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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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*
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* This file is a part of LEMON, a generic C++ optimization library.
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*
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* Copyright (C) 2003-2008
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* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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* (Egervary Research Group on Combinatorial Optimization, EGRES).
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*
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* Permission to use, modify and distribute this software is granted
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* provided that this copyright notice appears in all copies. For
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* precise terms see the accompanying LICENSE file.
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*
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* This software is provided "AS IS" with no warranty of any kind,
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* express or implied, and with no claim as to its suitability for any
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* purpose.
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*
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*/
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#ifndef LEMON_UNION_FIND_H
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#define LEMON_UNION_FIND_H
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//!\ingroup auxdat
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//!\file
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//!\brief Union-Find data structures.
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//!
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#include <vector>
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#include <list>
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#include <utility>
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#include <algorithm>
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#include <functional>
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#include <lemon/core.h>
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namespace lemon {
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/// \ingroup auxdat
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///
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/// \brief A \e Union-Find data structure implementation
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///
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/// The class implements the \e Union-Find data structure.
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/// The union operation uses rank heuristic, while
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/// the find operation uses path compression.
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/// This is a very simple but efficient implementation, providing
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/// only four methods: join (union), find, insert and size.
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/// For more features see the \ref UnionFindEnum class.
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///
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/// It is primarily used in Kruskal algorithm for finding minimal
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/// cost spanning tree in a graph.
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/// \sa kruskal()
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///
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/// \pre You need to add all the elements by the \ref insert()
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/// method.
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template <typename _ItemIntMap>
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class UnionFind {
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public:
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typedef _ItemIntMap ItemIntMap;
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typedef typename ItemIntMap::Key Item;
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private:
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// If the items vector stores negative value for an item then
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// that item is root item and it has -items[it] component size.
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// Else the items[it] contains the index of the parent.
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std::vector<int> items;
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ItemIntMap& index;
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bool rep(int idx) const {
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return items[idx] < 0;
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}
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int repIndex(int idx) const {
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int k = idx;
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while (!rep(k)) {
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k = items[k] ;
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}
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while (idx != k) {
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int next = items[idx];
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const_cast<int&>(items[idx]) = k;
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idx = next;
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}
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return k;
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}
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public:
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/// \brief Constructor
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///
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/// Constructor of the UnionFind class. You should give an item to
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/// integer map which will be used from the data structure. If you
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/// modify directly this map that may cause segmentation fault,
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/// invalid data structure, or infinite loop when you use again
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/// the union-find.
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UnionFind(ItemIntMap& m) : index(m) {}
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/// \brief Returns the index of the element's component.
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///
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/// The method returns the index of the element's component.
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/// This is an integer between zero and the number of inserted elements.
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///
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int find(const Item& a) {
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return repIndex(index[a]);
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}
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/// \brief Clears the union-find data structure
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///
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/// Erase each item from the data structure.
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void clear() {
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items.clear();
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}
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/// \brief Inserts a new element into the structure.
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///
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/// This method inserts a new element into the data structure.
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///
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/// The method returns the index of the new component.
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int insert(const Item& a) {
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int n = items.size();
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items.push_back(-1);
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index.set(a,n);
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return n;
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}
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/// \brief Joining the components of element \e a and element \e b.
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///
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/// This is the \e union operation of the Union-Find structure.
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/// Joins the component of element \e a and component of
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/// element \e b. If \e a and \e b are in the same component then
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/// it returns false otherwise it returns true.
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bool join(const Item& a, const Item& b) {
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int ka = repIndex(index[a]);
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int kb = repIndex(index[b]);
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if ( ka == kb )
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return false;
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if (items[ka] < items[kb]) {
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items[ka] += items[kb];
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items[kb] = ka;
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} else {
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items[kb] += items[ka];
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items[ka] = kb;
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}
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return true;
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}
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/// \brief Returns the size of the component of element \e a.
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///
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/// Returns the size of the component of element \e a.
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int size(const Item& a) {
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int k = repIndex(index[a]);
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return - items[k];
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}
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};
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/// \ingroup auxdat
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///
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/// \brief A \e Union-Find data structure implementation which
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/// is able to enumerate the components.
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///
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/// The class implements a \e Union-Find data structure
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/// which is able to enumerate the components and the items in
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/// a component. If you don't need this feature then perhaps it's
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/// better to use the \ref UnionFind class which is more efficient.
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///
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/// The union operation uses rank heuristic, while
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/// the find operation uses path compression.
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///
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/// \pre You need to add all the elements by the \ref insert()
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/// method.
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///
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template <typename _ItemIntMap>
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class UnionFindEnum {
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public:
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typedef _ItemIntMap ItemIntMap;
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typedef typename ItemIntMap::Key Item;
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private:
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ItemIntMap& index;
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// If the parent stores negative value for an item then that item
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// is root item and it has ~(items[it].parent) component id. Else
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// the items[it].parent contains the index of the parent.
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//
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// The \c next and \c prev provides the double-linked
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// cyclic list of one component's items.
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struct ItemT {
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int parent;
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Item item;
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int next, prev;
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};
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std::vector<ItemT> items;
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int firstFreeItem;
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struct ClassT {
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int size;
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int firstItem;
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int next, prev;
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};
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std::vector<ClassT> classes;
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int firstClass, firstFreeClass;
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int newClass() {
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if (firstFreeClass == -1) {
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int cdx = classes.size();
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classes.push_back(ClassT());
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return cdx;
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} else {
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int cdx = firstFreeClass;
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firstFreeClass = classes[firstFreeClass].next;
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return cdx;
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}
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}
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int newItem() {
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if (firstFreeItem == -1) {
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int idx = items.size();
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items.push_back(ItemT());
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return idx;
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} else {
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int idx = firstFreeItem;
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firstFreeItem = items[firstFreeItem].next;
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return idx;
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}
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}
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bool rep(int idx) const {
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return items[idx].parent < 0;
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}
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int repIndex(int idx) const {
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alpar@103
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int k = idx;
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while (!rep(k)) {
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k = items[k].parent;
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}
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while (idx != k) {
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int next = items[idx].parent;
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const_cast<int&>(items[idx].parent) = k;
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idx = next;
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}
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return k;
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alpar@103
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}
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int classIndex(int idx) const {
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return ~(items[repIndex(idx)].parent);
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}
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alpar@103
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void singletonItem(int idx) {
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alpar@103
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items[idx].next = idx;
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items[idx].prev = idx;
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}
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alpar@103
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void laceItem(int idx, int rdx) {
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items[idx].prev = rdx;
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items[idx].next = items[rdx].next;
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items[items[rdx].next].prev = idx;
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items[rdx].next = idx;
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}
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alpar@103
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void unlaceItem(int idx) {
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items[items[idx].prev].next = items[idx].next;
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items[items[idx].next].prev = items[idx].prev;
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items[idx].next = firstFreeItem;
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firstFreeItem = idx;
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}
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void spliceItems(int ak, int bk) {
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alpar@103
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items[items[ak].prev].next = bk;
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items[items[bk].prev].next = ak;
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alpar@103
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int tmp = items[ak].prev;
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items[ak].prev = items[bk].prev;
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items[bk].prev = tmp;
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}
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void laceClass(int cls) {
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if (firstClass != -1) {
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classes[firstClass].prev = cls;
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}
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classes[cls].next = firstClass;
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classes[cls].prev = -1;
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alpar@103
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firstClass = cls;
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alpar@209
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}
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alpar@103
|
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alpar@103
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void unlaceClass(int cls) {
|
alpar@103
|
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if (classes[cls].prev != -1) {
|
alpar@103
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classes[classes[cls].prev].next = classes[cls].next;
|
alpar@103
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} else {
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firstClass = classes[cls].next;
|
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}
|
alpar@103
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if (classes[cls].next != -1) {
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alpar@103
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classes[classes[cls].next].prev = classes[cls].prev;
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alpar@103
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301 |
}
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alpar@209
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alpar@103
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classes[cls].next = firstFreeClass;
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alpar@103
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firstFreeClass = cls;
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alpar@209
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305 |
}
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alpar@103
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alpar@103
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307 |
public:
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alpar@103
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|
alpar@209
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309 |
UnionFindEnum(ItemIntMap& _index)
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alpar@209
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310 |
: index(_index), items(), firstFreeItem(-1),
|
alpar@209
|
311 |
firstClass(-1), firstFreeClass(-1) {}
|
alpar@209
|
312 |
|
alpar@103
|
313 |
/// \brief Inserts the given element into a new component.
|
alpar@103
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///
|
alpar@103
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315 |
/// This method creates a new component consisting only of the
|
alpar@103
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/// given element.
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alpar@103
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///
|
alpar@103
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318 |
int insert(const Item& item) {
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alpar@103
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319 |
int idx = newItem();
|
alpar@103
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320 |
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alpar@103
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321 |
index.set(item, idx);
|
alpar@103
|
322 |
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alpar@103
|
323 |
singletonItem(idx);
|
alpar@103
|
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items[idx].item = item;
|
alpar@103
|
325 |
|
alpar@103
|
326 |
int cdx = newClass();
|
alpar@103
|
327 |
|
alpar@103
|
328 |
items[idx].parent = ~cdx;
|
alpar@103
|
329 |
|
alpar@103
|
330 |
laceClass(cdx);
|
alpar@103
|
331 |
classes[cdx].size = 1;
|
alpar@103
|
332 |
classes[cdx].firstItem = idx;
|
alpar@103
|
333 |
|
alpar@103
|
334 |
firstClass = cdx;
|
alpar@209
|
335 |
|
alpar@103
|
336 |
return cdx;
|
alpar@103
|
337 |
}
|
alpar@103
|
338 |
|
alpar@103
|
339 |
/// \brief Inserts the given element into the component of the others.
|
alpar@103
|
340 |
///
|
alpar@103
|
341 |
/// This methods inserts the element \e a into the component of the
|
alpar@209
|
342 |
/// element \e comp.
|
alpar@103
|
343 |
void insert(const Item& item, int cls) {
|
alpar@103
|
344 |
int rdx = classes[cls].firstItem;
|
alpar@103
|
345 |
int idx = newItem();
|
alpar@103
|
346 |
|
alpar@103
|
347 |
index.set(item, idx);
|
alpar@103
|
348 |
|
alpar@103
|
349 |
laceItem(idx, rdx);
|
alpar@103
|
350 |
|
alpar@103
|
351 |
items[idx].item = item;
|
alpar@103
|
352 |
items[idx].parent = rdx;
|
alpar@103
|
353 |
|
alpar@103
|
354 |
++classes[~(items[rdx].parent)].size;
|
alpar@103
|
355 |
}
|
alpar@103
|
356 |
|
alpar@103
|
357 |
/// \brief Clears the union-find data structure
|
alpar@103
|
358 |
///
|
alpar@103
|
359 |
/// Erase each item from the data structure.
|
alpar@103
|
360 |
void clear() {
|
alpar@103
|
361 |
items.clear();
|
alpar@103
|
362 |
firstClass = -1;
|
alpar@103
|
363 |
firstFreeItem = -1;
|
alpar@103
|
364 |
}
|
alpar@103
|
365 |
|
alpar@103
|
366 |
/// \brief Finds the component of the given element.
|
alpar@103
|
367 |
///
|
alpar@103
|
368 |
/// The method returns the component id of the given element.
|
alpar@103
|
369 |
int find(const Item &item) const {
|
alpar@103
|
370 |
return ~(items[repIndex(index[item])].parent);
|
alpar@103
|
371 |
}
|
alpar@103
|
372 |
|
alpar@103
|
373 |
/// \brief Joining the component of element \e a and element \e b.
|
alpar@103
|
374 |
///
|
alpar@209
|
375 |
/// This is the \e union operation of the Union-Find structure.
|
alpar@103
|
376 |
/// Joins the component of element \e a and component of
|
alpar@103
|
377 |
/// element \e b. If \e a and \e b are in the same component then
|
alpar@103
|
378 |
/// returns -1 else returns the remaining class.
|
alpar@103
|
379 |
int join(const Item& a, const Item& b) {
|
alpar@103
|
380 |
|
alpar@103
|
381 |
int ak = repIndex(index[a]);
|
alpar@103
|
382 |
int bk = repIndex(index[b]);
|
alpar@103
|
383 |
|
alpar@103
|
384 |
if (ak == bk) {
|
alpar@209
|
385 |
return -1;
|
alpar@103
|
386 |
}
|
alpar@103
|
387 |
|
alpar@103
|
388 |
int acx = ~(items[ak].parent);
|
alpar@103
|
389 |
int bcx = ~(items[bk].parent);
|
alpar@103
|
390 |
|
alpar@103
|
391 |
int rcx;
|
alpar@103
|
392 |
|
alpar@103
|
393 |
if (classes[acx].size > classes[bcx].size) {
|
alpar@209
|
394 |
classes[acx].size += classes[bcx].size;
|
alpar@209
|
395 |
items[bk].parent = ak;
|
alpar@103
|
396 |
unlaceClass(bcx);
|
alpar@209
|
397 |
rcx = acx;
|
alpar@103
|
398 |
} else {
|
alpar@209
|
399 |
classes[bcx].size += classes[acx].size;
|
alpar@209
|
400 |
items[ak].parent = bk;
|
alpar@103
|
401 |
unlaceClass(acx);
|
alpar@209
|
402 |
rcx = bcx;
|
alpar@103
|
403 |
}
|
alpar@103
|
404 |
spliceItems(ak, bk);
|
alpar@103
|
405 |
|
alpar@103
|
406 |
return rcx;
|
alpar@103
|
407 |
}
|
alpar@103
|
408 |
|
alpar@103
|
409 |
/// \brief Returns the size of the class.
|
alpar@103
|
410 |
///
|
alpar@103
|
411 |
/// Returns the size of the class.
|
alpar@103
|
412 |
int size(int cls) const {
|
alpar@103
|
413 |
return classes[cls].size;
|
alpar@103
|
414 |
}
|
alpar@103
|
415 |
|
alpar@209
|
416 |
/// \brief Splits up the component.
|
alpar@103
|
417 |
///
|
alpar@103
|
418 |
/// Splitting the component into singleton components (component
|
alpar@103
|
419 |
/// of size one).
|
alpar@103
|
420 |
void split(int cls) {
|
alpar@103
|
421 |
int fdx = classes[cls].firstItem;
|
alpar@103
|
422 |
int idx = items[fdx].next;
|
alpar@103
|
423 |
while (idx != fdx) {
|
alpar@103
|
424 |
int next = items[idx].next;
|
alpar@103
|
425 |
|
alpar@209
|
426 |
singletonItem(idx);
|
alpar@103
|
427 |
|
alpar@209
|
428 |
int cdx = newClass();
|
alpar@103
|
429 |
items[idx].parent = ~cdx;
|
alpar@103
|
430 |
|
alpar@209
|
431 |
laceClass(cdx);
|
alpar@209
|
432 |
classes[cdx].size = 1;
|
alpar@209
|
433 |
classes[cdx].firstItem = idx;
|
alpar@209
|
434 |
|
alpar@103
|
435 |
idx = next;
|
alpar@103
|
436 |
}
|
alpar@103
|
437 |
|
alpar@103
|
438 |
items[idx].prev = idx;
|
alpar@103
|
439 |
items[idx].next = idx;
|
alpar@103
|
440 |
|
alpar@103
|
441 |
classes[~(items[idx].parent)].size = 1;
|
alpar@209
|
442 |
|
alpar@103
|
443 |
}
|
alpar@103
|
444 |
|
alpar@103
|
445 |
/// \brief Removes the given element from the structure.
|
alpar@103
|
446 |
///
|
alpar@103
|
447 |
/// Removes the element from its component and if the component becomes
|
alpar@103
|
448 |
/// empty then removes that component from the component list.
|
alpar@103
|
449 |
///
|
alpar@103
|
450 |
/// \warning It is an error to remove an element which is not in
|
alpar@103
|
451 |
/// the structure.
|
alpar@103
|
452 |
/// \warning This running time of this operation is proportional to the
|
alpar@103
|
453 |
/// number of the items in this class.
|
alpar@103
|
454 |
void erase(const Item& item) {
|
alpar@103
|
455 |
int idx = index[item];
|
alpar@103
|
456 |
int fdx = items[idx].next;
|
alpar@103
|
457 |
|
alpar@103
|
458 |
int cdx = classIndex(idx);
|
alpar@103
|
459 |
if (idx == fdx) {
|
alpar@209
|
460 |
unlaceClass(cdx);
|
alpar@209
|
461 |
items[idx].next = firstFreeItem;
|
alpar@209
|
462 |
firstFreeItem = idx;
|
alpar@209
|
463 |
return;
|
alpar@103
|
464 |
} else {
|
alpar@209
|
465 |
classes[cdx].firstItem = fdx;
|
alpar@209
|
466 |
--classes[cdx].size;
|
alpar@209
|
467 |
items[fdx].parent = ~cdx;
|
alpar@103
|
468 |
|
alpar@209
|
469 |
unlaceItem(idx);
|
alpar@209
|
470 |
idx = items[fdx].next;
|
alpar@209
|
471 |
while (idx != fdx) {
|
alpar@209
|
472 |
items[idx].parent = fdx;
|
alpar@209
|
473 |
idx = items[idx].next;
|
alpar@209
|
474 |
}
|
alpar@209
|
475 |
|
alpar@103
|
476 |
}
|
alpar@103
|
477 |
|
alpar@103
|
478 |
}
|
alpar@103
|
479 |
|
alpar@103
|
480 |
/// \brief Gives back a representant item of the component.
|
alpar@103
|
481 |
///
|
alpar@103
|
482 |
/// Gives back a representant item of the component.
|
alpar@103
|
483 |
Item item(int cls) const {
|
alpar@103
|
484 |
return items[classes[cls].firstItem].item;
|
alpar@103
|
485 |
}
|
alpar@103
|
486 |
|
alpar@103
|
487 |
/// \brief Removes the component of the given element from the structure.
|
alpar@103
|
488 |
///
|
alpar@103
|
489 |
/// Removes the component of the given element from the structure.
|
alpar@103
|
490 |
///
|
alpar@103
|
491 |
/// \warning It is an error to give an element which is not in the
|
alpar@103
|
492 |
/// structure.
|
alpar@103
|
493 |
void eraseClass(int cls) {
|
alpar@103
|
494 |
int fdx = classes[cls].firstItem;
|
alpar@103
|
495 |
unlaceClass(cls);
|
alpar@103
|
496 |
items[items[fdx].prev].next = firstFreeItem;
|
alpar@103
|
497 |
firstFreeItem = fdx;
|
alpar@103
|
498 |
}
|
alpar@103
|
499 |
|
ladanyi@236
|
500 |
/// \brief LEMON style iterator for the representant items.
|
alpar@103
|
501 |
///
|
alpar@103
|
502 |
/// ClassIt is a lemon style iterator for the components. It iterates
|
alpar@103
|
503 |
/// on the ids of the classes.
|
alpar@103
|
504 |
class ClassIt {
|
alpar@103
|
505 |
public:
|
alpar@103
|
506 |
/// \brief Constructor of the iterator
|
alpar@103
|
507 |
///
|
alpar@103
|
508 |
/// Constructor of the iterator
|
alpar@103
|
509 |
ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) {
|
alpar@103
|
510 |
cdx = unionFind->firstClass;
|
alpar@103
|
511 |
}
|
alpar@103
|
512 |
|
alpar@103
|
513 |
/// \brief Constructor to get invalid iterator
|
alpar@103
|
514 |
///
|
alpar@103
|
515 |
/// Constructor to get invalid iterator
|
alpar@103
|
516 |
ClassIt(Invalid) : unionFind(0), cdx(-1) {}
|
alpar@209
|
517 |
|
alpar@103
|
518 |
/// \brief Increment operator
|
alpar@103
|
519 |
///
|
alpar@103
|
520 |
/// It steps to the next representant item.
|
alpar@103
|
521 |
ClassIt& operator++() {
|
alpar@103
|
522 |
cdx = unionFind->classes[cdx].next;
|
alpar@103
|
523 |
return *this;
|
alpar@103
|
524 |
}
|
alpar@209
|
525 |
|
alpar@103
|
526 |
/// \brief Conversion operator
|
alpar@103
|
527 |
///
|
alpar@103
|
528 |
/// It converts the iterator to the current representant item.
|
alpar@103
|
529 |
operator int() const {
|
alpar@103
|
530 |
return cdx;
|
alpar@103
|
531 |
}
|
alpar@103
|
532 |
|
alpar@103
|
533 |
/// \brief Equality operator
|
alpar@103
|
534 |
///
|
alpar@103
|
535 |
/// Equality operator
|
alpar@209
|
536 |
bool operator==(const ClassIt& i) {
|
alpar@103
|
537 |
return i.cdx == cdx;
|
alpar@103
|
538 |
}
|
alpar@103
|
539 |
|
alpar@103
|
540 |
/// \brief Inequality operator
|
alpar@103
|
541 |
///
|
alpar@103
|
542 |
/// Inequality operator
|
alpar@209
|
543 |
bool operator!=(const ClassIt& i) {
|
alpar@103
|
544 |
return i.cdx != cdx;
|
alpar@103
|
545 |
}
|
alpar@209
|
546 |
|
alpar@103
|
547 |
private:
|
alpar@103
|
548 |
const UnionFindEnum* unionFind;
|
alpar@103
|
549 |
int cdx;
|
alpar@103
|
550 |
};
|
alpar@103
|
551 |
|
ladanyi@236
|
552 |
/// \brief LEMON style iterator for the items of a component.
|
alpar@103
|
553 |
///
|
alpar@103
|
554 |
/// ClassIt is a lemon style iterator for the components. It iterates
|
alpar@103
|
555 |
/// on the items of a class. By example if you want to iterate on
|
alpar@103
|
556 |
/// each items of each classes then you may write the next code.
|
alpar@103
|
557 |
///\code
|
alpar@103
|
558 |
/// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
|
alpar@103
|
559 |
/// std::cout << "Class: ";
|
alpar@103
|
560 |
/// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
|
alpar@103
|
561 |
/// std::cout << toString(iit) << ' ' << std::endl;
|
alpar@103
|
562 |
/// }
|
alpar@103
|
563 |
/// std::cout << std::endl;
|
alpar@103
|
564 |
/// }
|
alpar@103
|
565 |
///\endcode
|
alpar@103
|
566 |
class ItemIt {
|
alpar@103
|
567 |
public:
|
alpar@103
|
568 |
/// \brief Constructor of the iterator
|
alpar@103
|
569 |
///
|
alpar@103
|
570 |
/// Constructor of the iterator. The iterator iterates
|
alpar@103
|
571 |
/// on the class of the \c item.
|
alpar@103
|
572 |
ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) {
|
alpar@103
|
573 |
fdx = idx = unionFind->classes[cls].firstItem;
|
alpar@103
|
574 |
}
|
alpar@103
|
575 |
|
alpar@103
|
576 |
/// \brief Constructor to get invalid iterator
|
alpar@103
|
577 |
///
|
alpar@103
|
578 |
/// Constructor to get invalid iterator
|
alpar@103
|
579 |
ItemIt(Invalid) : unionFind(0), idx(-1) {}
|
alpar@209
|
580 |
|
alpar@103
|
581 |
/// \brief Increment operator
|
alpar@103
|
582 |
///
|
alpar@103
|
583 |
/// It steps to the next item in the class.
|
alpar@103
|
584 |
ItemIt& operator++() {
|
alpar@103
|
585 |
idx = unionFind->items[idx].next;
|
alpar@103
|
586 |
if (idx == fdx) idx = -1;
|
alpar@103
|
587 |
return *this;
|
alpar@103
|
588 |
}
|
alpar@209
|
589 |
|
alpar@103
|
590 |
/// \brief Conversion operator
|
alpar@103
|
591 |
///
|
alpar@103
|
592 |
/// It converts the iterator to the current item.
|
alpar@103
|
593 |
operator const Item&() const {
|
alpar@103
|
594 |
return unionFind->items[idx].item;
|
alpar@103
|
595 |
}
|
alpar@103
|
596 |
|
alpar@103
|
597 |
/// \brief Equality operator
|
alpar@103
|
598 |
///
|
alpar@103
|
599 |
/// Equality operator
|
alpar@209
|
600 |
bool operator==(const ItemIt& i) {
|
alpar@103
|
601 |
return i.idx == idx;
|
alpar@103
|
602 |
}
|
alpar@103
|
603 |
|
alpar@103
|
604 |
/// \brief Inequality operator
|
alpar@103
|
605 |
///
|
alpar@103
|
606 |
/// Inequality operator
|
alpar@209
|
607 |
bool operator!=(const ItemIt& i) {
|
alpar@103
|
608 |
return i.idx != idx;
|
alpar@103
|
609 |
}
|
alpar@209
|
610 |
|
alpar@103
|
611 |
private:
|
alpar@103
|
612 |
const UnionFindEnum* unionFind;
|
alpar@103
|
613 |
int idx, fdx;
|
alpar@103
|
614 |
};
|
alpar@103
|
615 |
|
alpar@103
|
616 |
};
|
alpar@103
|
617 |
|
alpar@103
|
618 |
/// \ingroup auxdat
|
alpar@103
|
619 |
///
|
alpar@103
|
620 |
/// \brief A \e Extend-Find data structure implementation which
|
alpar@103
|
621 |
/// is able to enumerate the components.
|
alpar@103
|
622 |
///
|
alpar@103
|
623 |
/// The class implements an \e Extend-Find data structure which is
|
alpar@103
|
624 |
/// able to enumerate the components and the items in a
|
alpar@103
|
625 |
/// component. The data structure is a simplification of the
|
alpar@103
|
626 |
/// Union-Find structure, and it does not allow to merge two components.
|
alpar@103
|
627 |
///
|
alpar@103
|
628 |
/// \pre You need to add all the elements by the \ref insert()
|
alpar@103
|
629 |
/// method.
|
alpar@103
|
630 |
template <typename _ItemIntMap>
|
alpar@103
|
631 |
class ExtendFindEnum {
|
alpar@103
|
632 |
public:
|
alpar@209
|
633 |
|
alpar@103
|
634 |
typedef _ItemIntMap ItemIntMap;
|
alpar@103
|
635 |
typedef typename ItemIntMap::Key Item;
|
alpar@103
|
636 |
|
alpar@103
|
637 |
private:
|
alpar@209
|
638 |
|
alpar@103
|
639 |
ItemIntMap& index;
|
alpar@103
|
640 |
|
alpar@103
|
641 |
struct ItemT {
|
alpar@103
|
642 |
int cls;
|
alpar@103
|
643 |
Item item;
|
alpar@103
|
644 |
int next, prev;
|
alpar@103
|
645 |
};
|
alpar@103
|
646 |
|
alpar@103
|
647 |
std::vector<ItemT> items;
|
alpar@103
|
648 |
int firstFreeItem;
|
alpar@103
|
649 |
|
alpar@103
|
650 |
struct ClassT {
|
alpar@103
|
651 |
int firstItem;
|
alpar@103
|
652 |
int next, prev;
|
alpar@103
|
653 |
};
|
alpar@103
|
654 |
|
alpar@103
|
655 |
std::vector<ClassT> classes;
|
alpar@103
|
656 |
|
alpar@103
|
657 |
int firstClass, firstFreeClass;
|
alpar@103
|
658 |
|
alpar@103
|
659 |
int newClass() {
|
alpar@103
|
660 |
if (firstFreeClass != -1) {
|
alpar@209
|
661 |
int cdx = firstFreeClass;
|
alpar@209
|
662 |
firstFreeClass = classes[cdx].next;
|
alpar@209
|
663 |
return cdx;
|
alpar@103
|
664 |
} else {
|
alpar@209
|
665 |
classes.push_back(ClassT());
|
alpar@209
|
666 |
return classes.size() - 1;
|
alpar@103
|
667 |
}
|
alpar@103
|
668 |
}
|
alpar@103
|
669 |
|
alpar@103
|
670 |
int newItem() {
|
alpar@103
|
671 |
if (firstFreeItem != -1) {
|
alpar@209
|
672 |
int idx = firstFreeItem;
|
alpar@209
|
673 |
firstFreeItem = items[idx].next;
|
alpar@209
|
674 |
return idx;
|
alpar@103
|
675 |
} else {
|
alpar@209
|
676 |
items.push_back(ItemT());
|
alpar@209
|
677 |
return items.size() - 1;
|
alpar@103
|
678 |
}
|
alpar@103
|
679 |
}
|
alpar@103
|
680 |
|
alpar@103
|
681 |
public:
|
alpar@103
|
682 |
|
alpar@103
|
683 |
/// \brief Constructor
|
alpar@209
|
684 |
ExtendFindEnum(ItemIntMap& _index)
|
alpar@209
|
685 |
: index(_index), items(), firstFreeItem(-1),
|
alpar@209
|
686 |
classes(), firstClass(-1), firstFreeClass(-1) {}
|
alpar@209
|
687 |
|
alpar@103
|
688 |
/// \brief Inserts the given element into a new component.
|
alpar@103
|
689 |
///
|
alpar@103
|
690 |
/// This method creates a new component consisting only of the
|
alpar@103
|
691 |
/// given element.
|
alpar@103
|
692 |
int insert(const Item& item) {
|
alpar@103
|
693 |
int cdx = newClass();
|
alpar@103
|
694 |
classes[cdx].prev = -1;
|
alpar@103
|
695 |
classes[cdx].next = firstClass;
|
alpar@103
|
696 |
if (firstClass != -1) {
|
alpar@209
|
697 |
classes[firstClass].prev = cdx;
|
alpar@103
|
698 |
}
|
alpar@103
|
699 |
firstClass = cdx;
|
alpar@209
|
700 |
|
alpar@103
|
701 |
int idx = newItem();
|
alpar@103
|
702 |
items[idx].item = item;
|
alpar@103
|
703 |
items[idx].cls = cdx;
|
alpar@103
|
704 |
items[idx].prev = idx;
|
alpar@103
|
705 |
items[idx].next = idx;
|
alpar@103
|
706 |
|
alpar@103
|
707 |
classes[cdx].firstItem = idx;
|
alpar@103
|
708 |
|
alpar@103
|
709 |
index.set(item, idx);
|
alpar@209
|
710 |
|
alpar@103
|
711 |
return cdx;
|
alpar@103
|
712 |
}
|
alpar@103
|
713 |
|
alpar@103
|
714 |
/// \brief Inserts the given element into the given component.
|
alpar@103
|
715 |
///
|
alpar@103
|
716 |
/// This methods inserts the element \e item a into the \e cls class.
|
alpar@103
|
717 |
void insert(const Item& item, int cls) {
|
alpar@103
|
718 |
int idx = newItem();
|
alpar@103
|
719 |
int rdx = classes[cls].firstItem;
|
alpar@103
|
720 |
items[idx].item = item;
|
alpar@103
|
721 |
items[idx].cls = cls;
|
alpar@103
|
722 |
|
alpar@103
|
723 |
items[idx].prev = rdx;
|
alpar@103
|
724 |
items[idx].next = items[rdx].next;
|
alpar@103
|
725 |
items[items[rdx].next].prev = idx;
|
alpar@103
|
726 |
items[rdx].next = idx;
|
alpar@103
|
727 |
|
alpar@103
|
728 |
index.set(item, idx);
|
alpar@103
|
729 |
}
|
alpar@103
|
730 |
|
alpar@103
|
731 |
/// \brief Clears the union-find data structure
|
alpar@103
|
732 |
///
|
alpar@103
|
733 |
/// Erase each item from the data structure.
|
alpar@103
|
734 |
void clear() {
|
alpar@103
|
735 |
items.clear();
|
alpar@103
|
736 |
classes.clear;
|
alpar@103
|
737 |
firstClass = firstFreeClass = firstFreeItem = -1;
|
alpar@103
|
738 |
}
|
alpar@103
|
739 |
|
alpar@103
|
740 |
/// \brief Gives back the class of the \e item.
|
alpar@103
|
741 |
///
|
alpar@103
|
742 |
/// Gives back the class of the \e item.
|
alpar@103
|
743 |
int find(const Item &item) const {
|
alpar@103
|
744 |
return items[index[item]].cls;
|
alpar@103
|
745 |
}
|
alpar@103
|
746 |
|
alpar@103
|
747 |
/// \brief Gives back a representant item of the component.
|
alpar@103
|
748 |
///
|
alpar@103
|
749 |
/// Gives back a representant item of the component.
|
alpar@103
|
750 |
Item item(int cls) const {
|
alpar@103
|
751 |
return items[classes[cls].firstItem].item;
|
alpar@103
|
752 |
}
|
alpar@209
|
753 |
|
alpar@103
|
754 |
/// \brief Removes the given element from the structure.
|
alpar@103
|
755 |
///
|
alpar@103
|
756 |
/// Removes the element from its component and if the component becomes
|
alpar@103
|
757 |
/// empty then removes that component from the component list.
|
alpar@103
|
758 |
///
|
alpar@103
|
759 |
/// \warning It is an error to remove an element which is not in
|
alpar@103
|
760 |
/// the structure.
|
alpar@103
|
761 |
void erase(const Item &item) {
|
alpar@103
|
762 |
int idx = index[item];
|
alpar@103
|
763 |
int cdx = items[idx].cls;
|
alpar@209
|
764 |
|
alpar@103
|
765 |
if (idx == items[idx].next) {
|
alpar@209
|
766 |
if (classes[cdx].prev != -1) {
|
alpar@209
|
767 |
classes[classes[cdx].prev].next = classes[cdx].next;
|
alpar@209
|
768 |
} else {
|
alpar@209
|
769 |
firstClass = classes[cdx].next;
|
alpar@209
|
770 |
}
|
alpar@209
|
771 |
if (classes[cdx].next != -1) {
|
alpar@209
|
772 |
classes[classes[cdx].next].prev = classes[cdx].prev;
|
alpar@209
|
773 |
}
|
alpar@209
|
774 |
classes[cdx].next = firstFreeClass;
|
alpar@209
|
775 |
firstFreeClass = cdx;
|
alpar@103
|
776 |
} else {
|
alpar@209
|
777 |
classes[cdx].firstItem = items[idx].next;
|
alpar@209
|
778 |
items[items[idx].next].prev = items[idx].prev;
|
alpar@209
|
779 |
items[items[idx].prev].next = items[idx].next;
|
alpar@103
|
780 |
}
|
alpar@103
|
781 |
items[idx].next = firstFreeItem;
|
alpar@103
|
782 |
firstFreeItem = idx;
|
alpar@103
|
783 |
|
alpar@209
|
784 |
}
|
alpar@209
|
785 |
|
alpar@209
|
786 |
|
alpar@103
|
787 |
/// \brief Removes the component of the given element from the structure.
|
alpar@103
|
788 |
///
|
alpar@103
|
789 |
/// Removes the component of the given element from the structure.
|
alpar@103
|
790 |
///
|
alpar@103
|
791 |
/// \warning It is an error to give an element which is not in the
|
alpar@103
|
792 |
/// structure.
|
alpar@103
|
793 |
void eraseClass(int cdx) {
|
alpar@103
|
794 |
int idx = classes[cdx].firstItem;
|
alpar@103
|
795 |
items[items[idx].prev].next = firstFreeItem;
|
alpar@103
|
796 |
firstFreeItem = idx;
|
alpar@103
|
797 |
|
alpar@103
|
798 |
if (classes[cdx].prev != -1) {
|
alpar@209
|
799 |
classes[classes[cdx].prev].next = classes[cdx].next;
|
alpar@103
|
800 |
} else {
|
alpar@209
|
801 |
firstClass = classes[cdx].next;
|
alpar@103
|
802 |
}
|
alpar@103
|
803 |
if (classes[cdx].next != -1) {
|
alpar@209
|
804 |
classes[classes[cdx].next].prev = classes[cdx].prev;
|
alpar@103
|
805 |
}
|
alpar@103
|
806 |
classes[cdx].next = firstFreeClass;
|
alpar@103
|
807 |
firstFreeClass = cdx;
|
alpar@103
|
808 |
}
|
alpar@103
|
809 |
|
ladanyi@236
|
810 |
/// \brief LEMON style iterator for the classes.
|
alpar@103
|
811 |
///
|
alpar@103
|
812 |
/// ClassIt is a lemon style iterator for the components. It iterates
|
alpar@103
|
813 |
/// on the ids of classes.
|
alpar@103
|
814 |
class ClassIt {
|
alpar@103
|
815 |
public:
|
alpar@103
|
816 |
/// \brief Constructor of the iterator
|
alpar@103
|
817 |
///
|
alpar@103
|
818 |
/// Constructor of the iterator
|
alpar@103
|
819 |
ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) {
|
alpar@103
|
820 |
cdx = extendFind->firstClass;
|
alpar@103
|
821 |
}
|
alpar@103
|
822 |
|
alpar@103
|
823 |
/// \brief Constructor to get invalid iterator
|
alpar@103
|
824 |
///
|
alpar@103
|
825 |
/// Constructor to get invalid iterator
|
alpar@103
|
826 |
ClassIt(Invalid) : extendFind(0), cdx(-1) {}
|
alpar@209
|
827 |
|
alpar@103
|
828 |
/// \brief Increment operator
|
alpar@103
|
829 |
///
|
alpar@103
|
830 |
/// It steps to the next representant item.
|
alpar@103
|
831 |
ClassIt& operator++() {
|
alpar@103
|
832 |
cdx = extendFind->classes[cdx].next;
|
alpar@103
|
833 |
return *this;
|
alpar@103
|
834 |
}
|
alpar@209
|
835 |
|
alpar@103
|
836 |
/// \brief Conversion operator
|
alpar@103
|
837 |
///
|
alpar@103
|
838 |
/// It converts the iterator to the current class id.
|
alpar@103
|
839 |
operator int() const {
|
alpar@103
|
840 |
return cdx;
|
alpar@103
|
841 |
}
|
alpar@103
|
842 |
|
alpar@103
|
843 |
/// \brief Equality operator
|
alpar@103
|
844 |
///
|
alpar@103
|
845 |
/// Equality operator
|
alpar@209
|
846 |
bool operator==(const ClassIt& i) {
|
alpar@103
|
847 |
return i.cdx == cdx;
|
alpar@103
|
848 |
}
|
alpar@103
|
849 |
|
alpar@103
|
850 |
/// \brief Inequality operator
|
alpar@103
|
851 |
///
|
alpar@103
|
852 |
/// Inequality operator
|
alpar@209
|
853 |
bool operator!=(const ClassIt& i) {
|
alpar@103
|
854 |
return i.cdx != cdx;
|
alpar@103
|
855 |
}
|
alpar@209
|
856 |
|
alpar@103
|
857 |
private:
|
alpar@103
|
858 |
const ExtendFindEnum* extendFind;
|
alpar@103
|
859 |
int cdx;
|
alpar@103
|
860 |
};
|
alpar@103
|
861 |
|
ladanyi@236
|
862 |
/// \brief LEMON style iterator for the items of a component.
|
alpar@103
|
863 |
///
|
alpar@103
|
864 |
/// ClassIt is a lemon style iterator for the components. It iterates
|
alpar@103
|
865 |
/// on the items of a class. By example if you want to iterate on
|
alpar@103
|
866 |
/// each items of each classes then you may write the next code.
|
alpar@103
|
867 |
///\code
|
alpar@103
|
868 |
/// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
|
alpar@103
|
869 |
/// std::cout << "Class: ";
|
alpar@103
|
870 |
/// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
|
alpar@103
|
871 |
/// std::cout << toString(iit) << ' ' << std::endl;
|
alpar@103
|
872 |
/// }
|
alpar@103
|
873 |
/// std::cout << std::endl;
|
alpar@103
|
874 |
/// }
|
alpar@103
|
875 |
///\endcode
|
alpar@103
|
876 |
class ItemIt {
|
alpar@103
|
877 |
public:
|
alpar@103
|
878 |
/// \brief Constructor of the iterator
|
alpar@103
|
879 |
///
|
alpar@103
|
880 |
/// Constructor of the iterator. The iterator iterates
|
alpar@103
|
881 |
/// on the class of the \c item.
|
alpar@103
|
882 |
ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) {
|
alpar@103
|
883 |
fdx = idx = extendFind->classes[cls].firstItem;
|
alpar@103
|
884 |
}
|
alpar@103
|
885 |
|
alpar@103
|
886 |
/// \brief Constructor to get invalid iterator
|
alpar@103
|
887 |
///
|
alpar@103
|
888 |
/// Constructor to get invalid iterator
|
alpar@103
|
889 |
ItemIt(Invalid) : extendFind(0), idx(-1) {}
|
alpar@209
|
890 |
|
alpar@103
|
891 |
/// \brief Increment operator
|
alpar@103
|
892 |
///
|
alpar@103
|
893 |
/// It steps to the next item in the class.
|
alpar@103
|
894 |
ItemIt& operator++() {
|
alpar@103
|
895 |
idx = extendFind->items[idx].next;
|
alpar@209
|
896 |
if (fdx == idx) idx = -1;
|
alpar@103
|
897 |
return *this;
|
alpar@103
|
898 |
}
|
alpar@209
|
899 |
|
alpar@103
|
900 |
/// \brief Conversion operator
|
alpar@103
|
901 |
///
|
alpar@103
|
902 |
/// It converts the iterator to the current item.
|
alpar@103
|
903 |
operator const Item&() const {
|
alpar@103
|
904 |
return extendFind->items[idx].item;
|
alpar@103
|
905 |
}
|
alpar@103
|
906 |
|
alpar@103
|
907 |
/// \brief Equality operator
|
alpar@103
|
908 |
///
|
alpar@103
|
909 |
/// Equality operator
|
alpar@209
|
910 |
bool operator==(const ItemIt& i) {
|
alpar@103
|
911 |
return i.idx == idx;
|
alpar@103
|
912 |
}
|
alpar@103
|
913 |
|
alpar@103
|
914 |
/// \brief Inequality operator
|
alpar@103
|
915 |
///
|
alpar@103
|
916 |
/// Inequality operator
|
alpar@209
|
917 |
bool operator!=(const ItemIt& i) {
|
alpar@103
|
918 |
return i.idx != idx;
|
alpar@103
|
919 |
}
|
alpar@209
|
920 |
|
alpar@103
|
921 |
private:
|
alpar@103
|
922 |
const ExtendFindEnum* extendFind;
|
alpar@103
|
923 |
int idx, fdx;
|
alpar@103
|
924 |
};
|
alpar@103
|
925 |
|
alpar@103
|
926 |
};
|
alpar@103
|
927 |
|
alpar@103
|
928 |
/// \ingroup auxdat
|
alpar@103
|
929 |
///
|
alpar@103
|
930 |
/// \brief A \e Union-Find data structure implementation which
|
alpar@103
|
931 |
/// is able to store a priority for each item and retrieve the minimum of
|
alpar@103
|
932 |
/// each class.
|
alpar@103
|
933 |
///
|
alpar@103
|
934 |
/// A \e Union-Find data structure implementation which is able to
|
alpar@103
|
935 |
/// store a priority for each item and retrieve the minimum of each
|
alpar@103
|
936 |
/// class. In addition, it supports the joining and splitting the
|
alpar@103
|
937 |
/// components. If you don't need this feature then you makes
|
alpar@103
|
938 |
/// better to use the \ref UnionFind class which is more efficient.
|
alpar@103
|
939 |
///
|
alpar@103
|
940 |
/// The union-find data strcuture based on a (2, 16)-tree with a
|
alpar@103
|
941 |
/// tournament minimum selection on the internal nodes. The insert
|
alpar@103
|
942 |
/// operation takes O(1), the find, set, decrease and increase takes
|
alpar@103
|
943 |
/// O(log(n)), where n is the number of nodes in the current
|
alpar@103
|
944 |
/// component. The complexity of join and split is O(log(n)*k),
|
alpar@103
|
945 |
/// where n is the sum of the number of the nodes and k is the
|
alpar@103
|
946 |
/// number of joined components or the number of the components
|
alpar@103
|
947 |
/// after the split.
|
alpar@103
|
948 |
///
|
alpar@103
|
949 |
/// \pre You need to add all the elements by the \ref insert()
|
alpar@103
|
950 |
/// method.
|
alpar@103
|
951 |
///
|
alpar@209
|
952 |
template <typename _Value, typename _ItemIntMap,
|
alpar@103
|
953 |
typename _Comp = std::less<_Value> >
|
alpar@103
|
954 |
class HeapUnionFind {
|
alpar@103
|
955 |
public:
|
alpar@209
|
956 |
|
alpar@103
|
957 |
typedef _Value Value;
|
alpar@103
|
958 |
typedef typename _ItemIntMap::Key Item;
|
alpar@103
|
959 |
|
alpar@103
|
960 |
typedef _ItemIntMap ItemIntMap;
|
alpar@103
|
961 |
|
alpar@103
|
962 |
typedef _Comp Comp;
|
alpar@103
|
963 |
|
alpar@103
|
964 |
private:
|
alpar@103
|
965 |
|
alpar@103
|
966 |
static const int cmax = 16;
|
alpar@103
|
967 |
|
alpar@103
|
968 |
ItemIntMap& index;
|
alpar@103
|
969 |
|
alpar@103
|
970 |
struct ClassNode {
|
alpar@103
|
971 |
int parent;
|
alpar@103
|
972 |
int depth;
|
alpar@103
|
973 |
|
alpar@103
|
974 |
int left, right;
|
alpar@103
|
975 |
int next, prev;
|
alpar@103
|
976 |
};
|
alpar@103
|
977 |
|
alpar@103
|
978 |
int first_class;
|
alpar@103
|
979 |
int first_free_class;
|
alpar@103
|
980 |
std::vector<ClassNode> classes;
|
alpar@103
|
981 |
|
alpar@103
|
982 |
int newClass() {
|
alpar@103
|
983 |
if (first_free_class < 0) {
|
alpar@103
|
984 |
int id = classes.size();
|
alpar@103
|
985 |
classes.push_back(ClassNode());
|
alpar@103
|
986 |
return id;
|
alpar@103
|
987 |
} else {
|
alpar@103
|
988 |
int id = first_free_class;
|
alpar@103
|
989 |
first_free_class = classes[id].next;
|
alpar@103
|
990 |
return id;
|
alpar@103
|
991 |
}
|
alpar@103
|
992 |
}
|
alpar@103
|
993 |
|
alpar@103
|
994 |
void deleteClass(int id) {
|
alpar@103
|
995 |
classes[id].next = first_free_class;
|
alpar@103
|
996 |
first_free_class = id;
|
alpar@103
|
997 |
}
|
alpar@103
|
998 |
|
alpar@103
|
999 |
struct ItemNode {
|
alpar@103
|
1000 |
int parent;
|
alpar@103
|
1001 |
Item item;
|
alpar@103
|
1002 |
Value prio;
|
alpar@103
|
1003 |
int next, prev;
|
alpar@103
|
1004 |
int left, right;
|
alpar@103
|
1005 |
int size;
|
alpar@103
|
1006 |
};
|
alpar@103
|
1007 |
|
alpar@103
|
1008 |
int first_free_node;
|
alpar@103
|
1009 |
std::vector<ItemNode> nodes;
|
alpar@103
|
1010 |
|
alpar@103
|
1011 |
int newNode() {
|
alpar@103
|
1012 |
if (first_free_node < 0) {
|
alpar@103
|
1013 |
int id = nodes.size();
|
alpar@103
|
1014 |
nodes.push_back(ItemNode());
|
alpar@103
|
1015 |
return id;
|
alpar@103
|
1016 |
} else {
|
alpar@103
|
1017 |
int id = first_free_node;
|
alpar@103
|
1018 |
first_free_node = nodes[id].next;
|
alpar@103
|
1019 |
return id;
|
alpar@103
|
1020 |
}
|
alpar@103
|
1021 |
}
|
alpar@103
|
1022 |
|
alpar@103
|
1023 |
void deleteNode(int id) {
|
alpar@103
|
1024 |
nodes[id].next = first_free_node;
|
alpar@103
|
1025 |
first_free_node = id;
|
alpar@103
|
1026 |
}
|
alpar@103
|
1027 |
|
alpar@103
|
1028 |
Comp comp;
|
alpar@103
|
1029 |
|
alpar@103
|
1030 |
int findClass(int id) const {
|
alpar@103
|
1031 |
int kd = id;
|
alpar@103
|
1032 |
while (kd >= 0) {
|
alpar@103
|
1033 |
kd = nodes[kd].parent;
|
alpar@103
|
1034 |
}
|
alpar@103
|
1035 |
return ~kd;
|
alpar@103
|
1036 |
}
|
alpar@103
|
1037 |
|
alpar@103
|
1038 |
int leftNode(int id) const {
|
alpar@103
|
1039 |
int kd = ~(classes[id].parent);
|
alpar@103
|
1040 |
for (int i = 0; i < classes[id].depth; ++i) {
|
alpar@103
|
1041 |
kd = nodes[kd].left;
|
alpar@103
|
1042 |
}
|
alpar@103
|
1043 |
return kd;
|
alpar@103
|
1044 |
}
|
alpar@103
|
1045 |
|
alpar@103
|
1046 |
int nextNode(int id) const {
|
alpar@103
|
1047 |
int depth = 0;
|
alpar@103
|
1048 |
while (id >= 0 && nodes[id].next == -1) {
|
alpar@103
|
1049 |
id = nodes[id].parent;
|
alpar@103
|
1050 |
++depth;
|
alpar@103
|
1051 |
}
|
alpar@103
|
1052 |
if (id < 0) {
|
alpar@103
|
1053 |
return -1;
|
alpar@103
|
1054 |
}
|
alpar@103
|
1055 |
id = nodes[id].next;
|
alpar@103
|
1056 |
while (depth--) {
|
alpar@209
|
1057 |
id = nodes[id].left;
|
alpar@103
|
1058 |
}
|
alpar@103
|
1059 |
return id;
|
alpar@103
|
1060 |
}
|
alpar@103
|
1061 |
|
alpar@103
|
1062 |
|
alpar@103
|
1063 |
void setPrio(int id) {
|
alpar@103
|
1064 |
int jd = nodes[id].left;
|
alpar@103
|
1065 |
nodes[id].prio = nodes[jd].prio;
|
alpar@103
|
1066 |
nodes[id].item = nodes[jd].item;
|
alpar@103
|
1067 |
jd = nodes[jd].next;
|
alpar@103
|
1068 |
while (jd != -1) {
|
alpar@103
|
1069 |
if (comp(nodes[jd].prio, nodes[id].prio)) {
|
alpar@103
|
1070 |
nodes[id].prio = nodes[jd].prio;
|
alpar@103
|
1071 |
nodes[id].item = nodes[jd].item;
|
alpar@103
|
1072 |
}
|
alpar@103
|
1073 |
jd = nodes[jd].next;
|
alpar@103
|
1074 |
}
|
alpar@103
|
1075 |
}
|
alpar@103
|
1076 |
|
alpar@103
|
1077 |
void push(int id, int jd) {
|
alpar@103
|
1078 |
nodes[id].size = 1;
|
alpar@103
|
1079 |
nodes[id].left = nodes[id].right = jd;
|
alpar@103
|
1080 |
nodes[jd].next = nodes[jd].prev = -1;
|
alpar@103
|
1081 |
nodes[jd].parent = id;
|
alpar@103
|
1082 |
}
|
alpar@103
|
1083 |
|
alpar@103
|
1084 |
void pushAfter(int id, int jd) {
|
alpar@103
|
1085 |
int kd = nodes[id].parent;
|
alpar@103
|
1086 |
if (nodes[id].next != -1) {
|
alpar@103
|
1087 |
nodes[nodes[id].next].prev = jd;
|
alpar@103
|
1088 |
if (kd >= 0) {
|
alpar@103
|
1089 |
nodes[kd].size += 1;
|
alpar@103
|
1090 |
}
|
alpar@103
|
1091 |
} else {
|
alpar@103
|
1092 |
if (kd >= 0) {
|
alpar@103
|
1093 |
nodes[kd].right = jd;
|
alpar@103
|
1094 |
nodes[kd].size += 1;
|
alpar@103
|
1095 |
}
|
alpar@103
|
1096 |
}
|
alpar@103
|
1097 |
nodes[jd].next = nodes[id].next;
|
alpar@103
|
1098 |
nodes[jd].prev = id;
|
alpar@103
|
1099 |
nodes[id].next = jd;
|
alpar@103
|
1100 |
nodes[jd].parent = kd;
|
alpar@103
|
1101 |
}
|
alpar@103
|
1102 |
|
alpar@103
|
1103 |
void pushRight(int id, int jd) {
|
alpar@103
|
1104 |
nodes[id].size += 1;
|
alpar@103
|
1105 |
nodes[jd].prev = nodes[id].right;
|
alpar@103
|
1106 |
nodes[jd].next = -1;
|
alpar@103
|
1107 |
nodes[nodes[id].right].next = jd;
|
alpar@103
|
1108 |
nodes[id].right = jd;
|
alpar@103
|
1109 |
nodes[jd].parent = id;
|
alpar@103
|
1110 |
}
|
alpar@103
|
1111 |
|
alpar@103
|
1112 |
void popRight(int id) {
|
alpar@103
|
1113 |
nodes[id].size -= 1;
|
alpar@103
|
1114 |
int jd = nodes[id].right;
|
alpar@103
|
1115 |
nodes[nodes[jd].prev].next = -1;
|
alpar@103
|
1116 |
nodes[id].right = nodes[jd].prev;
|
alpar@103
|
1117 |
}
|
alpar@103
|
1118 |
|
alpar@103
|
1119 |
void splice(int id, int jd) {
|
alpar@103
|
1120 |
nodes[id].size += nodes[jd].size;
|
alpar@103
|
1121 |
nodes[nodes[id].right].next = nodes[jd].left;
|
alpar@103
|
1122 |
nodes[nodes[jd].left].prev = nodes[id].right;
|
alpar@103
|
1123 |
int kd = nodes[jd].left;
|
alpar@103
|
1124 |
while (kd != -1) {
|
alpar@103
|
1125 |
nodes[kd].parent = id;
|
alpar@103
|
1126 |
kd = nodes[kd].next;
|
alpar@103
|
1127 |
}
|
alpar@103
|
1128 |
nodes[id].right = nodes[jd].right;
|
alpar@103
|
1129 |
}
|
alpar@103
|
1130 |
|
alpar@103
|
1131 |
void split(int id, int jd) {
|
alpar@103
|
1132 |
int kd = nodes[id].parent;
|
alpar@103
|
1133 |
nodes[kd].right = nodes[id].prev;
|
alpar@103
|
1134 |
nodes[nodes[id].prev].next = -1;
|
alpar@209
|
1135 |
|
alpar@103
|
1136 |
nodes[jd].left = id;
|
alpar@103
|
1137 |
nodes[id].prev = -1;
|
alpar@103
|
1138 |
int num = 0;
|
alpar@103
|
1139 |
while (id != -1) {
|
alpar@103
|
1140 |
nodes[id].parent = jd;
|
alpar@103
|
1141 |
nodes[jd].right = id;
|
alpar@103
|
1142 |
id = nodes[id].next;
|
alpar@103
|
1143 |
++num;
|
alpar@209
|
1144 |
}
|
alpar@103
|
1145 |
nodes[kd].size -= num;
|
alpar@103
|
1146 |
nodes[jd].size = num;
|
alpar@103
|
1147 |
}
|
alpar@103
|
1148 |
|
alpar@103
|
1149 |
void pushLeft(int id, int jd) {
|
alpar@103
|
1150 |
nodes[id].size += 1;
|
alpar@103
|
1151 |
nodes[jd].next = nodes[id].left;
|
alpar@103
|
1152 |
nodes[jd].prev = -1;
|
alpar@103
|
1153 |
nodes[nodes[id].left].prev = jd;
|
alpar@103
|
1154 |
nodes[id].left = jd;
|
alpar@103
|
1155 |
nodes[jd].parent = id;
|
alpar@103
|
1156 |
}
|
alpar@103
|
1157 |
|
alpar@103
|
1158 |
void popLeft(int id) {
|
alpar@103
|
1159 |
nodes[id].size -= 1;
|
alpar@103
|
1160 |
int jd = nodes[id].left;
|
alpar@103
|
1161 |
nodes[nodes[jd].next].prev = -1;
|
alpar@103
|
1162 |
nodes[id].left = nodes[jd].next;
|
alpar@103
|
1163 |
}
|
alpar@103
|
1164 |
|
alpar@103
|
1165 |
void repairLeft(int id) {
|
alpar@103
|
1166 |
int jd = ~(classes[id].parent);
|
alpar@103
|
1167 |
while (nodes[jd].left != -1) {
|
alpar@209
|
1168 |
int kd = nodes[jd].left;
|
alpar@209
|
1169 |
if (nodes[jd].size == 1) {
|
alpar@209
|
1170 |
if (nodes[jd].parent < 0) {
|
alpar@209
|
1171 |
classes[id].parent = ~kd;
|
alpar@209
|
1172 |
classes[id].depth -= 1;
|
alpar@209
|
1173 |
nodes[kd].parent = ~id;
|
alpar@209
|
1174 |
deleteNode(jd);
|
alpar@209
|
1175 |
jd = kd;
|
alpar@209
|
1176 |
} else {
|
alpar@209
|
1177 |
int pd = nodes[jd].parent;
|
alpar@209
|
1178 |
if (nodes[nodes[jd].next].size < cmax) {
|
alpar@209
|
1179 |
pushLeft(nodes[jd].next, nodes[jd].left);
|
deba@353
|
1180 |
if (less(jd, nodes[jd].next) ||
|
deba@353
|
1181 |
nodes[jd].item == nodes[pd].item) {
|
deba@351
|
1182 |
nodes[nodes[jd].next].prio = nodes[jd].prio;
|
deba@351
|
1183 |
nodes[nodes[jd].next].item = nodes[jd].item;
|
alpar@209
|
1184 |
}
|
alpar@209
|
1185 |
popLeft(pd);
|
alpar@209
|
1186 |
deleteNode(jd);
|
alpar@209
|
1187 |
jd = pd;
|
alpar@209
|
1188 |
} else {
|
alpar@209
|
1189 |
int ld = nodes[nodes[jd].next].left;
|
alpar@209
|
1190 |
popLeft(nodes[jd].next);
|
alpar@209
|
1191 |
pushRight(jd, ld);
|
deba@351
|
1192 |
if (less(ld, nodes[jd].left) ||
|
deba@351
|
1193 |
nodes[ld].item == nodes[pd].item) {
|
alpar@209
|
1194 |
nodes[jd].item = nodes[ld].item;
|
deba@351
|
1195 |
nodes[jd].prio = nodes[ld].prio;
|
alpar@209
|
1196 |
}
|
alpar@209
|
1197 |
if (nodes[nodes[jd].next].item == nodes[ld].item) {
|
alpar@209
|
1198 |
setPrio(nodes[jd].next);
|
alpar@209
|
1199 |
}
|
alpar@209
|
1200 |
jd = nodes[jd].left;
|
alpar@209
|
1201 |
}
|
alpar@209
|
1202 |
}
|
alpar@209
|
1203 |
} else {
|
alpar@209
|
1204 |
jd = nodes[jd].left;
|
alpar@209
|
1205 |
}
|
alpar@103
|
1206 |
}
|
alpar@209
|
1207 |
}
|
alpar@103
|
1208 |
|
alpar@103
|
1209 |
void repairRight(int id) {
|
alpar@103
|
1210 |
int jd = ~(classes[id].parent);
|
alpar@103
|
1211 |
while (nodes[jd].right != -1) {
|
alpar@209
|
1212 |
int kd = nodes[jd].right;
|
alpar@209
|
1213 |
if (nodes[jd].size == 1) {
|
alpar@209
|
1214 |
if (nodes[jd].parent < 0) {
|
alpar@209
|
1215 |
classes[id].parent = ~kd;
|
alpar@209
|
1216 |
classes[id].depth -= 1;
|
alpar@209
|
1217 |
nodes[kd].parent = ~id;
|
alpar@209
|
1218 |
deleteNode(jd);
|
alpar@209
|
1219 |
jd = kd;
|
alpar@209
|
1220 |
} else {
|
alpar@209
|
1221 |
int pd = nodes[jd].parent;
|
alpar@209
|
1222 |
if (nodes[nodes[jd].prev].size < cmax) {
|
alpar@209
|
1223 |
pushRight(nodes[jd].prev, nodes[jd].right);
|
deba@353
|
1224 |
if (less(jd, nodes[jd].prev) ||
|
deba@353
|
1225 |
nodes[jd].item == nodes[pd].item) {
|
deba@351
|
1226 |
nodes[nodes[jd].prev].prio = nodes[jd].prio;
|
deba@351
|
1227 |
nodes[nodes[jd].prev].item = nodes[jd].item;
|
alpar@209
|
1228 |
}
|
alpar@209
|
1229 |
popRight(pd);
|
alpar@209
|
1230 |
deleteNode(jd);
|
alpar@209
|
1231 |
jd = pd;
|
alpar@209
|
1232 |
} else {
|
alpar@209
|
1233 |
int ld = nodes[nodes[jd].prev].right;
|
alpar@209
|
1234 |
popRight(nodes[jd].prev);
|
alpar@209
|
1235 |
pushLeft(jd, ld);
|
deba@351
|
1236 |
if (less(ld, nodes[jd].right) ||
|
deba@351
|
1237 |
nodes[ld].item == nodes[pd].item) {
|
alpar@209
|
1238 |
nodes[jd].item = nodes[ld].item;
|
deba@351
|
1239 |
nodes[jd].prio = nodes[ld].prio;
|
alpar@209
|
1240 |
}
|
alpar@209
|
1241 |
if (nodes[nodes[jd].prev].item == nodes[ld].item) {
|
alpar@209
|
1242 |
setPrio(nodes[jd].prev);
|
alpar@209
|
1243 |
}
|
alpar@209
|
1244 |
jd = nodes[jd].right;
|
alpar@209
|
1245 |
}
|
alpar@209
|
1246 |
}
|
alpar@209
|
1247 |
} else {
|
alpar@209
|
1248 |
jd = nodes[jd].right;
|
alpar@209
|
1249 |
}
|
alpar@103
|
1250 |
}
|
alpar@103
|
1251 |
}
|
alpar@103
|
1252 |
|
alpar@103
|
1253 |
|
alpar@103
|
1254 |
bool less(int id, int jd) const {
|
alpar@103
|
1255 |
return comp(nodes[id].prio, nodes[jd].prio);
|
alpar@103
|
1256 |
}
|
alpar@103
|
1257 |
|
alpar@103
|
1258 |
public:
|
alpar@103
|
1259 |
|
alpar@103
|
1260 |
/// \brief Returns true when the given class is alive.
|
alpar@103
|
1261 |
///
|
alpar@103
|
1262 |
/// Returns true when the given class is alive, ie. the class is
|
alpar@103
|
1263 |
/// not nested into other class.
|
alpar@103
|
1264 |
bool alive(int cls) const {
|
alpar@103
|
1265 |
return classes[cls].parent < 0;
|
alpar@103
|
1266 |
}
|
alpar@103
|
1267 |
|
alpar@103
|
1268 |
/// \brief Returns true when the given class is trivial.
|
alpar@103
|
1269 |
///
|
alpar@103
|
1270 |
/// Returns true when the given class is trivial, ie. the class
|
alpar@103
|
1271 |
/// contains just one item directly.
|
alpar@103
|
1272 |
bool trivial(int cls) const {
|
alpar@103
|
1273 |
return classes[cls].left == -1;
|
alpar@103
|
1274 |
}
|
alpar@103
|
1275 |
|
alpar@103
|
1276 |
/// \brief Constructs the union-find.
|
alpar@103
|
1277 |
///
|
alpar@209
|
1278 |
/// Constructs the union-find.
|
alpar@103
|
1279 |
/// \brief _index The index map of the union-find. The data
|
alpar@103
|
1280 |
/// structure uses internally for store references.
|
alpar@209
|
1281 |
HeapUnionFind(ItemIntMap& _index)
|
alpar@209
|
1282 |
: index(_index), first_class(-1),
|
alpar@209
|
1283 |
first_free_class(-1), first_free_node(-1) {}
|
alpar@103
|
1284 |
|
alpar@103
|
1285 |
/// \brief Insert a new node into a new component.
|
alpar@103
|
1286 |
///
|
alpar@103
|
1287 |
/// Insert a new node into a new component.
|
alpar@103
|
1288 |
/// \param item The item of the new node.
|
alpar@103
|
1289 |
/// \param prio The priority of the new node.
|
alpar@103
|
1290 |
/// \return The class id of the one-item-heap.
|
alpar@103
|
1291 |
int insert(const Item& item, const Value& prio) {
|
alpar@103
|
1292 |
int id = newNode();
|
alpar@103
|
1293 |
nodes[id].item = item;
|
alpar@103
|
1294 |
nodes[id].prio = prio;
|
alpar@103
|
1295 |
nodes[id].size = 0;
|
alpar@103
|
1296 |
|
alpar@103
|
1297 |
nodes[id].prev = -1;
|
alpar@103
|
1298 |
nodes[id].next = -1;
|
alpar@103
|
1299 |
|
alpar@103
|
1300 |
nodes[id].left = -1;
|
alpar@103
|
1301 |
nodes[id].right = -1;
|
alpar@103
|
1302 |
|
alpar@103
|
1303 |
nodes[id].item = item;
|
alpar@103
|
1304 |
index[item] = id;
|
alpar@209
|
1305 |
|
alpar@103
|
1306 |
int class_id = newClass();
|
alpar@103
|
1307 |
classes[class_id].parent = ~id;
|
alpar@103
|
1308 |
classes[class_id].depth = 0;
|
alpar@103
|
1309 |
|
alpar@103
|
1310 |
classes[class_id].left = -1;
|
alpar@103
|
1311 |
classes[class_id].right = -1;
|
alpar@209
|
1312 |
|
alpar@103
|
1313 |
if (first_class != -1) {
|
alpar@103
|
1314 |
classes[first_class].prev = class_id;
|
alpar@103
|
1315 |
}
|
alpar@103
|
1316 |
classes[class_id].next = first_class;
|
alpar@103
|
1317 |
classes[class_id].prev = -1;
|
alpar@103
|
1318 |
first_class = class_id;
|
alpar@103
|
1319 |
|
alpar@103
|
1320 |
nodes[id].parent = ~class_id;
|
alpar@209
|
1321 |
|
alpar@103
|
1322 |
return class_id;
|
alpar@103
|
1323 |
}
|
alpar@103
|
1324 |
|
alpar@103
|
1325 |
/// \brief The class of the item.
|
alpar@103
|
1326 |
///
|
alpar@103
|
1327 |
/// \return The alive class id of the item, which is not nested into
|
alpar@103
|
1328 |
/// other classes.
|
alpar@103
|
1329 |
///
|
alpar@103
|
1330 |
/// The time complexity is O(log(n)).
|
alpar@103
|
1331 |
int find(const Item& item) const {
|
alpar@103
|
1332 |
return findClass(index[item]);
|
alpar@103
|
1333 |
}
|
alpar@209
|
1334 |
|
alpar@103
|
1335 |
/// \brief Joins the classes.
|
alpar@103
|
1336 |
///
|
alpar@103
|
1337 |
/// The current function joins the given classes. The parameter is
|
alpar@103
|
1338 |
/// an STL range which should be contains valid class ids. The
|
alpar@103
|
1339 |
/// time complexity is O(log(n)*k) where n is the overall number
|
alpar@103
|
1340 |
/// of the joined nodes and k is the number of classes.
|
alpar@103
|
1341 |
/// \return The class of the joined classes.
|
alpar@103
|
1342 |
/// \pre The range should contain at least two class ids.
|
alpar@103
|
1343 |
template <typename Iterator>
|
alpar@103
|
1344 |
int join(Iterator begin, Iterator end) {
|
alpar@103
|
1345 |
std::vector<int> cs;
|
alpar@103
|
1346 |
for (Iterator it = begin; it != end; ++it) {
|
alpar@103
|
1347 |
cs.push_back(*it);
|
alpar@103
|
1348 |
}
|
alpar@103
|
1349 |
|
alpar@103
|
1350 |
int class_id = newClass();
|
alpar@103
|
1351 |
{ // creation union-find
|
alpar@103
|
1352 |
|
alpar@103
|
1353 |
if (first_class != -1) {
|
alpar@103
|
1354 |
classes[first_class].prev = class_id;
|
alpar@103
|
1355 |
}
|
alpar@103
|
1356 |
classes[class_id].next = first_class;
|
alpar@103
|
1357 |
classes[class_id].prev = -1;
|
alpar@103
|
1358 |
first_class = class_id;
|
alpar@103
|
1359 |
|
alpar@103
|
1360 |
classes[class_id].depth = classes[cs[0]].depth;
|
alpar@103
|
1361 |
classes[class_id].parent = classes[cs[0]].parent;
|
alpar@103
|
1362 |
nodes[~(classes[class_id].parent)].parent = ~class_id;
|
alpar@103
|
1363 |
|
alpar@103
|
1364 |
int l = cs[0];
|
alpar@103
|
1365 |
|
alpar@103
|
1366 |
classes[class_id].left = l;
|
alpar@103
|
1367 |
classes[class_id].right = l;
|
alpar@103
|
1368 |
|
alpar@103
|
1369 |
if (classes[l].next != -1) {
|
alpar@103
|
1370 |
classes[classes[l].next].prev = classes[l].prev;
|
alpar@103
|
1371 |
}
|
alpar@103
|
1372 |
classes[classes[l].prev].next = classes[l].next;
|
alpar@209
|
1373 |
|
alpar@103
|
1374 |
classes[l].prev = -1;
|
alpar@103
|
1375 |
classes[l].next = -1;
|
alpar@103
|
1376 |
|
alpar@103
|
1377 |
classes[l].depth = leftNode(l);
|
alpar@103
|
1378 |
classes[l].parent = class_id;
|
alpar@209
|
1379 |
|
alpar@103
|
1380 |
}
|
alpar@103
|
1381 |
|
alpar@103
|
1382 |
{ // merging of heap
|
alpar@103
|
1383 |
int l = class_id;
|
alpar@103
|
1384 |
for (int ci = 1; ci < int(cs.size()); ++ci) {
|
alpar@103
|
1385 |
int r = cs[ci];
|
alpar@103
|
1386 |
int rln = leftNode(r);
|
alpar@103
|
1387 |
if (classes[l].depth > classes[r].depth) {
|
alpar@103
|
1388 |
int id = ~(classes[l].parent);
|
alpar@103
|
1389 |
for (int i = classes[r].depth + 1; i < classes[l].depth; ++i) {
|
alpar@103
|
1390 |
id = nodes[id].right;
|
alpar@103
|
1391 |
}
|
alpar@103
|
1392 |
while (id >= 0 && nodes[id].size == cmax) {
|
alpar@103
|
1393 |
int new_id = newNode();
|
alpar@103
|
1394 |
int right_id = nodes[id].right;
|
alpar@103
|
1395 |
|
alpar@103
|
1396 |
popRight(id);
|
alpar@103
|
1397 |
if (nodes[id].item == nodes[right_id].item) {
|
alpar@103
|
1398 |
setPrio(id);
|
alpar@103
|
1399 |
}
|
alpar@103
|
1400 |
push(new_id, right_id);
|
alpar@103
|
1401 |
pushRight(new_id, ~(classes[r].parent));
|
deba@351
|
1402 |
|
deba@351
|
1403 |
if (less(~classes[r].parent, right_id)) {
|
deba@351
|
1404 |
nodes[new_id].item = nodes[~classes[r].parent].item;
|
deba@351
|
1405 |
nodes[new_id].prio = nodes[~classes[r].parent].prio;
|
deba@351
|
1406 |
} else {
|
deba@351
|
1407 |
nodes[new_id].item = nodes[right_id].item;
|
deba@351
|
1408 |
nodes[new_id].prio = nodes[right_id].prio;
|
deba@351
|
1409 |
}
|
alpar@103
|
1410 |
|
alpar@103
|
1411 |
id = nodes[id].parent;
|
alpar@103
|
1412 |
classes[r].parent = ~new_id;
|
alpar@103
|
1413 |
}
|
alpar@103
|
1414 |
if (id < 0) {
|
alpar@103
|
1415 |
int new_parent = newNode();
|
alpar@103
|
1416 |
nodes[new_parent].next = -1;
|
alpar@103
|
1417 |
nodes[new_parent].prev = -1;
|
alpar@103
|
1418 |
nodes[new_parent].parent = ~l;
|
alpar@103
|
1419 |
|
alpar@103
|
1420 |
push(new_parent, ~(classes[l].parent));
|
alpar@103
|
1421 |
pushRight(new_parent, ~(classes[r].parent));
|
alpar@103
|
1422 |
setPrio(new_parent);
|
alpar@103
|
1423 |
|
alpar@103
|
1424 |
classes[l].parent = ~new_parent;
|
alpar@103
|
1425 |
classes[l].depth += 1;
|
alpar@103
|
1426 |
} else {
|
alpar@103
|
1427 |
pushRight(id, ~(classes[r].parent));
|
alpar@103
|
1428 |
while (id >= 0 && less(~(classes[r].parent), id)) {
|
alpar@103
|
1429 |
nodes[id].prio = nodes[~(classes[r].parent)].prio;
|
alpar@103
|
1430 |
nodes[id].item = nodes[~(classes[r].parent)].item;
|
alpar@103
|
1431 |
id = nodes[id].parent;
|
alpar@103
|
1432 |
}
|
alpar@103
|
1433 |
}
|
alpar@103
|
1434 |
} else if (classes[r].depth > classes[l].depth) {
|
alpar@103
|
1435 |
int id = ~(classes[r].parent);
|
alpar@103
|
1436 |
for (int i = classes[l].depth + 1; i < classes[r].depth; ++i) {
|
alpar@103
|
1437 |
id = nodes[id].left;
|
alpar@103
|
1438 |
}
|
alpar@103
|
1439 |
while (id >= 0 && nodes[id].size == cmax) {
|
alpar@103
|
1440 |
int new_id = newNode();
|
alpar@103
|
1441 |
int left_id = nodes[id].left;
|
alpar@103
|
1442 |
|
alpar@103
|
1443 |
popLeft(id);
|
alpar@103
|
1444 |
if (nodes[id].prio == nodes[left_id].prio) {
|
alpar@103
|
1445 |
setPrio(id);
|
alpar@103
|
1446 |
}
|
alpar@103
|
1447 |
push(new_id, left_id);
|
alpar@103
|
1448 |
pushLeft(new_id, ~(classes[l].parent));
|
deba@351
|
1449 |
|
deba@351
|
1450 |
if (less(~classes[l].parent, left_id)) {
|
deba@351
|
1451 |
nodes[new_id].item = nodes[~classes[l].parent].item;
|
deba@351
|
1452 |
nodes[new_id].prio = nodes[~classes[l].parent].prio;
|
deba@351
|
1453 |
} else {
|
deba@351
|
1454 |
nodes[new_id].item = nodes[left_id].item;
|
deba@351
|
1455 |
nodes[new_id].prio = nodes[left_id].prio;
|
deba@351
|
1456 |
}
|
alpar@103
|
1457 |
|
alpar@103
|
1458 |
id = nodes[id].parent;
|
alpar@103
|
1459 |
classes[l].parent = ~new_id;
|
alpar@103
|
1460 |
|
alpar@103
|
1461 |
}
|
alpar@103
|
1462 |
if (id < 0) {
|
alpar@103
|
1463 |
int new_parent = newNode();
|
alpar@103
|
1464 |
nodes[new_parent].next = -1;
|
alpar@103
|
1465 |
nodes[new_parent].prev = -1;
|
alpar@103
|
1466 |
nodes[new_parent].parent = ~l;
|
alpar@103
|
1467 |
|
alpar@103
|
1468 |
push(new_parent, ~(classes[r].parent));
|
alpar@103
|
1469 |
pushLeft(new_parent, ~(classes[l].parent));
|
alpar@103
|
1470 |
setPrio(new_parent);
|
alpar@209
|
1471 |
|
alpar@103
|
1472 |
classes[r].parent = ~new_parent;
|
alpar@103
|
1473 |
classes[r].depth += 1;
|
alpar@103
|
1474 |
} else {
|
alpar@103
|
1475 |
pushLeft(id, ~(classes[l].parent));
|
alpar@103
|
1476 |
while (id >= 0 && less(~(classes[l].parent), id)) {
|
alpar@103
|
1477 |
nodes[id].prio = nodes[~(classes[l].parent)].prio;
|
alpar@103
|
1478 |
nodes[id].item = nodes[~(classes[l].parent)].item;
|
alpar@103
|
1479 |
id = nodes[id].parent;
|
alpar@103
|
1480 |
}
|
alpar@103
|
1481 |
}
|
alpar@103
|
1482 |
nodes[~(classes[r].parent)].parent = ~l;
|
alpar@103
|
1483 |
classes[l].parent = classes[r].parent;
|
alpar@103
|
1484 |
classes[l].depth = classes[r].depth;
|
alpar@103
|
1485 |
} else {
|
alpar@209
|
1486 |
if (classes[l].depth != 0 &&
|
alpar@209
|
1487 |
nodes[~(classes[l].parent)].size +
|
alpar@103
|
1488 |
nodes[~(classes[r].parent)].size <= cmax) {
|
alpar@103
|
1489 |
splice(~(classes[l].parent), ~(classes[r].parent));
|
alpar@103
|
1490 |
deleteNode(~(classes[r].parent));
|
alpar@103
|
1491 |
if (less(~(classes[r].parent), ~(classes[l].parent))) {
|
alpar@209
|
1492 |
nodes[~(classes[l].parent)].prio =
|
alpar@103
|
1493 |
nodes[~(classes[r].parent)].prio;
|
alpar@209
|
1494 |
nodes[~(classes[l].parent)].item =
|
alpar@103
|
1495 |
nodes[~(classes[r].parent)].item;
|
alpar@103
|
1496 |
}
|
alpar@103
|
1497 |
} else {
|
alpar@103
|
1498 |
int new_parent = newNode();
|
alpar@103
|
1499 |
nodes[new_parent].next = nodes[new_parent].prev = -1;
|
alpar@103
|
1500 |
push(new_parent, ~(classes[l].parent));
|
alpar@103
|
1501 |
pushRight(new_parent, ~(classes[r].parent));
|
alpar@103
|
1502 |
setPrio(new_parent);
|
alpar@209
|
1503 |
|
alpar@103
|
1504 |
classes[l].parent = ~new_parent;
|
alpar@103
|
1505 |
classes[l].depth += 1;
|
alpar@103
|
1506 |
nodes[new_parent].parent = ~l;
|
alpar@103
|
1507 |
}
|
alpar@103
|
1508 |
}
|
alpar@103
|
1509 |
if (classes[r].next != -1) {
|
alpar@103
|
1510 |
classes[classes[r].next].prev = classes[r].prev;
|
alpar@103
|
1511 |
}
|
alpar@103
|
1512 |
classes[classes[r].prev].next = classes[r].next;
|
alpar@103
|
1513 |
|
alpar@103
|
1514 |
classes[r].prev = classes[l].right;
|
alpar@103
|
1515 |
classes[classes[l].right].next = r;
|
alpar@103
|
1516 |
classes[l].right = r;
|
alpar@103
|
1517 |
classes[r].parent = l;
|
alpar@103
|
1518 |
|
alpar@103
|
1519 |
classes[r].next = -1;
|
alpar@103
|
1520 |
classes[r].depth = rln;
|
alpar@103
|
1521 |
}
|
alpar@103
|
1522 |
}
|
alpar@103
|
1523 |
return class_id;
|
alpar@103
|
1524 |
}
|
alpar@103
|
1525 |
|
alpar@103
|
1526 |
/// \brief Split the class to subclasses.
|
alpar@103
|
1527 |
///
|
alpar@103
|
1528 |
/// The current function splits the given class. The join, which
|
alpar@103
|
1529 |
/// made the current class, stored a reference to the
|
alpar@103
|
1530 |
/// subclasses. The \c splitClass() member restores the classes
|
alpar@103
|
1531 |
/// and creates the heaps. The parameter is an STL output iterator
|
alpar@103
|
1532 |
/// which will be filled with the subclass ids. The time
|
alpar@103
|
1533 |
/// complexity is O(log(n)*k) where n is the overall number of
|
alpar@103
|
1534 |
/// nodes in the splitted classes and k is the number of the
|
alpar@103
|
1535 |
/// classes.
|
alpar@103
|
1536 |
template <typename Iterator>
|
alpar@103
|
1537 |
void split(int cls, Iterator out) {
|
alpar@103
|
1538 |
std::vector<int> cs;
|
alpar@103
|
1539 |
{ // splitting union-find
|
alpar@103
|
1540 |
int id = cls;
|
alpar@103
|
1541 |
int l = classes[id].left;
|
alpar@103
|
1542 |
|
alpar@103
|
1543 |
classes[l].parent = classes[id].parent;
|
alpar@103
|
1544 |
classes[l].depth = classes[id].depth;
|
alpar@103
|
1545 |
|
alpar@103
|
1546 |
nodes[~(classes[l].parent)].parent = ~l;
|
alpar@103
|
1547 |
|
alpar@103
|
1548 |
*out++ = l;
|
alpar@103
|
1549 |
|
alpar@103
|
1550 |
while (l != -1) {
|
alpar@103
|
1551 |
cs.push_back(l);
|
alpar@103
|
1552 |
l = classes[l].next;
|
alpar@103
|
1553 |
}
|
alpar@103
|
1554 |
|
alpar@103
|
1555 |
classes[classes[id].right].next = first_class;
|
alpar@103
|
1556 |
classes[first_class].prev = classes[id].right;
|
alpar@103
|
1557 |
first_class = classes[id].left;
|
alpar@209
|
1558 |
|
alpar@103
|
1559 |
if (classes[id].next != -1) {
|
alpar@103
|
1560 |
classes[classes[id].next].prev = classes[id].prev;
|
alpar@103
|
1561 |
}
|
alpar@103
|
1562 |
classes[classes[id].prev].next = classes[id].next;
|
alpar@209
|
1563 |
|
alpar@103
|
1564 |
deleteClass(id);
|
alpar@103
|
1565 |
}
|
alpar@103
|
1566 |
|
alpar@103
|
1567 |
{
|
alpar@103
|
1568 |
for (int i = 1; i < int(cs.size()); ++i) {
|
alpar@103
|
1569 |
int l = classes[cs[i]].depth;
|
alpar@103
|
1570 |
while (nodes[nodes[l].parent].left == l) {
|
alpar@103
|
1571 |
l = nodes[l].parent;
|
alpar@103
|
1572 |
}
|
alpar@209
|
1573 |
int r = l;
|
alpar@103
|
1574 |
while (nodes[l].parent >= 0) {
|
alpar@103
|
1575 |
l = nodes[l].parent;
|
alpar@103
|
1576 |
int new_node = newNode();
|
alpar@103
|
1577 |
|
alpar@103
|
1578 |
nodes[new_node].prev = -1;
|
alpar@103
|
1579 |
nodes[new_node].next = -1;
|
alpar@103
|
1580 |
|
alpar@103
|
1581 |
split(r, new_node);
|
alpar@103
|
1582 |
pushAfter(l, new_node);
|
alpar@103
|
1583 |
setPrio(l);
|
alpar@103
|
1584 |
setPrio(new_node);
|
alpar@103
|
1585 |
r = new_node;
|
alpar@103
|
1586 |
}
|
alpar@103
|
1587 |
classes[cs[i]].parent = ~r;
|
alpar@103
|
1588 |
classes[cs[i]].depth = classes[~(nodes[l].parent)].depth;
|
alpar@103
|
1589 |
nodes[r].parent = ~cs[i];
|
alpar@103
|
1590 |
|
alpar@103
|
1591 |
nodes[l].next = -1;
|
alpar@103
|
1592 |
nodes[r].prev = -1;
|
alpar@103
|
1593 |
|
alpar@103
|
1594 |
repairRight(~(nodes[l].parent));
|
alpar@103
|
1595 |
repairLeft(cs[i]);
|
alpar@209
|
1596 |
|
alpar@103
|
1597 |
*out++ = cs[i];
|
alpar@103
|
1598 |
}
|
alpar@103
|
1599 |
}
|
alpar@103
|
1600 |
}
|
alpar@103
|
1601 |
|
alpar@103
|
1602 |
/// \brief Gives back the priority of the current item.
|
alpar@103
|
1603 |
///
|
alpar@103
|
1604 |
/// \return Gives back the priority of the current item.
|
alpar@103
|
1605 |
const Value& operator[](const Item& item) const {
|
alpar@103
|
1606 |
return nodes[index[item]].prio;
|
alpar@103
|
1607 |
}
|
alpar@103
|
1608 |
|
alpar@103
|
1609 |
/// \brief Sets the priority of the current item.
|
alpar@103
|
1610 |
///
|
alpar@103
|
1611 |
/// Sets the priority of the current item.
|
alpar@103
|
1612 |
void set(const Item& item, const Value& prio) {
|
alpar@103
|
1613 |
if (comp(prio, nodes[index[item]].prio)) {
|
alpar@103
|
1614 |
decrease(item, prio);
|
alpar@103
|
1615 |
} else if (!comp(prio, nodes[index[item]].prio)) {
|
alpar@103
|
1616 |
increase(item, prio);
|
alpar@103
|
1617 |
}
|
alpar@103
|
1618 |
}
|
alpar@209
|
1619 |
|
alpar@103
|
1620 |
/// \brief Increase the priority of the current item.
|
alpar@103
|
1621 |
///
|
alpar@103
|
1622 |
/// Increase the priority of the current item.
|
alpar@103
|
1623 |
void increase(const Item& item, const Value& prio) {
|
alpar@103
|
1624 |
int id = index[item];
|
alpar@103
|
1625 |
int kd = nodes[id].parent;
|
alpar@103
|
1626 |
nodes[id].prio = prio;
|
alpar@103
|
1627 |
while (kd >= 0 && nodes[kd].item == item) {
|
alpar@103
|
1628 |
setPrio(kd);
|
alpar@103
|
1629 |
kd = nodes[kd].parent;
|
alpar@103
|
1630 |
}
|
alpar@103
|
1631 |
}
|
alpar@103
|
1632 |
|
alpar@103
|
1633 |
/// \brief Increase the priority of the current item.
|
alpar@103
|
1634 |
///
|
alpar@103
|
1635 |
/// Increase the priority of the current item.
|
alpar@103
|
1636 |
void decrease(const Item& item, const Value& prio) {
|
alpar@103
|
1637 |
int id = index[item];
|
alpar@103
|
1638 |
int kd = nodes[id].parent;
|
alpar@103
|
1639 |
nodes[id].prio = prio;
|
alpar@103
|
1640 |
while (kd >= 0 && less(id, kd)) {
|
alpar@103
|
1641 |
nodes[kd].prio = prio;
|
alpar@103
|
1642 |
nodes[kd].item = item;
|
alpar@103
|
1643 |
kd = nodes[kd].parent;
|
alpar@103
|
1644 |
}
|
alpar@103
|
1645 |
}
|
alpar@209
|
1646 |
|
alpar@103
|
1647 |
/// \brief Gives back the minimum priority of the class.
|
alpar@103
|
1648 |
///
|
alpar@103
|
1649 |
/// \return Gives back the minimum priority of the class.
|
alpar@103
|
1650 |
const Value& classPrio(int cls) const {
|
alpar@103
|
1651 |
return nodes[~(classes[cls].parent)].prio;
|
alpar@103
|
1652 |
}
|
alpar@103
|
1653 |
|
alpar@103
|
1654 |
/// \brief Gives back the minimum priority item of the class.
|
alpar@103
|
1655 |
///
|
alpar@103
|
1656 |
/// \return Gives back the minimum priority item of the class.
|
alpar@103
|
1657 |
const Item& classTop(int cls) const {
|
alpar@103
|
1658 |
return nodes[~(classes[cls].parent)].item;
|
alpar@103
|
1659 |
}
|
alpar@103
|
1660 |
|
alpar@103
|
1661 |
/// \brief Gives back a representant item of the class.
|
alpar@209
|
1662 |
///
|
alpar@103
|
1663 |
/// The representant is indpendent from the priorities of the
|
alpar@209
|
1664 |
/// items.
|
alpar@103
|
1665 |
/// \return Gives back a representant item of the class.
|
alpar@103
|
1666 |
const Item& classRep(int id) const {
|
alpar@103
|
1667 |
int parent = classes[id].parent;
|
alpar@103
|
1668 |
return nodes[parent >= 0 ? classes[id].depth : leftNode(id)].item;
|
alpar@103
|
1669 |
}
|
alpar@103
|
1670 |
|
ladanyi@236
|
1671 |
/// \brief LEMON style iterator for the items of a class.
|
alpar@103
|
1672 |
///
|
alpar@103
|
1673 |
/// ClassIt is a lemon style iterator for the components. It iterates
|
alpar@103
|
1674 |
/// on the items of a class. By example if you want to iterate on
|
alpar@103
|
1675 |
/// each items of each classes then you may write the next code.
|
alpar@103
|
1676 |
///\code
|
alpar@103
|
1677 |
/// for (ClassIt cit(huf); cit != INVALID; ++cit) {
|
alpar@103
|
1678 |
/// std::cout << "Class: ";
|
alpar@103
|
1679 |
/// for (ItemIt iit(huf, cit); iit != INVALID; ++iit) {
|
alpar@103
|
1680 |
/// std::cout << toString(iit) << ' ' << std::endl;
|
alpar@103
|
1681 |
/// }
|
alpar@103
|
1682 |
/// std::cout << std::endl;
|
alpar@103
|
1683 |
/// }
|
alpar@103
|
1684 |
///\endcode
|
alpar@103
|
1685 |
class ItemIt {
|
alpar@103
|
1686 |
private:
|
alpar@103
|
1687 |
|
alpar@103
|
1688 |
const HeapUnionFind* _huf;
|
alpar@103
|
1689 |
int _id, _lid;
|
alpar@209
|
1690 |
|
alpar@103
|
1691 |
public:
|
alpar@103
|
1692 |
|
alpar@209
|
1693 |
/// \brief Default constructor
|
alpar@103
|
1694 |
///
|
alpar@209
|
1695 |
/// Default constructor
|
alpar@103
|
1696 |
ItemIt() {}
|
alpar@103
|
1697 |
|
alpar@103
|
1698 |
ItemIt(const HeapUnionFind& huf, int cls) : _huf(&huf) {
|
alpar@103
|
1699 |
int id = cls;
|
alpar@103
|
1700 |
int parent = _huf->classes[id].parent;
|
alpar@103
|
1701 |
if (parent >= 0) {
|
alpar@103
|
1702 |
_id = _huf->classes[id].depth;
|
alpar@103
|
1703 |
if (_huf->classes[id].next != -1) {
|
alpar@103
|
1704 |
_lid = _huf->classes[_huf->classes[id].next].depth;
|
alpar@103
|
1705 |
} else {
|
alpar@103
|
1706 |
_lid = -1;
|
alpar@103
|
1707 |
}
|
alpar@103
|
1708 |
} else {
|
alpar@103
|
1709 |
_id = _huf->leftNode(id);
|
alpar@103
|
1710 |
_lid = -1;
|
alpar@209
|
1711 |
}
|
alpar@103
|
1712 |
}
|
alpar@209
|
1713 |
|
alpar@103
|
1714 |
/// \brief Increment operator
|
alpar@103
|
1715 |
///
|
alpar@103
|
1716 |
/// It steps to the next item in the class.
|
alpar@103
|
1717 |
ItemIt& operator++() {
|
alpar@103
|
1718 |
_id = _huf->nextNode(_id);
|
alpar@103
|
1719 |
return *this;
|
alpar@103
|
1720 |
}
|
alpar@103
|
1721 |
|
alpar@103
|
1722 |
/// \brief Conversion operator
|
alpar@103
|
1723 |
///
|
alpar@103
|
1724 |
/// It converts the iterator to the current item.
|
alpar@103
|
1725 |
operator const Item&() const {
|
alpar@103
|
1726 |
return _huf->nodes[_id].item;
|
alpar@103
|
1727 |
}
|
alpar@209
|
1728 |
|
alpar@103
|
1729 |
/// \brief Equality operator
|
alpar@103
|
1730 |
///
|
alpar@103
|
1731 |
/// Equality operator
|
alpar@209
|
1732 |
bool operator==(const ItemIt& i) {
|
alpar@103
|
1733 |
return i._id == _id;
|
alpar@103
|
1734 |
}
|
alpar@103
|
1735 |
|
alpar@103
|
1736 |
/// \brief Inequality operator
|
alpar@103
|
1737 |
///
|
alpar@103
|
1738 |
/// Inequality operator
|
alpar@209
|
1739 |
bool operator!=(const ItemIt& i) {
|
alpar@103
|
1740 |
return i._id != _id;
|
alpar@103
|
1741 |
}
|
alpar@103
|
1742 |
|
alpar@103
|
1743 |
/// \brief Equality operator
|
alpar@103
|
1744 |
///
|
alpar@103
|
1745 |
/// Equality operator
|
alpar@209
|
1746 |
bool operator==(Invalid) {
|
alpar@103
|
1747 |
return _id == _lid;
|
alpar@103
|
1748 |
}
|
alpar@103
|
1749 |
|
alpar@103
|
1750 |
/// \brief Inequality operator
|
alpar@103
|
1751 |
///
|
alpar@103
|
1752 |
/// Inequality operator
|
alpar@209
|
1753 |
bool operator!=(Invalid) {
|
alpar@103
|
1754 |
return _id != _lid;
|
alpar@103
|
1755 |
}
|
alpar@209
|
1756 |
|
alpar@103
|
1757 |
};
|
alpar@103
|
1758 |
|
alpar@103
|
1759 |
/// \brief Class iterator
|
alpar@103
|
1760 |
///
|
alpar@209
|
1761 |
/// The iterator stores
|
alpar@103
|
1762 |
class ClassIt {
|
alpar@103
|
1763 |
private:
|
alpar@103
|
1764 |
|
alpar@103
|
1765 |
const HeapUnionFind* _huf;
|
alpar@103
|
1766 |
int _id;
|
alpar@103
|
1767 |
|
alpar@103
|
1768 |
public:
|
alpar@103
|
1769 |
|
alpar@209
|
1770 |
ClassIt(const HeapUnionFind& huf)
|
alpar@103
|
1771 |
: _huf(&huf), _id(huf.first_class) {}
|
alpar@103
|
1772 |
|
alpar@209
|
1773 |
ClassIt(const HeapUnionFind& huf, int cls)
|
alpar@103
|
1774 |
: _huf(&huf), _id(huf.classes[cls].left) {}
|
alpar@103
|
1775 |
|
alpar@103
|
1776 |
ClassIt(Invalid) : _huf(0), _id(-1) {}
|
alpar@209
|
1777 |
|
alpar@103
|
1778 |
const ClassIt& operator++() {
|
alpar@103
|
1779 |
_id = _huf->classes[_id].next;
|
alpar@209
|
1780 |
return *this;
|
alpar@103
|
1781 |
}
|
alpar@103
|
1782 |
|
alpar@103
|
1783 |
/// \brief Equality operator
|
alpar@103
|
1784 |
///
|
alpar@103
|
1785 |
/// Equality operator
|
alpar@209
|
1786 |
bool operator==(const ClassIt& i) {
|
alpar@103
|
1787 |
return i._id == _id;
|
alpar@103
|
1788 |
}
|
alpar@103
|
1789 |
|
alpar@103
|
1790 |
/// \brief Inequality operator
|
alpar@103
|
1791 |
///
|
alpar@103
|
1792 |
/// Inequality operator
|
alpar@209
|
1793 |
bool operator!=(const ClassIt& i) {
|
alpar@103
|
1794 |
return i._id != _id;
|
alpar@209
|
1795 |
}
|
alpar@209
|
1796 |
|
alpar@103
|
1797 |
operator int() const {
|
alpar@209
|
1798 |
return _id;
|
alpar@103
|
1799 |
}
|
alpar@209
|
1800 |
|
alpar@103
|
1801 |
};
|
alpar@103
|
1802 |
|
alpar@103
|
1803 |
};
|
alpar@103
|
1804 |
|
alpar@103
|
1805 |
//! @}
|
alpar@103
|
1806 |
|
alpar@103
|
1807 |
} //namespace lemon
|
alpar@103
|
1808 |
|
alpar@103
|
1809 |
#endif //LEMON_UNION_FIND_H
|