alpar@906: /* -*- C++ -*-
alpar@906: *
alpar@1956: * This file is a part of LEMON, a generic C++ optimization library
alpar@1956: *
alpar@2553: * Copyright (C) 2003-2008
alpar@1956: * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@1359: * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@906: *
alpar@906: * Permission to use, modify and distribute this software is granted
alpar@906: * provided that this copyright notice appears in all copies. For
alpar@906: * precise terms see the accompanying LICENSE file.
alpar@906: *
alpar@906: * This software is provided "AS IS" with no warranty of any kind,
alpar@906: * express or implied, and with no claim as to its suitability for any
alpar@906: * purpose.
alpar@906: *
alpar@906: */
alpar@906:
alpar@921: #ifndef LEMON_UNION_FIND_H
alpar@921: #define LEMON_UNION_FIND_H
beckerjc@483:
klao@491: //!\ingroup auxdat
beckerjc@483: //!\file
beckerjc@483: //!\brief Union-Find data structures.
alpar@774: //!
beckerjc@483:
beckerjc@483: #include <vector>
beckerjc@483: #include <list>
beckerjc@483: #include <utility>
beckerjc@483: #include <algorithm>
ladanyi@2551: #include <functional>
beckerjc@483:
deba@1993: #include <lemon/bits/invalid.h>
beckerjc@483:
alpar@921: namespace lemon {
beckerjc@483:
deba@2308: /// \ingroup auxdat
deba@2308: ///
deba@2205: /// \brief A \e Union-Find data structure implementation
deba@2205: ///
deba@2205: /// The class implements the \e Union-Find data structure.
deba@2205: /// The union operation uses rank heuristic, while
deba@2205: /// the find operation uses path compression.
deba@2205: /// This is a very simple but efficient implementation, providing
deba@2205: /// only four methods: join (union), find, insert and size.
deba@2205: /// For more features see the \ref UnionFindEnum class.
deba@2205: ///
deba@2205: /// It is primarily used in Kruskal algorithm for finding minimal
deba@2205: /// cost spanning tree in a graph.
deba@2205: /// \sa kruskal()
deba@2205: ///
deba@2205: /// \pre You need to add all the elements by the \ref insert()
deba@2205: /// method.
deba@2308: template <typename _ItemIntMap>
beckerjc@483: class UnionFind {
beckerjc@483: public:
deba@2308:
deba@2308: typedef _ItemIntMap ItemIntMap;
deba@2308: typedef typename ItemIntMap::Key Item;
beckerjc@483:
beckerjc@483: private:
deba@2205: // If the items vector stores negative value for an item then
deba@2205: // that item is root item and it has -items[it] component size.
deba@2205: // Else the items[it] contains the index of the parent.
deba@2205: std::vector<int> items;
deba@2205: ItemIntMap& index;
deba@2205:
deba@2205: bool rep(int idx) const {
deba@2205: return items[idx] < 0;
deba@2205: }
deba@2205:
deba@2205: int repIndex(int idx) const {
deba@2205: int k = idx;
deba@2205: while (!rep(k)) {
deba@2205: k = items[k] ;
deba@2205: }
deba@2205: while (idx != k) {
deba@2205: int next = items[idx];
deba@2205: const_cast<int&>(items[idx]) = k;
deba@2205: idx = next;
deba@2205: }
deba@2205: return k;
deba@2205: }
beckerjc@483:
beckerjc@483: public:
beckerjc@483:
deba@2205: /// \brief Constructor
deba@2205: ///
deba@2205: /// Constructor of the UnionFind class. You should give an item to
deba@2205: /// integer map which will be used from the data structure. If you
deba@2205: /// modify directly this map that may cause segmentation fault,
deba@2205: /// invalid data structure, or infinite loop when you use again
deba@2205: /// the union-find.
deba@2205: UnionFind(ItemIntMap& m) : index(m) {}
beckerjc@483:
deba@2205: /// \brief Returns the index of the element's component.
deba@2205: ///
deba@2205: /// The method returns the index of the element's component.
deba@2205: /// This is an integer between zero and the number of inserted elements.
deba@2205: ///
deba@2205: int find(const Item& a) {
deba@2205: return repIndex(index[a]);
beckerjc@483: }
beckerjc@483:
deba@2427: /// \brief Clears the union-find data structure
deba@2427: ///
deba@2427: /// Erase each item from the data structure.
deba@2427: void clear() {
deba@2427: items.clear();
deba@2427: }
deba@2427:
deba@2205: /// \brief Inserts a new element into the structure.
deba@2205: ///
deba@2205: /// This method inserts a new element into the data structure.
deba@2205: ///
deba@2205: /// The method returns the index of the new component.
deba@2205: int insert(const Item& a) {
deba@2205: int n = items.size();
deba@2205: items.push_back(-1);
deba@2205: index.set(a,n);
beckerjc@483: return n;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Joining the components of element \e a and element \e b.
deba@2205: ///
deba@2205: /// This is the \e union operation of the Union-Find structure.
deba@2205: /// Joins the component of element \e a and component of
deba@2205: /// element \e b. If \e a and \e b are in the same component then
deba@2205: /// it returns false otherwise it returns true.
deba@2205: bool join(const Item& a, const Item& b) {
deba@2205: int ka = repIndex(index[a]);
deba@2205: int kb = repIndex(index[b]);
beckerjc@483:
deba@2205: if ( ka == kb )
beckerjc@483: return false;
beckerjc@483:
deba@2205: if (items[ka] < items[kb]) {
deba@2205: items[ka] += items[kb];
deba@2205: items[kb] = ka;
deba@2205: } else {
deba@2205: items[kb] += items[ka];
deba@2205: items[ka] = kb;
beckerjc@483: }
beckerjc@483: return true;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Returns the size of the component of element \e a.
deba@2205: ///
deba@2205: /// Returns the size of the component of element \e a.
deba@2205: int size(const Item& a) {
deba@2205: int k = repIndex(index[a]);
deba@2205: return - items[k];
beckerjc@483: }
beckerjc@483:
beckerjc@483: };
beckerjc@483:
deba@2308: /// \ingroup auxdat
deba@2308: ///
deba@2205: /// \brief A \e Union-Find data structure implementation which
deba@2205: /// is able to enumerate the components.
deba@2205: ///
deba@2205: /// The class implements a \e Union-Find data structure
deba@2205: /// which is able to enumerate the components and the items in
deba@2205: /// a component. If you don't need this feature then perhaps it's
deba@2205: /// better to use the \ref UnionFind class which is more efficient.
deba@2205: ///
deba@2205: /// The union operation uses rank heuristic, while
deba@2205: /// the find operation uses path compression.
deba@2205: ///
deba@2205: /// \pre You need to add all the elements by the \ref insert()
deba@2205: /// method.
deba@2205: ///
deba@2308: template <typename _ItemIntMap>
deba@2205: class UnionFindEnum {
deba@2205: public:
deba@2205:
deba@2205: typedef _ItemIntMap ItemIntMap;
deba@2308: typedef typename ItemIntMap::Key Item;
deba@2308:
deba@2205: private:
deba@2205:
deba@2505: ItemIntMap& index;
deba@2505:
deba@2205: // If the parent stores negative value for an item then that item
deba@2505: // is root item and it has ~(items[it].parent) component id. Else
deba@2205: // the items[it].parent contains the index of the parent.
deba@2205: //
deba@2505: // The \c next and \c prev provides the double-linked
deba@2505: // cyclic list of one component's items.
deba@2205: struct ItemT {
deba@2205: int parent;
deba@2205: Item item;
beckerjc@483:
deba@2505: int next, prev;
deba@2205: };
beckerjc@483:
deba@2205: std::vector<ItemT> items;
deba@2505: int firstFreeItem;
beckerjc@483:
deba@2505: struct ClassT {
deba@2505: int size;
deba@2505: int firstItem;
deba@2505: int next, prev;
deba@2505: };
deba@2505:
deba@2505: std::vector<ClassT> classes;
deba@2505: int firstClass, firstFreeClass;
deba@2505:
deba@2505: int newClass() {
deba@2505: if (firstFreeClass == -1) {
deba@2505: int cdx = classes.size();
deba@2505: classes.push_back(ClassT());
deba@2505: return cdx;
deba@2505: } else {
deba@2505: int cdx = firstFreeClass;
deba@2505: firstFreeClass = classes[firstFreeClass].next;
deba@2505: return cdx;
deba@2505: }
deba@2505: }
deba@2505:
deba@2505: int newItem() {
deba@2505: if (firstFreeItem == -1) {
deba@2505: int idx = items.size();
deba@2505: items.push_back(ItemT());
deba@2505: return idx;
deba@2505: } else {
deba@2505: int idx = firstFreeItem;
deba@2505: firstFreeItem = items[firstFreeItem].next;
deba@2505: return idx;
deba@2505: }
deba@2505: }
beckerjc@483:
beckerjc@483:
deba@2205: bool rep(int idx) const {
deba@2205: return items[idx].parent < 0;
beckerjc@483: }
beckerjc@483:
deba@2205: int repIndex(int idx) const {
deba@2205: int k = idx;
deba@2205: while (!rep(k)) {
deba@2205: k = items[k].parent;
deba@2205: }
deba@2205: while (idx != k) {
deba@2205: int next = items[idx].parent;
deba@2205: const_cast<int&>(items[idx].parent) = k;
deba@2205: idx = next;
deba@2205: }
deba@2205: return k;
deba@2205: }
deba@2205:
deba@2505: int classIndex(int idx) const {
deba@2505: return ~(items[repIndex(idx)].parent);
deba@2505: }
deba@2505:
deba@2505: void singletonItem(int idx) {
deba@2505: items[idx].next = idx;
deba@2505: items[idx].prev = idx;
deba@2505: }
deba@2505:
deba@2505: void laceItem(int idx, int rdx) {
deba@2505: items[idx].prev = rdx;
deba@2505: items[idx].next = items[rdx].next;
deba@2505: items[items[rdx].next].prev = idx;
deba@2505: items[rdx].next = idx;
deba@2505: }
deba@2505:
deba@2505: void unlaceItem(int idx) {
deba@2505: items[items[idx].prev].next = items[idx].next;
deba@2505: items[items[idx].next].prev = items[idx].prev;
deba@2505:
deba@2505: items[idx].next = firstFreeItem;
deba@2505: firstFreeItem = idx;
deba@2505: }
deba@2505:
deba@2505: void spliceItems(int ak, int bk) {
deba@2505: items[items[ak].prev].next = bk;
deba@2505: items[items[bk].prev].next = ak;
deba@2505: int tmp = items[ak].prev;
deba@2505: items[ak].prev = items[bk].prev;
deba@2505: items[bk].prev = tmp;
deba@2505:
deba@2505: }
deba@2505:
deba@2505: void laceClass(int cls) {
deba@2505: if (firstClass != -1) {
deba@2505: classes[firstClass].prev = cls;
deba@2205: }
deba@2505: classes[cls].next = firstClass;
deba@2505: classes[cls].prev = -1;
deba@2505: firstClass = cls;
deba@2205: }
deba@2205:
deba@2505: void unlaceClass(int cls) {
deba@2505: if (classes[cls].prev != -1) {
deba@2505: classes[classes[cls].prev].next = classes[cls].next;
deba@2505: } else {
deba@2505: firstClass = classes[cls].next;
deba@2505: }
deba@2505: if (classes[cls].next != -1) {
deba@2505: classes[classes[cls].next].prev = classes[cls].prev;
deba@2505: }
deba@2505:
deba@2505: classes[cls].next = firstFreeClass;
deba@2505: firstFreeClass = cls;
deba@2505: }
klao@2003:
beckerjc@483: public:
beckerjc@483:
deba@2205: UnionFindEnum(ItemIntMap& _index)
deba@2505: : index(_index), items(), firstFreeItem(-1),
deba@2505: firstClass(-1), firstFreeClass(-1) {}
deba@2205:
deba@2205: /// \brief Inserts the given element into a new component.
deba@2205: ///
deba@2205: /// This method creates a new component consisting only of the
deba@2205: /// given element.
deba@2205: ///
deba@2505: int insert(const Item& item) {
deba@2505: int idx = newItem();
beckerjc@483:
deba@2205: index.set(item, idx);
beckerjc@483:
deba@2505: singletonItem(idx);
deba@2505: items[idx].item = item;
deba@2505:
deba@2505: int cdx = newClass();
deba@2505:
deba@2505: items[idx].parent = ~cdx;
deba@2505:
deba@2505: laceClass(cdx);
deba@2505: classes[cdx].size = 1;
deba@2505: classes[cdx].firstItem = idx;
deba@2505:
deba@2505: firstClass = cdx;
deba@2205:
deba@2505: return cdx;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Inserts the given element into the component of the others.
deba@2205: ///
deba@2205: /// This methods inserts the element \e a into the component of the
deba@2205: /// element \e comp.
deba@2505: void insert(const Item& item, int cls) {
deba@2505: int rdx = classes[cls].firstItem;
deba@2505: int idx = newItem();
beckerjc@483:
deba@2205: index.set(item, idx);
deba@2205:
deba@2505: laceItem(idx, rdx);
deba@2205:
deba@2505: items[idx].item = item;
deba@2505: items[idx].parent = rdx;
deba@2205:
deba@2505: ++classes[~(items[rdx].parent)].size;
beckerjc@483: }
beckerjc@483:
deba@2427: /// \brief Clears the union-find data structure
deba@2427: ///
deba@2427: /// Erase each item from the data structure.
deba@2427: void clear() {
deba@2427: items.clear();
deba@2427: firstClass = -1;
deba@2505: firstFreeItem = -1;
deba@2427: }
deba@2427:
deba@2505: /// \brief Finds the component of the given element.
deba@2205: ///
deba@2505: /// The method returns the component id of the given element.
deba@2505: int find(const Item &item) const {
deba@2505: return ~(items[repIndex(index[item])].parent);
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Joining the component of element \e a and element \e b.
deba@2205: ///
deba@2205: /// This is the \e union operation of the Union-Find structure.
deba@2205: /// Joins the component of element \e a and component of
deba@2205: /// element \e b. If \e a and \e b are in the same component then
deba@2505: /// returns -1 else returns the remaining class.
deba@2505: int join(const Item& a, const Item& b) {
beckerjc@483:
deba@2205: int ak = repIndex(index[a]);
deba@2205: int bk = repIndex(index[b]);
beckerjc@483:
deba@2205: if (ak == bk) {
deba@2505: return -1;
beckerjc@483: }
beckerjc@483:
deba@2505: int acx = ~(items[ak].parent);
deba@2505: int bcx = ~(items[bk].parent);
deba@2505:
deba@2505: int rcx;
deba@2505:
deba@2505: if (classes[acx].size > classes[bcx].size) {
deba@2505: classes[acx].size += classes[bcx].size;
deba@2205: items[bk].parent = ak;
deba@2505: unlaceClass(bcx);
deba@2505: rcx = acx;
deba@2205: } else {
deba@2505: classes[bcx].size += classes[acx].size;
deba@2205: items[ak].parent = bk;
deba@2505: unlaceClass(acx);
deba@2505: rcx = bcx;
beckerjc@483: }
deba@2205: spliceItems(ak, bk);
beckerjc@483:
deba@2505: return rcx;
beckerjc@483: }
beckerjc@483:
deba@2505: /// \brief Returns the size of the class.
deba@2205: ///
deba@2505: /// Returns the size of the class.
deba@2505: int size(int cls) const {
deba@2505: return classes[cls].size;
beckerjc@483: }
beckerjc@483:
deba@2505: /// \brief Splits up the component.
deba@2205: ///
deba@2505: /// Splitting the component into singleton components (component
deba@2505: /// of size one).
deba@2505: void split(int cls) {
deba@2505: int fdx = classes[cls].firstItem;
deba@2505: int idx = items[fdx].next;
deba@2505: while (idx != fdx) {
deba@2505: int next = items[idx].next;
deba@2505:
deba@2505: singletonItem(idx);
deba@2505:
deba@2505: int cdx = newClass();
deba@2505: items[idx].parent = ~cdx;
deba@2505:
deba@2505: laceClass(cdx);
deba@2505: classes[cdx].size = 1;
deba@2505: classes[cdx].firstItem = idx;
deba@2205:
deba@2205: idx = next;
beckerjc@483: }
beckerjc@483:
deba@2505: items[idx].prev = idx;
deba@2505: items[idx].next = idx;
deba@2505:
deba@2505: classes[~(items[idx].parent)].size = 1;
deba@2205:
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Removes the given element from the structure.
deba@2205: ///
deba@2205: /// Removes the element from its component and if the component becomes
deba@2205: /// empty then removes that component from the component list.
deba@2205: ///
deba@2205: /// \warning It is an error to remove an element which is not in
deba@2205: /// the structure.
deba@2505: /// \warning This running time of this operation is proportional to the
deba@2505: /// number of the items in this class.
deba@2505: void erase(const Item& item) {
deba@2205: int idx = index[item];
deba@2505: int fdx = items[idx].next;
deba@2505:
deba@2505: int cdx = classIndex(idx);
deba@2505: if (idx == fdx) {
deba@2505: unlaceClass(cdx);
deba@2505: items[idx].next = firstFreeItem;
deba@2505: firstFreeItem = idx;
deba@2505: return;
deba@2505: } else {
deba@2505: classes[cdx].firstItem = fdx;
deba@2505: --classes[cdx].size;
deba@2505: items[fdx].parent = ~cdx;
deba@2505:
deba@2505: unlaceItem(idx);
deba@2505: idx = items[fdx].next;
deba@2505: while (idx != fdx) {
deba@2505: items[idx].parent = fdx;
deba@2505: idx = items[idx].next;
deba@2505: }
deba@2205:
beckerjc@483: }
beckerjc@483:
deba@2506: }
deba@2506:
deba@2506: /// \brief Gives back a representant item of the component.
deba@2506: ///
deba@2506: /// Gives back a representant item of the component.
deba@2506: Item item(int cls) const {
deba@2506: return items[classes[cls].firstItem].item;
deba@2506: }
beckerjc@483:
deba@2205: /// \brief Removes the component of the given element from the structure.
deba@2205: ///
deba@2205: /// Removes the component of the given element from the structure.
deba@2205: ///
deba@2205: /// \warning It is an error to give an element which is not in the
deba@2205: /// structure.
deba@2505: void eraseClass(int cls) {
deba@2505: int fdx = classes[cls].firstItem;
deba@2505: unlaceClass(cls);
deba@2505: items[items[fdx].prev].next = firstFreeItem;
deba@2505: firstFreeItem = fdx;
deba@2205: }
beckerjc@483:
deba@2205: /// \brief Lemon style iterator for the representant items.
deba@2205: ///
deba@2205: /// ClassIt is a lemon style iterator for the components. It iterates
deba@2505: /// on the ids of the classes.
deba@2205: class ClassIt {
deba@2205: public:
deba@2205: /// \brief Constructor of the iterator
deba@2205: ///
deba@2205: /// Constructor of the iterator
deba@2205: ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) {
deba@2505: cdx = unionFind->firstClass;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Constructor to get invalid iterator
deba@2205: ///
deba@2205: /// Constructor to get invalid iterator
deba@2505: ClassIt(Invalid) : unionFind(0), cdx(-1) {}
deba@2205:
deba@2205: /// \brief Increment operator
deba@2205: ///
deba@2205: /// It steps to the next representant item.
deba@2205: ClassIt& operator++() {
deba@2505: cdx = unionFind->classes[cdx].next;
deba@2205: return *this;
deba@2205: }
deba@2205:
deba@2205: /// \brief Conversion operator
deba@2205: ///
deba@2205: /// It converts the iterator to the current representant item.
deba@2505: operator int() const {
deba@2505: return cdx;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Equality operator
deba@2205: ///
deba@2205: /// Equality operator
deba@2205: bool operator==(const ClassIt& i) {
deba@2505: return i.cdx == cdx;
deba@2205: }
beckerjc@483:
deba@2205: /// \brief Inequality operator
deba@2205: ///
deba@2205: /// Inequality operator
deba@2205: bool operator!=(const ClassIt& i) {
deba@2505: return i.cdx != cdx;
klao@2003: }
beckerjc@483:
deba@2205: private:
deba@2205: const UnionFindEnum* unionFind;
deba@2505: int cdx;
deba@2205: };
deba@2205:
deba@2205: /// \brief Lemon style iterator for the items of a component.
deba@2205: ///
deba@2205: /// ClassIt is a lemon style iterator for the components. It iterates
deba@2205: /// on the items of a class. By example if you want to iterate on
deba@2205: /// each items of each classes then you may write the next code.
deba@2205: ///\code
deba@2205: /// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
deba@2205: /// std::cout << "Class: ";
deba@2205: /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
deba@2205: /// std::cout << toString(iit) << ' ' << std::endl;
deba@2205: /// }
deba@2205: /// std::cout << std::endl;
deba@2205: /// }
deba@2205: ///\endcode
deba@2205: class ItemIt {
deba@2205: public:
deba@2205: /// \brief Constructor of the iterator
deba@2205: ///
deba@2205: /// Constructor of the iterator. The iterator iterates
deba@2205: /// on the class of the \c item.
deba@2505: ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) {
deba@2505: fdx = idx = unionFind->classes[cls].firstItem;
beckerjc@483: }
beckerjc@483:
deba@2205: /// \brief Constructor to get invalid iterator
deba@2205: ///
deba@2205: /// Constructor to get invalid iterator
deba@2205: ItemIt(Invalid) : unionFind(0), idx(-1) {}
deba@2205:
deba@2205: /// \brief Increment operator
deba@2205: ///
deba@2205: /// It steps to the next item in the class.
deba@2205: ItemIt& operator++() {
deba@2505: idx = unionFind->items[idx].next;
deba@2505: if (idx == fdx) idx = -1;
deba@2205: return *this;
klao@2003: }
deba@2205:
deba@2205: /// \brief Conversion operator
deba@2205: ///
deba@2205: /// It converts the iterator to the current item.
deba@2205: operator const Item&() const {
deba@2205: return unionFind->items[idx].item;
klao@2003: }
klao@2003:
deba@2205: /// \brief Equality operator
deba@2205: ///
deba@2205: /// Equality operator
deba@2205: bool operator==(const ItemIt& i) {
deba@2205: return i.idx == idx;
klao@2003: }
klao@2003:
deba@2205: /// \brief Inequality operator
deba@2205: ///
deba@2205: /// Inequality operator
deba@2205: bool operator!=(const ItemIt& i) {
deba@2205: return i.idx != idx;
deba@2205: }
deba@2205:
deba@2205: private:
deba@2205: const UnionFindEnum* unionFind;
deba@2505: int idx, fdx;
beckerjc@483: };
beckerjc@483:
beckerjc@483: };
beckerjc@483:
deba@2505: /// \ingroup auxdat
deba@2505: ///
deba@2505: /// \brief A \e Extend-Find data structure implementation which
deba@2505: /// is able to enumerate the components.
deba@2505: ///
deba@2505: /// The class implements an \e Extend-Find data structure which is
deba@2505: /// able to enumerate the components and the items in a
deba@2505: /// component. The data structure is a simplification of the
deba@2505: /// Union-Find structure, and it does not allow to merge two components.
deba@2505: ///
deba@2505: /// \pre You need to add all the elements by the \ref insert()
deba@2505: /// method.
deba@2505: template <typename _ItemIntMap>
deba@2505: class ExtendFindEnum {
deba@2505: public:
deba@2505:
deba@2505: typedef _ItemIntMap ItemIntMap;
deba@2505: typedef typename ItemIntMap::Key Item;
deba@2505:
deba@2505: private:
deba@2505:
deba@2505: ItemIntMap& index;
deba@2505:
deba@2505: struct ItemT {
deba@2505: int cls;
deba@2505: Item item;
deba@2505: int next, prev;
deba@2505: };
deba@2505:
deba@2505: std::vector<ItemT> items;
deba@2505: int firstFreeItem;
deba@2505:
deba@2505: struct ClassT {
deba@2505: int firstItem;
deba@2505: int next, prev;
deba@2505: };
deba@2505:
deba@2505: std::vector<ClassT> classes;
deba@2505:
deba@2505: int firstClass, firstFreeClass;
deba@2505:
deba@2505: int newClass() {
deba@2505: if (firstFreeClass != -1) {
deba@2505: int cdx = firstFreeClass;
deba@2505: firstFreeClass = classes[cdx].next;
deba@2505: return cdx;
deba@2505: } else {
deba@2505: classes.push_back(ClassT());
deba@2505: return classes.size() - 1;
deba@2505: }
deba@2505: }
deba@2505:
deba@2505: int newItem() {
deba@2505: if (firstFreeItem != -1) {
deba@2505: int idx = firstFreeItem;
deba@2505: firstFreeItem = items[idx].next;
deba@2505: return idx;
deba@2505: } else {
deba@2505: items.push_back(ItemT());
deba@2505: return items.size() - 1;
deba@2505: }
deba@2505: }
deba@2505:
deba@2505: public:
deba@2505:
deba@2505: /// \brief Constructor
deba@2505: ExtendFindEnum(ItemIntMap& _index)
deba@2505: : index(_index), items(), firstFreeItem(-1),
deba@2505: classes(), firstClass(-1), firstFreeClass(-1) {}
deba@2505:
deba@2505: /// \brief Inserts the given element into a new component.
deba@2505: ///
deba@2505: /// This method creates a new component consisting only of the
deba@2505: /// given element.
deba@2505: int insert(const Item& item) {
deba@2505: int cdx = newClass();
deba@2505: classes[cdx].prev = -1;
deba@2505: classes[cdx].next = firstClass;
deba@2542: if (firstClass != -1) {
deba@2542: classes[firstClass].prev = cdx;
deba@2542: }
deba@2505: firstClass = cdx;
deba@2505:
deba@2505: int idx = newItem();
deba@2505: items[idx].item = item;
deba@2505: items[idx].cls = cdx;
deba@2505: items[idx].prev = idx;
deba@2505: items[idx].next = idx;
deba@2505:
deba@2505: classes[cdx].firstItem = idx;
deba@2505:
deba@2505: index.set(item, idx);
deba@2505:
deba@2505: return cdx;
deba@2505: }
deba@2505:
deba@2505: /// \brief Inserts the given element into the given component.
deba@2505: ///
deba@2505: /// This methods inserts the element \e item a into the \e cls class.
deba@2505: void insert(const Item& item, int cls) {
deba@2505: int idx = newItem();
deba@2505: int rdx = classes[cls].firstItem;
deba@2505: items[idx].item = item;
deba@2505: items[idx].cls = cls;
deba@2505:
deba@2505: items[idx].prev = rdx;
deba@2505: items[idx].next = items[rdx].next;
deba@2505: items[items[rdx].next].prev = idx;
deba@2505: items[rdx].next = idx;
deba@2505:
deba@2505: index.set(item, idx);
deba@2505: }
deba@2505:
deba@2505: /// \brief Clears the union-find data structure
deba@2505: ///
deba@2505: /// Erase each item from the data structure.
deba@2505: void clear() {
deba@2505: items.clear();
deba@2505: classes.clear;
deba@2505: firstClass = firstFreeClass = firstFreeItem = -1;
deba@2505: }
deba@2505:
deba@2505: /// \brief Gives back the class of the \e item.
deba@2505: ///
deba@2505: /// Gives back the class of the \e item.
deba@2505: int find(const Item &item) const {
deba@2505: return items[index[item]].cls;
deba@2505: }
deba@2506:
deba@2506: /// \brief Gives back a representant item of the component.
deba@2506: ///
deba@2506: /// Gives back a representant item of the component.
deba@2506: Item item(int cls) const {
deba@2506: return items[classes[cls].firstItem].item;
deba@2506: }
deba@2505:
deba@2505: /// \brief Removes the given element from the structure.
deba@2505: ///
deba@2505: /// Removes the element from its component and if the component becomes
deba@2505: /// empty then removes that component from the component list.
deba@2505: ///
deba@2505: /// \warning It is an error to remove an element which is not in
deba@2505: /// the structure.
deba@2505: void erase(const Item &item) {
deba@2505: int idx = index[item];
deba@2505: int cdx = items[idx].cls;
deba@2505:
deba@2505: if (idx == items[idx].next) {
deba@2505: if (classes[cdx].prev != -1) {
deba@2505: classes[classes[cdx].prev].next = classes[cdx].next;
deba@2505: } else {
deba@2505: firstClass = classes[cdx].next;
deba@2505: }
deba@2505: if (classes[cdx].next != -1) {
deba@2505: classes[classes[cdx].next].prev = classes[cdx].prev;
deba@2505: }
deba@2505: classes[cdx].next = firstFreeClass;
deba@2505: firstFreeClass = cdx;
deba@2505: } else {
deba@2505: classes[cdx].firstItem = items[idx].next;
deba@2505: items[items[idx].next].prev = items[idx].prev;
deba@2505: items[items[idx].prev].next = items[idx].next;
deba@2505: }
deba@2505: items[idx].next = firstFreeItem;
deba@2505: firstFreeItem = idx;
deba@2505:
deba@2505: }
deba@2505:
deba@2505:
deba@2505: /// \brief Removes the component of the given element from the structure.
deba@2505: ///
deba@2505: /// Removes the component of the given element from the structure.
deba@2505: ///
deba@2505: /// \warning It is an error to give an element which is not in the
deba@2505: /// structure.
deba@2505: void eraseClass(int cdx) {
deba@2505: int idx = classes[cdx].firstItem;
deba@2505: items[items[idx].prev].next = firstFreeItem;
deba@2505: firstFreeItem = idx;
deba@2505:
deba@2505: if (classes[cdx].prev != -1) {
deba@2505: classes[classes[cdx].prev].next = classes[cdx].next;
deba@2505: } else {
deba@2505: firstClass = classes[cdx].next;
deba@2505: }
deba@2505: if (classes[cdx].next != -1) {
deba@2505: classes[classes[cdx].next].prev = classes[cdx].prev;
deba@2505: }
deba@2505: classes[cdx].next = firstFreeClass;
deba@2505: firstFreeClass = cdx;
deba@2505: }
deba@2505:
deba@2505: /// \brief Lemon style iterator for the classes.
deba@2505: ///
deba@2505: /// ClassIt is a lemon style iterator for the components. It iterates
deba@2505: /// on the ids of classes.
deba@2505: class ClassIt {
deba@2505: public:
deba@2505: /// \brief Constructor of the iterator
deba@2505: ///
deba@2505: /// Constructor of the iterator
deba@2505: ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) {
deba@2505: cdx = extendFind->firstClass;
deba@2505: }
deba@2505:
deba@2505: /// \brief Constructor to get invalid iterator
deba@2505: ///
deba@2505: /// Constructor to get invalid iterator
deba@2505: ClassIt(Invalid) : extendFind(0), cdx(-1) {}
deba@2505:
deba@2505: /// \brief Increment operator
deba@2505: ///
deba@2505: /// It steps to the next representant item.
deba@2505: ClassIt& operator++() {
deba@2505: cdx = extendFind->classes[cdx].next;
deba@2505: return *this;
deba@2505: }
deba@2505:
deba@2505: /// \brief Conversion operator
deba@2505: ///
deba@2505: /// It converts the iterator to the current class id.
deba@2505: operator int() const {
deba@2505: return cdx;
deba@2505: }
deba@2505:
deba@2505: /// \brief Equality operator
deba@2505: ///
deba@2505: /// Equality operator
deba@2505: bool operator==(const ClassIt& i) {
deba@2505: return i.cdx == cdx;
deba@2505: }
deba@2505:
deba@2505: /// \brief Inequality operator
deba@2505: ///
deba@2505: /// Inequality operator
deba@2505: bool operator!=(const ClassIt& i) {
deba@2505: return i.cdx != cdx;
deba@2505: }
deba@2505:
deba@2505: private:
deba@2505: const ExtendFindEnum* extendFind;
deba@2505: int cdx;
deba@2505: };
deba@2505:
deba@2505: /// \brief Lemon style iterator for the items of a component.
deba@2505: ///
deba@2505: /// ClassIt is a lemon style iterator for the components. It iterates
deba@2505: /// on the items of a class. By example if you want to iterate on
deba@2505: /// each items of each classes then you may write the next code.
deba@2505: ///\code
deba@2505: /// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
deba@2505: /// std::cout << "Class: ";
deba@2505: /// for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
deba@2505: /// std::cout << toString(iit) << ' ' << std::endl;
deba@2505: /// }
deba@2505: /// std::cout << std::endl;
deba@2505: /// }
deba@2505: ///\endcode
deba@2505: class ItemIt {
deba@2505: public:
deba@2505: /// \brief Constructor of the iterator
deba@2505: ///
deba@2505: /// Constructor of the iterator. The iterator iterates
deba@2505: /// on the class of the \c item.
deba@2505: ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) {
deba@2505: fdx = idx = extendFind->classes[cls].firstItem;
deba@2505: }
deba@2505:
deba@2505: /// \brief Constructor to get invalid iterator
deba@2505: ///
deba@2505: /// Constructor to get invalid iterator
deba@2505: ItemIt(Invalid) : extendFind(0), idx(-1) {}
deba@2505:
deba@2505: /// \brief Increment operator
deba@2505: ///
deba@2505: /// It steps to the next item in the class.
deba@2505: ItemIt& operator++() {
deba@2505: idx = extendFind->items[idx].next;
deba@2505: if (fdx == idx) idx = -1;
deba@2505: return *this;
deba@2505: }
deba@2505:
deba@2505: /// \brief Conversion operator
deba@2505: ///
deba@2505: /// It converts the iterator to the current item.
deba@2505: operator const Item&() const {
deba@2505: return extendFind->items[idx].item;
deba@2505: }
deba@2505:
deba@2505: /// \brief Equality operator
deba@2505: ///
deba@2505: /// Equality operator
deba@2505: bool operator==(const ItemIt& i) {
deba@2505: return i.idx == idx;
deba@2505: }
deba@2505:
deba@2505: /// \brief Inequality operator
deba@2505: ///
deba@2505: /// Inequality operator
deba@2505: bool operator!=(const ItemIt& i) {
deba@2505: return i.idx != idx;
deba@2505: }
deba@2505:
deba@2505: private:
deba@2505: const ExtendFindEnum* extendFind;
deba@2505: int idx, fdx;
deba@2505: };
deba@2505:
deba@2505: };
beckerjc@483:
deba@2548: /// \ingroup auxdat
deba@2548: ///
deba@2548: /// \brief A \e Union-Find data structure implementation which
deba@2548: /// is able to store a priority for each item and retrieve the minimum of
deba@2548: /// each class.
deba@2548: ///
deba@2548: /// A \e Union-Find data structure implementation which is able to
deba@2548: /// store a priority for each item and retrieve the minimum of each
deba@2548: /// class. In addition, it supports the joining and splitting the
deba@2548: /// components. If you don't need this feature then you makes
deba@2548: /// better to use the \ref UnionFind class which is more efficient.
deba@2548: ///
deba@2548: /// The union-find data strcuture based on a (2, 16)-tree with a
deba@2548: /// tournament minimum selection on the internal nodes. The insert
deba@2548: /// operation takes O(1), the find, set, decrease and increase takes
deba@2548: /// O(log(n)), where n is the number of nodes in the current
deba@2548: /// component. The complexity of join and split is O(log(n)*k),
deba@2548: /// where n is the sum of the number of the nodes and k is the
deba@2548: /// number of joined components or the number of the components
deba@2548: /// after the split.
deba@2548: ///
deba@2548: /// \pre You need to add all the elements by the \ref insert()
deba@2548: /// method.
deba@2548: ///
deba@2548: template <typename _Value, typename _ItemIntMap,
deba@2548: typename _Comp = std::less<_Value> >
deba@2548: class HeapUnionFind {
deba@2548: public:
deba@2548:
deba@2548: typedef _Value Value;
deba@2548: typedef typename _ItemIntMap::Key Item;
deba@2548:
deba@2548: typedef _ItemIntMap ItemIntMap;
deba@2548:
deba@2548: typedef _Comp Comp;
deba@2548:
deba@2548: private:
deba@2548:
deba@2550: static const int cmax = 16;
deba@2548:
deba@2548: ItemIntMap& index;
deba@2548:
deba@2548: struct ClassNode {
deba@2548: int parent;
deba@2548: int depth;
deba@2548:
deba@2548: int left, right;
deba@2548: int next, prev;
deba@2548: };
deba@2548:
deba@2548: int first_class;
deba@2548: int first_free_class;
deba@2548: std::vector<ClassNode> classes;
deba@2548:
deba@2548: int newClass() {
deba@2548: if (first_free_class < 0) {
deba@2548: int id = classes.size();
deba@2548: classes.push_back(ClassNode());
deba@2548: return id;
deba@2548: } else {
deba@2548: int id = first_free_class;
deba@2548: first_free_class = classes[id].next;
deba@2548: return id;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: void deleteClass(int id) {
deba@2548: classes[id].next = first_free_class;
deba@2548: first_free_class = id;
deba@2548: }
deba@2548:
deba@2548: struct ItemNode {
deba@2548: int parent;
deba@2548: Item item;
deba@2548: Value prio;
deba@2548: int next, prev;
deba@2548: int left, right;
deba@2548: int size;
deba@2548: };
deba@2548:
deba@2548: int first_free_node;
deba@2548: std::vector<ItemNode> nodes;
deba@2548:
deba@2548: int newNode() {
deba@2548: if (first_free_node < 0) {
deba@2548: int id = nodes.size();
deba@2548: nodes.push_back(ItemNode());
deba@2548: return id;
deba@2548: } else {
deba@2548: int id = first_free_node;
deba@2548: first_free_node = nodes[id].next;
deba@2548: return id;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: void deleteNode(int id) {
deba@2548: nodes[id].next = first_free_node;
deba@2548: first_free_node = id;
deba@2548: }
deba@2548:
deba@2548: Comp comp;
deba@2548:
deba@2548: int findClass(int id) const {
deba@2548: int kd = id;
deba@2548: while (kd >= 0) {
deba@2548: kd = nodes[kd].parent;
deba@2548: }
deba@2548: return ~kd;
deba@2548: }
deba@2548:
deba@2548: int leftNode(int id) const {
deba@2548: int kd = ~(classes[id].parent);
deba@2548: for (int i = 0; i < classes[id].depth; ++i) {
deba@2548: kd = nodes[kd].left;
deba@2548: }
deba@2548: return kd;
deba@2548: }
deba@2548:
deba@2548: int nextNode(int id) const {
deba@2548: int depth = 0;
deba@2548: while (id >= 0 && nodes[id].next == -1) {
deba@2548: id = nodes[id].parent;
deba@2548: ++depth;
deba@2548: }
deba@2548: if (id < 0) {
deba@2548: return -1;
deba@2548: }
deba@2548: id = nodes[id].next;
deba@2548: while (depth--) {
deba@2548: id = nodes[id].left;
deba@2548: }
deba@2548: return id;
deba@2548: }
deba@2548:
deba@2548:
deba@2548: void setPrio(int id) {
deba@2548: int jd = nodes[id].left;
deba@2548: nodes[id].prio = nodes[jd].prio;
deba@2548: nodes[id].item = nodes[jd].item;
deba@2548: jd = nodes[jd].next;
deba@2548: while (jd != -1) {
deba@2548: if (comp(nodes[jd].prio, nodes[id].prio)) {
deba@2548: nodes[id].prio = nodes[jd].prio;
deba@2548: nodes[id].item = nodes[jd].item;
deba@2548: }
deba@2548: jd = nodes[jd].next;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: void push(int id, int jd) {
deba@2548: nodes[id].size = 1;
deba@2548: nodes[id].left = nodes[id].right = jd;
deba@2548: nodes[jd].next = nodes[jd].prev = -1;
deba@2548: nodes[jd].parent = id;
deba@2548: }
deba@2548:
deba@2548: void pushAfter(int id, int jd) {
deba@2548: int kd = nodes[id].parent;
deba@2548: if (nodes[id].next != -1) {
deba@2548: nodes[nodes[id].next].prev = jd;
deba@2548: if (kd >= 0) {
deba@2548: nodes[kd].size += 1;
deba@2548: }
deba@2548: } else {
deba@2548: if (kd >= 0) {
deba@2548: nodes[kd].right = jd;
deba@2548: nodes[kd].size += 1;
deba@2548: }
deba@2548: }
deba@2548: nodes[jd].next = nodes[id].next;
deba@2548: nodes[jd].prev = id;
deba@2548: nodes[id].next = jd;
deba@2548: nodes[jd].parent = kd;
deba@2548: }
deba@2548:
deba@2548: void pushRight(int id, int jd) {
deba@2548: nodes[id].size += 1;
deba@2548: nodes[jd].prev = nodes[id].right;
deba@2548: nodes[jd].next = -1;
deba@2548: nodes[nodes[id].right].next = jd;
deba@2548: nodes[id].right = jd;
deba@2548: nodes[jd].parent = id;
deba@2548: }
deba@2548:
deba@2548: void popRight(int id) {
deba@2548: nodes[id].size -= 1;
deba@2548: int jd = nodes[id].right;
deba@2548: nodes[nodes[jd].prev].next = -1;
deba@2548: nodes[id].right = nodes[jd].prev;
deba@2548: }
deba@2548:
deba@2548: void splice(int id, int jd) {
deba@2548: nodes[id].size += nodes[jd].size;
deba@2548: nodes[nodes[id].right].next = nodes[jd].left;
deba@2548: nodes[nodes[jd].left].prev = nodes[id].right;
deba@2548: int kd = nodes[jd].left;
deba@2548: while (kd != -1) {
deba@2548: nodes[kd].parent = id;
deba@2548: kd = nodes[kd].next;
deba@2548: }
deba@2550: nodes[id].right = nodes[jd].right;
deba@2548: }
deba@2548:
deba@2548: void split(int id, int jd) {
deba@2548: int kd = nodes[id].parent;
deba@2548: nodes[kd].right = nodes[id].prev;
deba@2548: nodes[nodes[id].prev].next = -1;
deba@2548:
deba@2548: nodes[jd].left = id;
deba@2548: nodes[id].prev = -1;
deba@2548: int num = 0;
deba@2548: while (id != -1) {
deba@2548: nodes[id].parent = jd;
deba@2548: nodes[jd].right = id;
deba@2548: id = nodes[id].next;
deba@2548: ++num;
deba@2548: }
deba@2548: nodes[kd].size -= num;
deba@2548: nodes[jd].size = num;
deba@2548: }
deba@2548:
deba@2548: void pushLeft(int id, int jd) {
deba@2548: nodes[id].size += 1;
deba@2548: nodes[jd].next = nodes[id].left;
deba@2548: nodes[jd].prev = -1;
deba@2548: nodes[nodes[id].left].prev = jd;
deba@2548: nodes[id].left = jd;
deba@2548: nodes[jd].parent = id;
deba@2548: }
deba@2548:
deba@2548: void popLeft(int id) {
deba@2548: nodes[id].size -= 1;
deba@2548: int jd = nodes[id].left;
deba@2548: nodes[nodes[jd].next].prev = -1;
deba@2548: nodes[id].left = nodes[jd].next;
deba@2548: }
deba@2548:
deba@2548: void repairLeft(int id) {
deba@2548: int jd = ~(classes[id].parent);
deba@2548: while (nodes[jd].left != -1) {
deba@2548: int kd = nodes[jd].left;
deba@2548: if (nodes[jd].size == 1) {
deba@2548: if (nodes[jd].parent < 0) {
deba@2548: classes[id].parent = ~kd;
deba@2548: classes[id].depth -= 1;
deba@2548: nodes[kd].parent = ~id;
deba@2548: deleteNode(jd);
deba@2548: jd = kd;
deba@2548: } else {
deba@2548: int pd = nodes[jd].parent;
deba@2548: if (nodes[nodes[jd].next].size < cmax) {
deba@2548: pushLeft(nodes[jd].next, nodes[jd].left);
deba@2548: if (less(nodes[jd].left, nodes[jd].next)) {
deba@2548: nodes[nodes[jd].next].prio = nodes[nodes[jd].left].prio;
deba@2548: nodes[nodes[jd].next].item = nodes[nodes[jd].left].item;
deba@2548: }
deba@2548: popLeft(pd);
deba@2548: deleteNode(jd);
deba@2548: jd = pd;
deba@2548: } else {
deba@2548: int ld = nodes[nodes[jd].next].left;
deba@2548: popLeft(nodes[jd].next);
deba@2548: pushRight(jd, ld);
deba@2548: if (less(ld, nodes[jd].left)) {
deba@2548: nodes[jd].item = nodes[ld].item;
deba@2548: nodes[jd].prio = nodes[jd].prio;
deba@2548: }
deba@2548: if (nodes[nodes[jd].next].item == nodes[ld].item) {
deba@2548: setPrio(nodes[jd].next);
deba@2548: }
deba@2548: jd = nodes[jd].left;
deba@2548: }
deba@2548: }
deba@2548: } else {
deba@2548: jd = nodes[jd].left;
deba@2548: }
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: void repairRight(int id) {
deba@2548: int jd = ~(classes[id].parent);
deba@2548: while (nodes[jd].right != -1) {
deba@2548: int kd = nodes[jd].right;
deba@2548: if (nodes[jd].size == 1) {
deba@2548: if (nodes[jd].parent < 0) {
deba@2548: classes[id].parent = ~kd;
deba@2548: classes[id].depth -= 1;
deba@2548: nodes[kd].parent = ~id;
deba@2548: deleteNode(jd);
deba@2548: jd = kd;
deba@2548: } else {
deba@2548: int pd = nodes[jd].parent;
deba@2548: if (nodes[nodes[jd].prev].size < cmax) {
deba@2548: pushRight(nodes[jd].prev, nodes[jd].right);
deba@2548: if (less(nodes[jd].right, nodes[jd].prev)) {
deba@2548: nodes[nodes[jd].prev].prio = nodes[nodes[jd].right].prio;
deba@2548: nodes[nodes[jd].prev].item = nodes[nodes[jd].right].item;
deba@2548: }
deba@2548: popRight(pd);
deba@2548: deleteNode(jd);
deba@2548: jd = pd;
deba@2548: } else {
deba@2548: int ld = nodes[nodes[jd].prev].right;
deba@2548: popRight(nodes[jd].prev);
deba@2548: pushLeft(jd, ld);
deba@2548: if (less(ld, nodes[jd].right)) {
deba@2548: nodes[jd].item = nodes[ld].item;
deba@2548: nodes[jd].prio = nodes[jd].prio;
deba@2548: }
deba@2548: if (nodes[nodes[jd].prev].item == nodes[ld].item) {
deba@2548: setPrio(nodes[jd].prev);
deba@2548: }
deba@2548: jd = nodes[jd].right;
deba@2548: }
deba@2548: }
deba@2548: } else {
deba@2548: jd = nodes[jd].right;
deba@2548: }
deba@2548: }
deba@2548: }
deba@2548:
deba@2548:
deba@2548: bool less(int id, int jd) const {
deba@2548: return comp(nodes[id].prio, nodes[jd].prio);
deba@2548: }
deba@2548:
deba@2548: bool equal(int id, int jd) const {
deba@2548: return !less(id, jd) && !less(jd, id);
deba@2548: }
deba@2548:
deba@2548:
deba@2548: public:
deba@2548:
deba@2548: /// \brief Returns true when the given class is alive.
deba@2548: ///
deba@2548: /// Returns true when the given class is alive, ie. the class is
deba@2548: /// not nested into other class.
deba@2548: bool alive(int cls) const {
deba@2548: return classes[cls].parent < 0;
deba@2548: }
deba@2548:
deba@2548: /// \brief Returns true when the given class is trivial.
deba@2548: ///
deba@2548: /// Returns true when the given class is trivial, ie. the class
deba@2548: /// contains just one item directly.
deba@2548: bool trivial(int cls) const {
deba@2548: return classes[cls].left == -1;
deba@2548: }
deba@2548:
deba@2548: /// \brief Constructs the union-find.
deba@2548: ///
deba@2548: /// Constructs the union-find.
deba@2548: /// \brief _index The index map of the union-find. The data
deba@2548: /// structure uses internally for store references.
deba@2548: HeapUnionFind(ItemIntMap& _index)
deba@2548: : index(_index), first_class(-1),
deba@2548: first_free_class(-1), first_free_node(-1) {}
deba@2548:
deba@2548: /// \brief Insert a new node into a new component.
deba@2548: ///
deba@2548: /// Insert a new node into a new component.
deba@2548: /// \param item The item of the new node.
deba@2548: /// \param prio The priority of the new node.
deba@2548: /// \return The class id of the one-item-heap.
deba@2548: int insert(const Item& item, const Value& prio) {
deba@2548: int id = newNode();
deba@2548: nodes[id].item = item;
deba@2548: nodes[id].prio = prio;
deba@2548: nodes[id].size = 0;
deba@2548:
deba@2548: nodes[id].prev = -1;
deba@2548: nodes[id].next = -1;
deba@2548:
deba@2548: nodes[id].left = -1;
deba@2548: nodes[id].right = -1;
deba@2548:
deba@2548: nodes[id].item = item;
deba@2548: index[item] = id;
deba@2548:
deba@2548: int class_id = newClass();
deba@2548: classes[class_id].parent = ~id;
deba@2548: classes[class_id].depth = 0;
deba@2548:
deba@2548: classes[class_id].left = -1;
deba@2548: classes[class_id].right = -1;
deba@2548:
deba@2548: if (first_class != -1) {
deba@2548: classes[first_class].prev = class_id;
deba@2548: }
deba@2548: classes[class_id].next = first_class;
deba@2548: classes[class_id].prev = -1;
deba@2548: first_class = class_id;
deba@2548:
deba@2548: nodes[id].parent = ~class_id;
deba@2548:
deba@2548: return class_id;
deba@2548: }
deba@2548:
deba@2548: /// \brief The class of the item.
deba@2548: ///
deba@2548: /// \return The alive class id of the item, which is not nested into
deba@2548: /// other classes.
deba@2548: ///
deba@2548: /// The time complexity is O(log(n)).
deba@2548: int find(const Item& item) const {
deba@2548: return findClass(index[item]);
deba@2548: }
deba@2548:
deba@2548: /// \brief Joins the classes.
deba@2548: ///
deba@2548: /// The current function joins the given classes. The parameter is
deba@2548: /// an STL range which should be contains valid class ids. The
deba@2548: /// time complexity is O(log(n)*k) where n is the overall number
deba@2548: /// of the joined nodes and k is the number of classes.
deba@2548: /// \return The class of the joined classes.
deba@2548: /// \pre The range should contain at least two class ids.
deba@2548: template <typename Iterator>
deba@2548: int join(Iterator begin, Iterator end) {
deba@2548: std::vector<int> cs;
deba@2548: for (Iterator it = begin; it != end; ++it) {
deba@2548: cs.push_back(*it);
deba@2548: }
deba@2548:
deba@2548: int class_id = newClass();
deba@2548: { // creation union-find
deba@2548:
deba@2548: if (first_class != -1) {
deba@2548: classes[first_class].prev = class_id;
deba@2548: }
deba@2548: classes[class_id].next = first_class;
deba@2548: classes[class_id].prev = -1;
deba@2548: first_class = class_id;
deba@2548:
deba@2548: classes[class_id].depth = classes[cs[0]].depth;
deba@2548: classes[class_id].parent = classes[cs[0]].parent;
deba@2548: nodes[~(classes[class_id].parent)].parent = ~class_id;
deba@2548:
deba@2548: int l = cs[0];
deba@2548:
deba@2548: classes[class_id].left = l;
deba@2548: classes[class_id].right = l;
deba@2548:
deba@2548: if (classes[l].next != -1) {
deba@2548: classes[classes[l].next].prev = classes[l].prev;
deba@2548: }
deba@2548: classes[classes[l].prev].next = classes[l].next;
deba@2548:
deba@2548: classes[l].prev = -1;
deba@2548: classes[l].next = -1;
deba@2548:
deba@2548: classes[l].depth = leftNode(l);
deba@2548: classes[l].parent = class_id;
deba@2548:
deba@2548: }
deba@2548:
deba@2548: { // merging of heap
deba@2548: int l = class_id;
deba@2548: for (int ci = 1; ci < int(cs.size()); ++ci) {
deba@2548: int r = cs[ci];
deba@2548: int rln = leftNode(r);
deba@2548: if (classes[l].depth > classes[r].depth) {
deba@2548: int id = ~(classes[l].parent);
deba@2548: for (int i = classes[r].depth + 1; i < classes[l].depth; ++i) {
deba@2548: id = nodes[id].right;
deba@2548: }
deba@2548: while (id >= 0 && nodes[id].size == cmax) {
deba@2548: int new_id = newNode();
deba@2548: int right_id = nodes[id].right;
deba@2548:
deba@2548: popRight(id);
deba@2548: if (nodes[id].item == nodes[right_id].item) {
deba@2548: setPrio(id);
deba@2548: }
deba@2548: push(new_id, right_id);
deba@2548: pushRight(new_id, ~(classes[r].parent));
deba@2548: setPrio(new_id);
deba@2548:
deba@2548: id = nodes[id].parent;
deba@2548: classes[r].parent = ~new_id;
deba@2548: }
deba@2548: if (id < 0) {
deba@2548: int new_parent = newNode();
deba@2548: nodes[new_parent].next = -1;
deba@2548: nodes[new_parent].prev = -1;
deba@2548: nodes[new_parent].parent = ~l;
deba@2548:
deba@2548: push(new_parent, ~(classes[l].parent));
deba@2548: pushRight(new_parent, ~(classes[r].parent));
deba@2548: setPrio(new_parent);
deba@2548:
deba@2548: classes[l].parent = ~new_parent;
deba@2548: classes[l].depth += 1;
deba@2548: } else {
deba@2548: pushRight(id, ~(classes[r].parent));
deba@2548: while (id >= 0 && less(~(classes[r].parent), id)) {
deba@2548: nodes[id].prio = nodes[~(classes[r].parent)].prio;
deba@2548: nodes[id].item = nodes[~(classes[r].parent)].item;
deba@2548: id = nodes[id].parent;
deba@2548: }
deba@2548: }
deba@2548: } else if (classes[r].depth > classes[l].depth) {
deba@2548: int id = ~(classes[r].parent);
deba@2548: for (int i = classes[l].depth + 1; i < classes[r].depth; ++i) {
deba@2548: id = nodes[id].left;
deba@2548: }
deba@2548: while (id >= 0 && nodes[id].size == cmax) {
deba@2548: int new_id = newNode();
deba@2548: int left_id = nodes[id].left;
deba@2548:
deba@2548: popLeft(id);
deba@2548: if (nodes[id].prio == nodes[left_id].prio) {
deba@2548: setPrio(id);
deba@2548: }
deba@2548: push(new_id, left_id);
deba@2548: pushLeft(new_id, ~(classes[l].parent));
deba@2548: setPrio(new_id);
deba@2548:
deba@2548: id = nodes[id].parent;
deba@2548: classes[l].parent = ~new_id;
deba@2548:
deba@2548: }
deba@2548: if (id < 0) {
deba@2548: int new_parent = newNode();
deba@2548: nodes[new_parent].next = -1;
deba@2548: nodes[new_parent].prev = -1;
deba@2548: nodes[new_parent].parent = ~l;
deba@2548:
deba@2548: push(new_parent, ~(classes[r].parent));
deba@2548: pushLeft(new_parent, ~(classes[l].parent));
deba@2548: setPrio(new_parent);
deba@2548:
deba@2548: classes[r].parent = ~new_parent;
deba@2548: classes[r].depth += 1;
deba@2548: } else {
deba@2548: pushLeft(id, ~(classes[l].parent));
deba@2548: while (id >= 0 && less(~(classes[l].parent), id)) {
deba@2548: nodes[id].prio = nodes[~(classes[l].parent)].prio;
deba@2548: nodes[id].item = nodes[~(classes[l].parent)].item;
deba@2548: id = nodes[id].parent;
deba@2548: }
deba@2548: }
deba@2548: nodes[~(classes[r].parent)].parent = ~l;
deba@2548: classes[l].parent = classes[r].parent;
deba@2548: classes[l].depth = classes[r].depth;
deba@2548: } else {
deba@2548: if (classes[l].depth != 0 &&
deba@2548: nodes[~(classes[l].parent)].size +
deba@2548: nodes[~(classes[r].parent)].size <= cmax) {
deba@2548: splice(~(classes[l].parent), ~(classes[r].parent));
deba@2548: deleteNode(~(classes[r].parent));
deba@2548: if (less(~(classes[r].parent), ~(classes[l].parent))) {
deba@2548: nodes[~(classes[l].parent)].prio =
deba@2548: nodes[~(classes[r].parent)].prio;
deba@2548: nodes[~(classes[l].parent)].item =
deba@2548: nodes[~(classes[r].parent)].item;
deba@2548: }
deba@2548: } else {
deba@2548: int new_parent = newNode();
deba@2548: nodes[new_parent].next = nodes[new_parent].prev = -1;
deba@2548: push(new_parent, ~(classes[l].parent));
deba@2548: pushRight(new_parent, ~(classes[r].parent));
deba@2548: setPrio(new_parent);
deba@2548:
deba@2548: classes[l].parent = ~new_parent;
deba@2548: classes[l].depth += 1;
deba@2548: nodes[new_parent].parent = ~l;
deba@2548: }
deba@2548: }
deba@2548: if (classes[r].next != -1) {
deba@2548: classes[classes[r].next].prev = classes[r].prev;
deba@2548: }
deba@2548: classes[classes[r].prev].next = classes[r].next;
deba@2548:
deba@2548: classes[r].prev = classes[l].right;
deba@2548: classes[classes[l].right].next = r;
deba@2548: classes[l].right = r;
deba@2548: classes[r].parent = l;
deba@2548:
deba@2548: classes[r].next = -1;
deba@2548: classes[r].depth = rln;
deba@2548: }
deba@2548: }
deba@2548: return class_id;
deba@2548: }
deba@2548:
deba@2548: /// \brief Split the class to subclasses.
deba@2548: ///
deba@2548: /// The current function splits the given class. The join, which
deba@2548: /// made the current class, stored a reference to the
deba@2548: /// subclasses. The \c splitClass() member restores the classes
deba@2548: /// and creates the heaps. The parameter is an STL output iterator
deba@2548: /// which will be filled with the subclass ids. The time
deba@2548: /// complexity is O(log(n)*k) where n is the overall number of
deba@2548: /// nodes in the splitted classes and k is the number of the
deba@2548: /// classes.
deba@2548: template <typename Iterator>
deba@2548: void split(int cls, Iterator out) {
deba@2548: std::vector<int> cs;
deba@2548: { // splitting union-find
deba@2548: int id = cls;
deba@2548: int l = classes[id].left;
deba@2548:
deba@2548: classes[l].parent = classes[id].parent;
deba@2548: classes[l].depth = classes[id].depth;
deba@2548:
deba@2548: nodes[~(classes[l].parent)].parent = ~l;
deba@2548:
deba@2548: *out++ = l;
deba@2548:
deba@2548: while (l != -1) {
deba@2548: cs.push_back(l);
deba@2548: l = classes[l].next;
deba@2548: }
deba@2548:
deba@2548: classes[classes[id].right].next = first_class;
deba@2548: classes[first_class].prev = classes[id].right;
deba@2548: first_class = classes[id].left;
deba@2548:
deba@2548: if (classes[id].next != -1) {
deba@2548: classes[classes[id].next].prev = classes[id].prev;
deba@2548: }
deba@2548: classes[classes[id].prev].next = classes[id].next;
deba@2548:
deba@2548: deleteClass(id);
deba@2548: }
deba@2548:
deba@2548: {
deba@2548: for (int i = 1; i < int(cs.size()); ++i) {
deba@2548: int l = classes[cs[i]].depth;
deba@2548: while (nodes[nodes[l].parent].left == l) {
deba@2548: l = nodes[l].parent;
deba@2548: }
deba@2548: int r = l;
deba@2548: while (nodes[l].parent >= 0) {
deba@2548: l = nodes[l].parent;
deba@2548: int new_node = newNode();
deba@2548:
deba@2548: nodes[new_node].prev = -1;
deba@2548: nodes[new_node].next = -1;
deba@2548:
deba@2548: split(r, new_node);
deba@2548: pushAfter(l, new_node);
deba@2548: setPrio(l);
deba@2548: setPrio(new_node);
deba@2548: r = new_node;
deba@2548: }
deba@2548: classes[cs[i]].parent = ~r;
deba@2548: classes[cs[i]].depth = classes[~(nodes[l].parent)].depth;
deba@2548: nodes[r].parent = ~cs[i];
deba@2548:
deba@2548: nodes[l].next = -1;
deba@2548: nodes[r].prev = -1;
deba@2548:
deba@2548: repairRight(~(nodes[l].parent));
deba@2548: repairLeft(cs[i]);
deba@2548:
deba@2548: *out++ = cs[i];
deba@2548: }
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: /// \brief Gives back the priority of the current item.
deba@2548: ///
deba@2548: /// \return Gives back the priority of the current item.
deba@2548: const Value& operator[](const Item& item) const {
deba@2548: return nodes[index[item]].prio;
deba@2548: }
deba@2548:
deba@2548: /// \brief Sets the priority of the current item.
deba@2548: ///
deba@2548: /// Sets the priority of the current item.
deba@2548: void set(const Item& item, const Value& prio) {
deba@2548: if (comp(prio, nodes[index[item]].prio)) {
deba@2548: decrease(item, prio);
deba@2548: } else if (!comp(prio, nodes[index[item]].prio)) {
deba@2548: increase(item, prio);
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: /// \brief Increase the priority of the current item.
deba@2548: ///
deba@2548: /// Increase the priority of the current item.
deba@2548: void increase(const Item& item, const Value& prio) {
deba@2548: int id = index[item];
deba@2548: int kd = nodes[id].parent;
deba@2548: nodes[id].prio = prio;
deba@2548: while (kd >= 0 && nodes[kd].item == item) {
deba@2548: setPrio(kd);
deba@2548: kd = nodes[kd].parent;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: /// \brief Increase the priority of the current item.
deba@2548: ///
deba@2548: /// Increase the priority of the current item.
deba@2548: void decrease(const Item& item, const Value& prio) {
deba@2548: int id = index[item];
deba@2548: int kd = nodes[id].parent;
deba@2548: nodes[id].prio = prio;
deba@2548: while (kd >= 0 && less(id, kd)) {
deba@2548: nodes[kd].prio = prio;
deba@2548: nodes[kd].item = item;
deba@2548: kd = nodes[kd].parent;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: /// \brief Gives back the minimum priority of the class.
deba@2548: ///
deba@2548: /// \return Gives back the minimum priority of the class.
deba@2548: const Value& classPrio(int cls) const {
deba@2548: return nodes[~(classes[cls].parent)].prio;
deba@2548: }
deba@2548:
deba@2548: /// \brief Gives back the minimum priority item of the class.
deba@2548: ///
deba@2548: /// \return Gives back the minimum priority item of the class.
deba@2548: const Item& classTop(int cls) const {
deba@2548: return nodes[~(classes[cls].parent)].item;
deba@2548: }
deba@2548:
deba@2548: /// \brief Gives back a representant item of the class.
deba@2548: ///
deba@2548: /// The representant is indpendent from the priorities of the
deba@2548: /// items.
deba@2548: /// \return Gives back a representant item of the class.
deba@2548: const Item& classRep(int id) const {
deba@2548: int parent = classes[id].parent;
deba@2548: return nodes[parent >= 0 ? classes[id].depth : leftNode(id)].item;
deba@2548: }
deba@2548:
deba@2548: /// \brief Lemon style iterator for the items of a class.
deba@2548: ///
deba@2548: /// ClassIt is a lemon style iterator for the components. It iterates
deba@2548: /// on the items of a class. By example if you want to iterate on
deba@2548: /// each items of each classes then you may write the next code.
deba@2548: ///\code
deba@2548: /// for (ClassIt cit(huf); cit != INVALID; ++cit) {
deba@2548: /// std::cout << "Class: ";
deba@2548: /// for (ItemIt iit(huf, cit); iit != INVALID; ++iit) {
deba@2548: /// std::cout << toString(iit) << ' ' << std::endl;
deba@2548: /// }
deba@2548: /// std::cout << std::endl;
deba@2548: /// }
deba@2548: ///\endcode
deba@2548: class ItemIt {
deba@2548: private:
deba@2548:
deba@2548: const HeapUnionFind* _huf;
deba@2548: int _id, _lid;
deba@2548:
deba@2548: public:
deba@2548:
deba@2548: /// \brief Default constructor
deba@2548: ///
deba@2548: /// Default constructor
deba@2548: ItemIt() {}
deba@2548:
deba@2548: ItemIt(const HeapUnionFind& huf, int cls) : _huf(&huf) {
deba@2548: int id = cls;
deba@2548: int parent = _huf->classes[id].parent;
deba@2548: if (parent >= 0) {
deba@2548: _id = _huf->classes[id].depth;
deba@2548: if (_huf->classes[id].next != -1) {
deba@2548: _lid = _huf->classes[_huf->classes[id].next].depth;
deba@2548: } else {
deba@2548: _lid = -1;
deba@2548: }
deba@2548: } else {
deba@2548: _id = _huf->leftNode(id);
deba@2548: _lid = -1;
deba@2548: }
deba@2548: }
deba@2548:
deba@2548: /// \brief Increment operator
deba@2548: ///
deba@2548: /// It steps to the next item in the class.
deba@2548: ItemIt& operator++() {
deba@2548: _id = _huf->nextNode(_id);
deba@2548: return *this;
deba@2548: }
deba@2548:
deba@2548: /// \brief Conversion operator
deba@2548: ///
deba@2548: /// It converts the iterator to the current item.
deba@2548: operator const Item&() const {
deba@2548: return _huf->nodes[_id].item;
deba@2548: }
deba@2548:
deba@2548: /// \brief Equality operator
deba@2548: ///
deba@2548: /// Equality operator
deba@2548: bool operator==(const ItemIt& i) {
deba@2548: return i._id == _id;
deba@2548: }
deba@2548:
deba@2548: /// \brief Inequality operator
deba@2548: ///
deba@2548: /// Inequality operator
deba@2548: bool operator!=(const ItemIt& i) {
deba@2548: return i._id != _id;
deba@2548: }
deba@2548:
deba@2548: /// \brief Equality operator
deba@2548: ///
deba@2548: /// Equality operator
deba@2548: bool operator==(Invalid) {
deba@2548: return _id == _lid;
deba@2548: }
deba@2548:
deba@2548: /// \brief Inequality operator
deba@2548: ///
deba@2548: /// Inequality operator
deba@2548: bool operator!=(Invalid) {
deba@2548: return _id != _lid;
deba@2548: }
deba@2548:
deba@2548: };
deba@2548:
deba@2548: /// \brief Class iterator
deba@2548: ///
deba@2548: /// The iterator stores
deba@2548: class ClassIt {
deba@2548: private:
deba@2548:
deba@2548: const HeapUnionFind* _huf;
deba@2548: int _id;
deba@2548:
deba@2548: public:
deba@2548:
deba@2548: ClassIt(const HeapUnionFind& huf)
deba@2548: : _huf(&huf), _id(huf.first_class) {}
deba@2548:
deba@2548: ClassIt(const HeapUnionFind& huf, int cls)
deba@2548: : _huf(&huf), _id(huf.classes[cls].left) {}
deba@2548:
deba@2548: ClassIt(Invalid) : _huf(0), _id(-1) {}
deba@2548:
deba@2548: const ClassIt& operator++() {
deba@2548: _id = _huf->classes[_id].next;
deba@2548: return *this;
deba@2548: }
deba@2548:
deba@2548: /// \brief Equality operator
deba@2548: ///
deba@2548: /// Equality operator
deba@2548: bool operator==(const ClassIt& i) {
deba@2548: return i._id == _id;
deba@2548: }
deba@2548:
deba@2548: /// \brief Inequality operator
deba@2548: ///
deba@2548: /// Inequality operator
deba@2548: bool operator!=(const ClassIt& i) {
deba@2548: return i._id != _id;
deba@2548: }
deba@2548:
deba@2548: operator int() const {
deba@2548: return _id;
deba@2548: }
deba@2548:
deba@2548: };
deba@2548:
deba@2548: };
deba@2548:
beckerjc@483: //! @}
beckerjc@483:
alpar@921: } //namespace lemon
beckerjc@483:
alpar@921: #endif //LEMON_UNION_FIND_H