + inline + const T& + fibonacci_heap_node<P,T>::value() const + { + return value_; + } + + + template <typename P, typename T> + inline + const P& + fibonacci_heap_node<P,T>::priority() const + { + return priority_; + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T> * + fibonacci_heap_node<P,T>::left() const + { + return left_; + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T> * + fibonacci_heap_node<P,T>::right() const + { + return right_; + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T> * + fibonacci_heap_node<P,T>::parent() const + { + return parent_; + } + + + template <typename P, typename T> + inline + fibonacci_heap_node<P,T> * + fibonacci_heap_node<P,T>::child() const + { + return child_; + } + + + template <typename P, typename T> + inline + short + fibonacci_heap_node<P,T>::degree() const + { + return degree_; + } + + + template <typename P, typename T> + inline + short + fibonacci_heap_node<P,T>::mark() const + { + return mark_; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_value(const T& value) + { + value_ = value; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_left(fibonacci_heap_node<P,T> *node) + { + left_ = node; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_right(fibonacci_heap_node<P,T> *node) + { + right_ = node; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_parent(fibonacci_heap_node<P,T> *node) + { + parent_ = node; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_child(fibonacci_heap_node<P,T> *node) + { + child_ = node; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_degree(short degree) + { + degree_ = degree; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap_node<P,T>::set_mark(short mark) + { + mark_ = mark; + } + + + template <typename P, typename T> + inline + void fibonacci_heap_node<P,T>::operator=(fibonacci_heap_node<P,T>& rhs) + { + priority_ = rhs.priority(); + value_ = rhs.value(); + } + + + template <typename P, typename T> + inline + bool + fibonacci_heap_node<P,T>::operator==(fibonacci_heap_node<P,T>& rhs) + { + return priority_ == rhs.priority() && value_ == rhs.value(); + } + + + template <typename P, typename T> + inline + bool + fibonacci_heap_node<P,T>::operator<(fibonacci_heap_node<P,T>& rhs) + { + return util::ord_strict(priority_, rhs.priority()) + || (priority_ == rhs.priority() && util::ord_strict(value_, rhs.value())); + } + + + template <typename P, typename T> + inline + void fibonacci_heap_node<P,T>::print_() const + { + std::cout << value_ << " (" << priority_ << ")"; + } + + + } // end of namespace mln::util::internal + + + + /*---------------\ + | fibonacci_heap | + `---------------*/ + + template <typename P, typename T> + inline + fibonacci_heap<P,T>::fibonacci_heap() + { + soft_clear_(); + } + + + template <typename P, typename T> + inline + fibonacci_heap<P,T>::fibonacci_heap(const fibonacci_heap<P,T>& rhs) + : Object< fibonacci_heap<P,T> >() + { + min_root = rhs.min_root; + num_nodes = rhs.num_nodes; + num_trees = rhs.num_trees; + num_marked_nodes = rhs.num_marked_nodes; + +// rhs is const, we cannot call that method. +// rhs.soft_clear_(); + rhs.min_root = 0; + rhs.num_nodes = 0; + rhs.num_trees = 0; + rhs.num_marked_nodes = 0; + } + + + template <typename P, typename T> + inline + fibonacci_heap<P,T>::~fibonacci_heap() + { + clear(); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::push(const P& priority, const T& value) + { + typedef internal::fibonacci_heap_node<P,T> node_t; + node_t *new_node = new node_t(priority, value); + + insert(new_node); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::push(fibonacci_heap<P,T>& other_heap) + { + if (other_heap.is_empty() || &other_heap == this) + return; + + if (min_root != 0) + { + internal::fibonacci_heap_node<P,T> *min1, *min2, *next1, *next2; + + // We join the two circular lists by cutting each list between its + // min node and the node after the min. This code just pulls those + // nodes into temporary variables so we don't get lost as changes + // are made. + min1 = min_root; + min2 = other_heap.min_root; + next1 = min1->right(); + next2 = min2->right(); + + // To join the two circles, we join the minimum nodes to the next + // nodes on the opposite chains. Conceptually, it looks like the way + // two bubbles join to form one larger bubble. They meet at one point + // of contact, then expand out to make the bigger circle. + min1->set_right(next2); + next2->set_left(min1); + min2->set_right(next1); + next1->set_left(min2); + + // Choose the new minimum for the heap + if (*min2 < *min1) + min_root = min2; + } + else + min_root = other_heap.min_root; + + // Set the amortized analysis statistics and size of the new heap + num_nodes += other_heap.num_nodes; + num_marked_nodes += other_heap.num_marked_nodes; + num_trees += other_heap.num_trees; + + // Complete the union by setting the other heap to emptiness + other_heap.soft_clear_(); + + mln_postcondition(other_heap.is_empty()); + } + + + template <typename P, typename T> + inline + const T& + fibonacci_heap<P,T>::front() const + { + return min_root->value(); + } + + + template <typename P, typename T> + inline + T + fibonacci_heap<P,T>::pop_front() + { + mln_precondition(is_valid()); + mln_precondition(!is_empty()); + + internal::fibonacci_heap_node<P,T> *result = min_root; + fibonacci_heap<P,T> *child_heap = 0; + + // Remove minimum node and set min_root to next node + min_root = result->right(); + result->right()->set_left(result->left()); + result->left()->set_right(result->right()); + result->set_left(0); + result->set_right(0); + + --num_nodes; + if (result->mark()) + { + --num_marked_nodes; + result->set_mark(0); + } + result->set_degree(0); + + // Attach child list of minimum node to the root list of the heap + // If there is no child list, then do no work + if (result->child() == 0) + { + if (min_root == result) + min_root = 0; + } + + // If min_root==result then there was only one root tree, so the + // root list is simply the child list of that node (which is + // 0 if this is the last node in the list) + else if (min_root == result) + min_root = result->child(); + + // If min_root is different, then the child list is pushed into a + // new temporary heap, which is then merged by union() onto the + // root list of this heap. + else + { + child_heap = new fibonacci_heap<P,T>(); + child_heap->min_root = result->child(); + } + + // Complete the disassociation of the result node from the heap + if (result->child() != 0) + result->child()->set_parent(0); + result->set_child(0); + result->set_parent(0); + + // If there was a child list, then we now merge it with the + // rest of the root list + if (child_heap) + { + push(*child_heap); + delete child_heap; + } + + // Consolidate heap to find new minimum and do reorganize work + if (min_root != 0) + consolidate(); + + // Return the minimum node, which is now disassociated with the heap + // It has left, right, parent, child, mark and degree cleared. + T val = result->value(); + delete result; + + return val; + } + + + template <typename P, typename T> + inline + int + fibonacci_heap<P,T>::decrease_key(internal::fibonacci_heap_node<P,T> *node, + internal::fibonacci_heap_node<P,T>& key) + { + internal::fibonacci_heap_node<P,T> *parent; + + if (node == 0 || *node < key) + return -1; + + *node = key; + + parent = node->parent(); + if (parent != 0 && *node < *parent) + { + cut(node, parent); + cascading_cut(parent); + } + + if (*node < *min_root) + min_root = node; + + return 0; + } + + + template <typename P, typename T> + inline + int + fibonacci_heap<P,T>::remove(internal::fibonacci_heap_node<P,T> *node) + { + internal::fibonacci_heap_node<P,T> temp; + int result; + + if (node == 0) + return -1; + + result = decrease_key(node, temp); + + if (result == 0) + if (pop_front() == 0) + result = -1; + + if (result == 0) + delete node; + + return result; + } + + + template <typename P, typename T> + inline + bool + fibonacci_heap<P,T>::is_empty() const + { + return min_root == 0; + } + + + template <typename P, typename T> + inline + bool + fibonacci_heap<P,T>::is_valid() const + { + return min_root != 0; + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::clear() + { + while (min_root != 0) + pop_front(); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::soft_clear_() + { + min_root = 0; + num_nodes = 0; + num_trees = 0; + num_marked_nodes = 0; + } + + + template <typename P, typename T> + inline + unsigned + fibonacci_heap<P,T>::nelements() const + { + return num_nodes; + }; + + + template <typename P, typename T> + inline + fibonacci_heap<P,T>& + fibonacci_heap<P,T>::operator=(fibonacci_heap<P,T>& rhs) + { + if (&rhs != this) + { + min_root = rhs.min_root; + num_nodes = rhs.num_nodes; + num_trees = rhs.num_trees; + num_marked_nodes = rhs.num_marked_nodes; + rhs.soft_clear_(); + } + return *this; + } + + + template <typename P, typename T> + std::ostream& + fibonacci_heap<P,T>::print_(std::ostream& cout, + internal::fibonacci_heap_node<P,T> *tree, + internal::fibonacci_heap_node<P,T> *parent) const + { + internal::fibonacci_heap_node<P,T>* temp = 0; + + if (tree == 0) + tree = min_root; + + temp = tree; + if (temp != 0) + { + do { + if (temp->left() == 0) + cout << "(left is 0)"; + temp->print_(); + if (temp->parent() != parent) + cout << "(parent is incorrect)"; + if (temp->right() == 0) + cout << "(right is 0)"; + else if (temp->right()->left() != temp) + cout << "(Error in left link left) ->"; + else + cout << " <-> "; + + temp = temp->right(); + + } while (temp != 0 && temp != tree); + } + else + cout << " <empty>" << std::endl; + cout << std::endl; + + temp = tree; + if (temp != 0) + { + do { + cout << "children of " << temp->value() << ": "; + if (temp->child() == 0) + cout << "NONE" << std::endl; + else print_(cout, temp->child(), temp); + temp = temp->right(); + } while (temp!=0 && temp != tree); + } + + return cout; + } + + + template <typename P, typename T> + inline + void fibonacci_heap<P,T>::consolidate() + { + internal::fibonacci_heap_node<P,T> *x, *y, *w; + internal::fibonacci_heap_node<P,T> *a[1 + 8 * sizeof (long)]; // 1+lg(n) + short dn = 1 + 8 * sizeof (long); + + // Initialize the consolidation detection array + for (int i = 0; i < dn; ++i) + a[i] = 0; + + // We need to loop through all elements on root list. + // When a collision of degree is found, the two trees + // are consolidated in favor of the one with the lesser + // element key value. We first need to break the circle + // so that we can have a stopping condition (we can't go + // around until we reach the tree we started with + // because all root trees are subject to becoming a + // child during the consolidation). + min_root->left()->set_right(0); + min_root->set_left(0); + w = min_root; + + short d; + do { + x = w; + d = x->degree(); + w = w->right(); + + // We need another loop here because the consolidated result + // may collide with another large tree on the root list. + while (a[d] != 0) + { + y = a[d]; + if (*y < *x) + exchange(x, y); + if (w == y) w = y->right(); + link(y, x); + a[d] = 0; + ++d; + } + a[d] = x; + + } while (w != 0); + + // Now we rebuild the root list, find the new minimum, + // set all root list nodes' parent pointers to 0 and + // count the number of subtrees. + min_root = 0; + num_trees = 0; + for (int i = 0; i < dn; ++i) + if (a[i] != 0) + add_to_root_list(a[i]); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::link(internal::fibonacci_heap_node<P,T> *y, + internal::fibonacci_heap_node<P,T> *x) + { + // Remove node y from root list + if (y->right() != 0) + y->right()->set_left(y->left()); + if (y->left() != 0) + y->left()->set_right(y->right()); + --num_trees; + + // Make node y a singleton circular list with a parent of x + y->set_left(y); + y->set_right(y); + y->set_parent(x); + + // If node x has no children, then list y is its new child list + if (x->child() == 0) + x->set_child(y); + + // Otherwise, node y must be added to node x's child list + else + { + y->set_left(x->child()); + y->set_right(x->child()->right()); + x->child()->set_right(y); + y->right()->set_left(y); + } + + // Increase the degree of node x because it's now a bigger tree + x->set_degree(x->degree() + 1); + + // node y has just been made a child, so clear its mark + if (y->mark()) + --num_marked_nodes; + y->set_mark(0); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::add_to_root_list(internal::fibonacci_heap_node<P,T> *x) + { + if (x->mark()) + --num_marked_nodes; + x->set_mark(0); + + --num_nodes; + insert(x); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::cut(internal::fibonacci_heap_node<P,T> *x, + internal::fibonacci_heap_node<P,T> *y) + { + if (y->child() == x) + y->child() = x->right(); + if (y->child() == x) + y->child() = 0; + + y->set_degree(y->degree() - 1); + + x->left()->right() = x->right(); + x->right()->left() = x->left(); + + add_to_root_list(x); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::cascading_cut(internal::fibonacci_heap_node<P,T> *y) + { + internal::fibonacci_heap_node<P,T> *z = y->parent(); + + while (z != 0) + { + if (y->mark() == 0) + { + y->mark() = 1; + ++num_marked_nodes; + z = 0; + } + else + { + cut(y, z); + y = z; + z = y->parent(); + } + } + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::insert(internal::fibonacci_heap_node<P,T> *node) + { + if (node == 0) + return; + + // If the heap is currently empty, then new node becomes singleton + // circular root list + if (min_root == 0) + { + min_root = node; + node->set_left(node); + node->set_right(node); + } + else + { + // Pointers from node set to insert between min_root and + // min_root->right() + node->set_right(min_root->right()); + node->set_left(min_root); + + // Set Pointers to node + node->left()->set_right(node); + node->right()->set_left(node); + + // The new node becomes new min_root if it is less than current + // min_root + if (*node < *min_root) + min_root = node; + } + + // We have one more node in the heap, and it is a tree on the root list + ++num_nodes; + ++num_trees; + node->set_parent(0); + } + + + template <typename P, typename T> + inline + void + fibonacci_heap<P,T>::exchange(internal::fibonacci_heap_node<P,T>*& n1, + internal::fibonacci_heap_node<P,T>*& n2) + { + internal::fibonacci_heap_node<P,T> *temp; + + temp = n1; + n1 = n2; + n2 = temp; + } + + + template <typename P, typename T> + std::ostream& + operator<<(std::ostream& cout, const fibonacci_heap<P,T>& heap) + { + return heap.print_(cout); + } + +# endif // ! MLN_INCLUDE_ONLY + + + + } // end of namespace mln::util + +} // end of namespace mln + +#endif // ! MLN_UTIL_FIBONACCI_HEAP_HH -- 1.6.1.2