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extern/quadriflow/3rd/lemon-1.3.1/lemon/radix_heap.h

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/* -*- mode: C++; indent-tabs-mode: nil; -*-
*
* This file is a part of LEMON, a generic C++ optimization library.
*
* Copyright (C) 2003-2009
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
*
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
*
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
* purpose.
*
*/
#ifndef LEMON_RADIX_HEAP_H
#define LEMON_RADIX_HEAP_H
///\ingroup heaps
///\file
///\brief Radix heap implementation.
#include <vector>
#include <lemon/error.h>
namespace lemon {
/// \ingroup heaps
///
/// \brief Radix heap data structure.
///
/// This class implements the \e radix \e heap data structure.
/// It practically conforms to the \ref concepts::Heap "heap concept",
/// but it has some limitations due its special implementation.
/// The type of the priorities must be \c int and the priority of an
/// item cannot be decreased under the priority of the last removed item.
///
/// \tparam IM A read-writable item map with \c int values, used
/// internally to handle the cross references.
template <typename IM>
class RadixHeap {
public:
/// Type of the item-int map.
typedef IM ItemIntMap;
/// Type of the priorities.
typedef int Prio;
/// Type of the items stored in the heap.
typedef typename ItemIntMap::Key Item;
/// \brief Exception thrown by RadixHeap.
///
/// This exception is thrown when an item is inserted into a
/// RadixHeap with a priority smaller than the last erased one.
/// \see RadixHeap
class PriorityUnderflowError : public Exception {
public:
virtual const char* what() const throw() {
return "lemon::RadixHeap::PriorityUnderflowError";
}
};
/// \brief Type to represent the states of the items.
///
/// Each item has a state associated to it. It can be "in heap",
/// "pre-heap" or "post-heap". The latter two are indifferent from the
/// heap's point of view, but may be useful to the user.
///
/// The item-int map must be initialized in such way that it assigns
/// \c PRE_HEAP (<tt>-1</tt>) to any element to be put in the heap.
enum State {
IN_HEAP = 0, ///< = 0.
PRE_HEAP = -1, ///< = -1.
POST_HEAP = -2 ///< = -2.
};
private:
struct RadixItem {
int prev, next, box;
Item item;
int prio;
RadixItem(Item _item, int _prio) : item(_item), prio(_prio) {}
};
struct RadixBox {
int first;
int min, size;
RadixBox(int _min, int _size) : first(-1), min(_min), size(_size) {}
};
std::vector<RadixItem> _data;
std::vector<RadixBox> _boxes;
ItemIntMap &_iim;
public:
/// \brief Constructor.
///
/// Constructor.
/// \param map A map that assigns \c int values to the items.
/// It is used internally to handle the cross references.
/// The assigned value must be \c PRE_HEAP (<tt>-1</tt>) for each item.
/// \param minimum The initial minimum value of the heap.
/// \param capacity The initial capacity of the heap.
RadixHeap(ItemIntMap &map, int minimum = 0, int capacity = 0)
: _iim(map)
{
_boxes.push_back(RadixBox(minimum, 1));
_boxes.push_back(RadixBox(minimum + 1, 1));
while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
extend();
}
}
/// \brief The number of items stored in the heap.
///
/// This function returns the number of items stored in the heap.
int size() const { return _data.size(); }
/// \brief Check if the heap is empty.
///
/// This function returns \c true if the heap is empty.
bool empty() const { return _data.empty(); }
/// \brief Make the heap empty.
///
/// This functon makes the heap empty.
/// It does not change the cross reference map. If you want to reuse
/// a heap that is not surely empty, you should first clear it and
/// then you should set the cross reference map to \c PRE_HEAP
/// for each item.
/// \param minimum The minimum value of the heap.
/// \param capacity The capacity of the heap.
void clear(int minimum = 0, int capacity = 0) {
_data.clear(); _boxes.clear();
_boxes.push_back(RadixBox(minimum, 1));
_boxes.push_back(RadixBox(minimum + 1, 1));
while (lower(_boxes.size() - 1, capacity + minimum - 1)) {
extend();
}
}
private:
bool upper(int box, Prio pr) {
return pr < _boxes[box].min;
}
bool lower(int box, Prio pr) {
return pr >= _boxes[box].min + _boxes[box].size;
}
// Remove item from the box list
void remove(int index) {
if (_data[index].prev >= 0) {
_data[_data[index].prev].next = _data[index].next;
} else {
_boxes[_data[index].box].first = _data[index].next;
}
if (_data[index].next >= 0) {
_data[_data[index].next].prev = _data[index].prev;
}
}
// Insert item into the box list
void insert(int box, int index) {
if (_boxes[box].first == -1) {
_boxes[box].first = index;
_data[index].next = _data[index].prev = -1;
} else {
_data[index].next = _boxes[box].first;
_data[_boxes[box].first].prev = index;
_data[index].prev = -1;
_boxes[box].first = index;
}
_data[index].box = box;
}
// Add a new box to the box list
void extend() {
int min = _boxes.back().min + _boxes.back().size;
int bs = 2 * _boxes.back().size;
_boxes.push_back(RadixBox(min, bs));
}
// Move an item up into the proper box.
void bubbleUp(int index) {
if (!lower(_data[index].box, _data[index].prio)) return;
remove(index);
int box = findUp(_data[index].box, _data[index].prio);
insert(box, index);
}
// Find up the proper box for the item with the given priority
int findUp(int start, int pr) {
while (lower(start, pr)) {
if (++start == int(_boxes.size())) {
extend();
}
}
return start;
}
// Move an item down into the proper box
void bubbleDown(int index) {
if (!upper(_data[index].box, _data[index].prio)) return;
remove(index);
int box = findDown(_data[index].box, _data[index].prio);
insert(box, index);
}
// Find down the proper box for the item with the given priority
int findDown(int start, int pr) {
while (upper(start, pr)) {
if (--start < 0) throw PriorityUnderflowError();
}
return start;
}
// Find the first non-empty box
int findFirst() {
int first = 0;
while (_boxes[first].first == -1) ++first;
return first;
}
// Gives back the minimum priority of the given box
int minValue(int box) {
int min = _data[_boxes[box].first].prio;
for (int k = _boxes[box].first; k != -1; k = _data[k].next) {
if (_data[k].prio < min) min = _data[k].prio;
}
return min;
}
// Rearrange the items of the heap and make the first box non-empty
void moveDown() {
int box = findFirst();
if (box == 0) return;
int min = minValue(box);
for (int i = 0; i <= box; ++i) {
_boxes[i].min = min;
min += _boxes[i].size;
}
int curr = _boxes[box].first, next;
while (curr != -1) {
next = _data[curr].next;
bubbleDown(curr);
curr = next;
}
}
void relocateLast(int index) {
if (index != int(_data.size()) - 1) {
_data[index] = _data.back();
if (_data[index].prev != -1) {
_data[_data[index].prev].next = index;
} else {
_boxes[_data[index].box].first = index;
}
if (_data[index].next != -1) {
_data[_data[index].next].prev = index;
}
_iim[_data[index].item] = index;
}
_data.pop_back();
}
public:
/// \brief Insert an item into the heap with the given priority.
///
/// This function inserts the given item into the heap with the
/// given priority.
/// \param i The item to insert.
/// \param p The priority of the item.
/// \pre \e i must not be stored in the heap.
/// \warning This method may throw an \c UnderFlowPriorityException.
void push(const Item &i, const Prio &p) {
int n = _data.size();
_iim.set(i, n);
_data.push_back(RadixItem(i, p));
while (lower(_boxes.size() - 1, p)) {
extend();
}
int box = findDown(_boxes.size() - 1, p);
insert(box, n);
}
/// \brief Return the item having minimum priority.
///
/// This function returns the item having minimum priority.
/// \pre The heap must be non-empty.
Item top() const {
const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
return _data[_boxes[0].first].item;
}
/// \brief The minimum priority.
///
/// This function returns the minimum priority.
/// \pre The heap must be non-empty.
Prio prio() const {
const_cast<RadixHeap<ItemIntMap>&>(*this).moveDown();
return _data[_boxes[0].first].prio;
}
/// \brief Remove the item having minimum priority.
///
/// This function removes the item having minimum priority.
/// \pre The heap must be non-empty.
void pop() {
moveDown();
int index = _boxes[0].first;
_iim[_data[index].item] = POST_HEAP;
remove(index);
relocateLast(index);
}
/// \brief Remove the given item from the heap.
///
/// This function removes the given item from the heap if it is
/// already stored.
/// \param i The item to delete.
/// \pre \e i must be in the heap.
void erase(const Item &i) {
int index = _iim[i];
_iim[i] = POST_HEAP;
remove(index);
relocateLast(index);
}
/// \brief The priority of the given item.
///
/// This function returns the priority of the given item.
/// \param i The item.
/// \pre \e i must be in the heap.
Prio operator[](const Item &i) const {
int idx = _iim[i];
return _data[idx].prio;
}
/// \brief Set the priority of an item or insert it, if it is
/// not stored in the heap.
///
/// This method sets the priority of the given item if it is
/// already stored in the heap. Otherwise it inserts the given
/// item into the heap with the given priority.
/// \param i The item.
/// \param p The priority.
/// \pre \e i must be in the heap.
/// \warning This method may throw an \c UnderFlowPriorityException.
void set(const Item &i, const Prio &p) {
int idx = _iim[i];
if( idx < 0 ) {
push(i, p);
}
else if( p >= _data[idx].prio ) {
_data[idx].prio = p;
bubbleUp(idx);
} else {
_data[idx].prio = p;
bubbleDown(idx);
}
}
/// \brief Decrease the priority of an item to the given value.
///
/// This function decreases the priority of an item to the given value.
/// \param i The item.
/// \param p The priority.
/// \pre \e i must be stored in the heap with priority at least \e p.
/// \warning This method may throw an \c UnderFlowPriorityException.
void decrease(const Item &i, const Prio &p) {
int idx = _iim[i];
_data[idx].prio = p;
bubbleDown(idx);
}
/// \brief Increase the priority of an item to the given value.
///
/// This function increases the priority of an item to the given value.
/// \param i The item.
/// \param p The priority.
/// \pre \e i must be stored in the heap with priority at most \e p.
void increase(const Item &i, const Prio &p) {
int idx = _iim[i];
_data[idx].prio = p;
bubbleUp(idx);
}
/// \brief Return the state of an item.
///
/// This method returns \c PRE_HEAP if the given item has never
/// been in the heap, \c IN_HEAP if it is in the heap at the moment,
/// and \c POST_HEAP otherwise.
/// In the latter case it is possible that the item will get back
/// to the heap again.
/// \param i The item.
State state(const Item &i) const {
int s = _iim[i];
if( s >= 0 ) s = 0;
return State(s);
}
/// \brief Set the state of an item in the heap.
///
/// This function sets the state of the given item in the heap.
/// It can be used to manually clear the heap when it is important
/// to achive better time complexity.
/// \param i The item.
/// \param st The state. It should not be \c IN_HEAP.
void state(const Item& i, State st) {
switch (st) {
case POST_HEAP:
case PRE_HEAP:
if (state(i) == IN_HEAP) {
erase(i);
}
_iim[i] = st;
break;
case IN_HEAP:
break;
}
}
}; // class RadixHeap
} // namespace lemon
#endif // LEMON_RADIX_HEAP_H