/* -*- C++ -*-
 *
 * This file is a part of LEMON, a generic C++ optimization library
 *
 * Copyright (C) 2003-2007
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
 *
 * Permission to use, modify and distribute this software is granted
 * provided that this copyright notice appears in all copies. For
 * precise terms see the accompanying LICENSE file.
 *
 * This software is provided "AS IS" with no warranty of any kind,
 * express or implied, and with no claim as to its suitability for any
 * purpose.
 *
 */

#ifndef LEMON_UNION_FIND_H
#define LEMON_UNION_FIND_H

//!\ingroup auxdat
//!\file
//!\brief Union-Find data structures.
//!

#include <vector>
#include <list>
#include <utility>
#include <algorithm>

#include <lemon/bits/invalid.h>

namespace lemon {

  /// \ingroup auxdat
  ///
  /// \brief A \e Union-Find data structure implementation
  ///
  /// The class implements the \e Union-Find data structure. 
  /// The union operation uses rank heuristic, while
  /// the find operation uses path compression.
  /// This is a very simple but efficient implementation, providing 
  /// only four methods: join (union), find, insert and size.
  /// For more features see the \ref UnionFindEnum class.
  ///
  /// It is primarily used in Kruskal algorithm for finding minimal
  /// cost spanning tree in a graph.
  /// \sa kruskal()
  ///
  /// \pre You need to add all the elements by the \ref insert()
  /// method.  
  template <typename _ItemIntMap>
  class UnionFind {
  public:

    typedef _ItemIntMap ItemIntMap;
    typedef typename ItemIntMap::Key Item;

  private:
    // If the items vector stores negative value for an item then
    // that item is root item and it has -items[it] component size.
    // Else the items[it] contains the index of the parent.
    std::vector<int> items;
    ItemIntMap& index;

    bool rep(int idx) const {
      return items[idx] < 0;
    }

    int repIndex(int idx) const {
      int k = idx;
      while (!rep(k)) {
        k = items[k] ;
      }
      while (idx != k) {
        int next = items[idx];
        const_cast<int&>(items[idx]) = k;
        idx = next;
      }
      return k;
    }

  public:

    /// \brief Constructor
    ///
    /// Constructor of the UnionFind class. You should give an item to
    /// integer map which will be used from the data structure. If you
    /// modify directly this map that may cause segmentation fault,
    /// invalid data structure, or infinite loop when you use again
    /// the union-find.
    UnionFind(ItemIntMap& m) : index(m) {}

    /// \brief Returns the index of the element's component.
    ///
    /// The method returns the index of the element's component.
    /// This is an integer between zero and the number of inserted elements.
    ///
    int find(const Item& a) {
      return repIndex(index[a]);
    }

    /// \brief Clears the union-find data structure
    ///
    /// Erase each item from the data structure.
    void clear() {
      items.clear();
    }

    /// \brief Inserts a new element into the structure.
    ///
    /// This method inserts a new element into the data structure. 
    ///
    /// The method returns the index of the new component.
    int insert(const Item& a) {
      int n = items.size();
      items.push_back(-1);
      index.set(a,n);
      return n;
    }

    /// \brief Joining the components of element \e a and element \e b.
    ///
    /// This is the \e union operation of the Union-Find structure. 
    /// Joins the component of element \e a and component of
    /// element \e b. If \e a and \e b are in the same component then
    /// it returns false otherwise it returns true.
    bool join(const Item& a, const Item& b) {
      int ka = repIndex(index[a]);
      int kb = repIndex(index[b]);

      if ( ka == kb ) 
	return false;

      if (items[ka] < items[kb]) {
	items[ka] += items[kb];
	items[kb] = ka;
      } else {
	items[kb] += items[ka];
	items[ka] = kb;
      }
      return true;
    }

    /// \brief Returns the size of the component of element \e a.
    ///
    /// Returns the size of the component of element \e a.
    int size(const Item& a) {
      int k = repIndex(index[a]);
      return - items[k];
    }

  };

  /// \ingroup auxdat
  ///
  /// \brief A \e Union-Find data structure implementation which
  /// is able to enumerate the components.
  ///
  /// The class implements a \e Union-Find data structure
  /// which is able to enumerate the components and the items in
  /// a component. If you don't need this feature then perhaps it's
  /// better to use the \ref UnionFind class which is more efficient.
  ///
  /// The union operation uses rank heuristic, while
  /// the find operation uses path compression.
  ///
  /// \pre You need to add all the elements by the \ref insert()
  /// method.
  ///
  template <typename _ItemIntMap>
  class UnionFindEnum {
  public:
    
    typedef _ItemIntMap ItemIntMap;
    typedef typename ItemIntMap::Key Item;

  private:
    
    ItemIntMap& index;

    // If the parent stores negative value for an item then that item
    // is root item and it has ~(items[it].parent) component id.  Else
    // the items[it].parent contains the index of the parent.
    //
    // The \c next and \c prev provides the double-linked
    // cyclic list of one component's items.
    struct ItemT {
      int parent;
      Item item;

      int next, prev;
    };

    std::vector<ItemT> items;
    int firstFreeItem;

    struct ClassT {
      int size;
      int firstItem;
      int next, prev;
    };
    
    std::vector<ClassT> classes;
    int firstClass, firstFreeClass;

    int newClass() {
      if (firstFreeClass == -1) {
	int cdx = classes.size();
	classes.push_back(ClassT());
	return cdx;
      } else {
	int cdx = firstFreeClass;
	firstFreeClass = classes[firstFreeClass].next;
	return cdx;
      }
    }

    int newItem() {
      if (firstFreeItem == -1) {
	int idx = items.size();
	items.push_back(ItemT());
	return idx;
      } else {
	int idx = firstFreeItem;
	firstFreeItem = items[firstFreeItem].next;
	return idx;
      }
    }


    bool rep(int idx) const {
      return items[idx].parent < 0;
    }

    int repIndex(int idx) const {
      int k = idx;
      while (!rep(k)) {
        k = items[k].parent;
      }
      while (idx != k) {
        int next = items[idx].parent;
        const_cast<int&>(items[idx].parent) = k;
        idx = next;
      }
      return k;
    }

    int classIndex(int idx) const {
      return ~(items[repIndex(idx)].parent);
    }

    void singletonItem(int idx) {
      items[idx].next = idx;
      items[idx].prev = idx;
    }

    void laceItem(int idx, int rdx) {
      items[idx].prev = rdx;
      items[idx].next = items[rdx].next;
      items[items[rdx].next].prev = idx;
      items[rdx].next = idx;
    }

    void unlaceItem(int idx) {
      items[items[idx].prev].next = items[idx].next;
      items[items[idx].next].prev = items[idx].prev;
      
      items[idx].next = firstFreeItem;
      firstFreeItem = idx;
    }

    void spliceItems(int ak, int bk) {
      items[items[ak].prev].next = bk;
      items[items[bk].prev].next = ak;
      int tmp = items[ak].prev;
      items[ak].prev = items[bk].prev;
      items[bk].prev = tmp;
        
    }

    void laceClass(int cls) {
      if (firstClass != -1) {
        classes[firstClass].prev = cls;
      }
      classes[cls].next = firstClass;
      classes[cls].prev = -1;
      firstClass = cls;
    } 

    void unlaceClass(int cls) {
      if (classes[cls].prev != -1) {
        classes[classes[cls].prev].next = classes[cls].next;
      } else {
        firstClass = classes[cls].next;
      }
      if (classes[cls].next != -1) {
        classes[classes[cls].next].prev = classes[cls].prev;
      }
      
      classes[cls].next = firstFreeClass;
      firstFreeClass = cls;
    } 

  public:

    UnionFindEnum(ItemIntMap& _index) 
      : index(_index), items(), firstFreeItem(-1), 
	firstClass(-1), firstFreeClass(-1) {}
    
    /// \brief Inserts the given element into a new component.
    ///
    /// This method creates a new component consisting only of the
    /// given element.
    ///
    int insert(const Item& item) {
      int idx = newItem();

      index.set(item, idx);

      singletonItem(idx);
      items[idx].item = item;

      int cdx = newClass();

      items[idx].parent = ~cdx;

      laceClass(cdx);
      classes[cdx].size = 1;
      classes[cdx].firstItem = idx;

      firstClass = cdx;
      
      return cdx;
    }

    /// \brief Inserts the given element into the component of the others.
    ///
    /// This methods inserts the element \e a into the component of the
    /// element \e comp. 
    void insert(const Item& item, int cls) {
      int rdx = classes[cls].firstItem;
      int idx = newItem();

      index.set(item, idx);

      laceItem(idx, rdx);

      items[idx].item = item;
      items[idx].parent = rdx;

      ++classes[~(items[rdx].parent)].size;
    }

    /// \brief Clears the union-find data structure
    ///
    /// Erase each item from the data structure.
    void clear() {
      items.clear();
      firstClass = -1;
      firstFreeItem = -1;
    }

    /// \brief Finds the component of the given element.
    ///
    /// The method returns the component id of the given element.
    int find(const Item &item) const {
      return ~(items[repIndex(index[item])].parent);
    }

    /// \brief Joining the component of element \e a and element \e b.
    ///
    /// This is the \e union operation of the Union-Find structure. 
    /// Joins the component of element \e a and component of
    /// element \e b. If \e a and \e b are in the same component then
    /// returns -1 else returns the remaining class.
    int join(const Item& a, const Item& b) {

      int ak = repIndex(index[a]);
      int bk = repIndex(index[b]);

      if (ak == bk) {
	return -1;
      }

      int acx = ~(items[ak].parent);
      int bcx = ~(items[bk].parent);

      int rcx;

      if (classes[acx].size > classes[bcx].size) {
	classes[acx].size += classes[bcx].size;
	items[bk].parent = ak;
        unlaceClass(bcx);
	rcx = acx;
      } else {
	classes[bcx].size += classes[acx].size;
	items[ak].parent = bk;
        unlaceClass(acx);
	rcx = bcx;
      }
      spliceItems(ak, bk);

      return rcx;
    }

    /// \brief Returns the size of the class.
    ///
    /// Returns the size of the class.
    int size(int cls) const {
      return classes[cls].size;
    }

    /// \brief Splits up the component. 
    ///
    /// Splitting the component into singleton components (component
    /// of size one).
    void split(int cls) {
      int fdx = classes[cls].firstItem;
      int idx = items[fdx].next;
      while (idx != fdx) {
        int next = items[idx].next;

	singletonItem(idx);

	int cdx = newClass();        
        items[idx].parent = ~cdx;

	laceClass(cdx);
	classes[cdx].size = 1;
	classes[cdx].firstItem = idx;
        
        idx = next;
      }

      items[idx].prev = idx;
      items[idx].next = idx;

      classes[~(items[idx].parent)].size = 1;
      
    }

    /// \brief Removes the given element from the structure.
    ///
    /// Removes the element from its component and if the component becomes
    /// empty then removes that component from the component list.
    ///
    /// \warning It is an error to remove an element which is not in
    /// the structure.
    /// \warning This running time of this operation is proportional to the
    /// number of the items in this class.
    void erase(const Item& item) {
      int idx = index[item];
      int fdx = items[idx].next;

      int cdx = classIndex(idx);
      if (idx == fdx) {
	unlaceClass(cdx);
	items[idx].next = firstFreeItem;
	firstFreeItem = idx;
	return;
      } else {
	classes[cdx].firstItem = fdx;
	--classes[cdx].size;
	items[fdx].parent = ~cdx;

	unlaceItem(idx);
	idx = items[fdx].next;
	while (idx != fdx) {
	  items[idx].parent = fdx;
	  idx = items[idx].next;
	}
          
      }

    }

    /// \brief Gives back a representant item of the component.
    ///
    /// Gives back a representant item of the component.
    Item item(int cls) const {
      return items[classes[cls].firstItem].item;
    }

    /// \brief Removes the component of the given element from the structure.
    ///
    /// Removes the component of the given element from the structure.
    ///
    /// \warning It is an error to give an element which is not in the
    /// structure.
    void eraseClass(int cls) {
      int fdx = classes[cls].firstItem;
      unlaceClass(cls);
      items[items[fdx].prev].next = firstFreeItem;
      firstFreeItem = fdx;
    }

    /// \brief Lemon style iterator for the representant items.
    ///
    /// ClassIt is a lemon style iterator for the components. It iterates
    /// on the ids of the classes.
    class ClassIt {
    public:
      /// \brief Constructor of the iterator
      ///
      /// Constructor of the iterator
      ClassIt(const UnionFindEnum& ufe) : unionFind(&ufe) {
        cdx = unionFind->firstClass;
      }

      /// \brief Constructor to get invalid iterator
      ///
      /// Constructor to get invalid iterator
      ClassIt(Invalid) : unionFind(0), cdx(-1) {}
      
      /// \brief Increment operator
      ///
      /// It steps to the next representant item.
      ClassIt& operator++() {
        cdx = unionFind->classes[cdx].next;
        return *this;
      }
      
      /// \brief Conversion operator
      ///
      /// It converts the iterator to the current representant item.
      operator int() const {
        return cdx;
      }

      /// \brief Equality operator
      ///
      /// Equality operator
      bool operator==(const ClassIt& i) { 
        return i.cdx == cdx;
      }

      /// \brief Inequality operator
      ///
      /// Inequality operator
      bool operator!=(const ClassIt& i) { 
        return i.cdx != cdx;
      }
      
    private:
      const UnionFindEnum* unionFind;
      int cdx;
    };

    /// \brief Lemon style iterator for the items of a component.
    ///
    /// ClassIt is a lemon style iterator for the components. It iterates
    /// on the items of a class. By example if you want to iterate on
    /// each items of each classes then you may write the next code.
    ///\code
    /// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
    ///   std::cout << "Class: ";
    ///   for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
    ///     std::cout << toString(iit) << ' ' << std::endl;
    ///   }
    ///   std::cout << std::endl;
    /// }
    ///\endcode
    class ItemIt {
    public:
      /// \brief Constructor of the iterator
      ///
      /// Constructor of the iterator. The iterator iterates
      /// on the class of the \c item.
      ItemIt(const UnionFindEnum& ufe, int cls) : unionFind(&ufe) {
        fdx = idx = unionFind->classes[cls].firstItem;
      }

      /// \brief Constructor to get invalid iterator
      ///
      /// Constructor to get invalid iterator
      ItemIt(Invalid) : unionFind(0), idx(-1) {}
      
      /// \brief Increment operator
      ///
      /// It steps to the next item in the class.
      ItemIt& operator++() {
        idx = unionFind->items[idx].next;
        if (idx == fdx) idx = -1;
        return *this;
      }
      
      /// \brief Conversion operator
      ///
      /// It converts the iterator to the current item.
      operator const Item&() const {
        return unionFind->items[idx].item;
      }

      /// \brief Equality operator
      ///
      /// Equality operator
      bool operator==(const ItemIt& i) { 
        return i.idx == idx;
      }

      /// \brief Inequality operator
      ///
      /// Inequality operator
      bool operator!=(const ItemIt& i) { 
        return i.idx != idx;
      }
      
    private:
      const UnionFindEnum* unionFind;
      int idx, fdx;
    };

  };

  /// \ingroup auxdat
  ///
  /// \brief A \e Extend-Find data structure implementation which
  /// is able to enumerate the components.
  ///
  /// The class implements an \e Extend-Find data structure which is
  /// able to enumerate the components and the items in a
  /// component. The data structure is a simplification of the
  /// Union-Find structure, and it does not allow to merge two components.
  ///
  /// \pre You need to add all the elements by the \ref insert()
  /// method.
  template <typename _ItemIntMap>
  class ExtendFindEnum {
  public:
    
    typedef _ItemIntMap ItemIntMap;
    typedef typename ItemIntMap::Key Item;

  private:
    
    ItemIntMap& index;

    struct ItemT {
      int cls;
      Item item;
      int next, prev;
    };

    std::vector<ItemT> items;
    int firstFreeItem;

    struct ClassT {
      int firstItem;
      int next, prev;
    };

    std::vector<ClassT> classes;

    int firstClass, firstFreeClass;

    int newClass() {
      if (firstFreeClass != -1) {
	int cdx = firstFreeClass;
	firstFreeClass = classes[cdx].next;
	return cdx;
      } else {
	classes.push_back(ClassT());
	return classes.size() - 1;
      }
    }

    int newItem() {
      if (firstFreeItem != -1) {
	int idx = firstFreeItem;
	firstFreeItem = items[idx].next;
	return idx;
      } else {
	items.push_back(ItemT());
	return items.size() - 1;
      }
    }

  public:

    /// \brief Constructor
    ExtendFindEnum(ItemIntMap& _index) 
      : index(_index), items(), firstFreeItem(-1), 
	classes(), firstClass(-1), firstFreeClass(-1) {}
    
    /// \brief Inserts the given element into a new component.
    ///
    /// This method creates a new component consisting only of the
    /// given element.
    int insert(const Item& item) {
      int cdx = newClass();
      classes[cdx].prev = -1;
      classes[cdx].next = firstClass;
      firstClass = cdx;
      
      int idx = newItem();
      items[idx].item = item;
      items[idx].cls = cdx;
      items[idx].prev = idx;
      items[idx].next = idx;

      classes[cdx].firstItem = idx;

      index.set(item, idx);
      
      return cdx;
    }

    /// \brief Inserts the given element into the given component.
    ///
    /// This methods inserts the element \e item a into the \e cls class.
    void insert(const Item& item, int cls) {
      int idx = newItem();
      int rdx = classes[cls].firstItem;
      items[idx].item = item;
      items[idx].cls = cls;

      items[idx].prev = rdx;
      items[idx].next = items[rdx].next;
      items[items[rdx].next].prev = idx;
      items[rdx].next = idx;

      index.set(item, idx);
    }

    /// \brief Clears the union-find data structure
    ///
    /// Erase each item from the data structure.
    void clear() {
      items.clear();
      classes.clear;
      firstClass = firstFreeClass = firstFreeItem = -1;
    }

    /// \brief Gives back the class of the \e item.
    ///
    /// Gives back the class of the \e item.
    int find(const Item &item) const {
      return items[index[item]].cls;
    }

    /// \brief Gives back a representant item of the component.
    ///
    /// Gives back a representant item of the component.
    Item item(int cls) const {
      return items[classes[cls].firstItem].item;
    }
    
    /// \brief Removes the given element from the structure.
    ///
    /// Removes the element from its component and if the component becomes
    /// empty then removes that component from the component list.
    ///
    /// \warning It is an error to remove an element which is not in
    /// the structure.
    void erase(const Item &item) {
      int idx = index[item];
      int cdx = items[idx].cls;
      
      if (idx == items[idx].next) {
	if (classes[cdx].prev != -1) {
	  classes[classes[cdx].prev].next = classes[cdx].next; 
	} else {
	  firstClass = classes[cdx].next;
	}
	if (classes[cdx].next != -1) {
	  classes[classes[cdx].next].prev = classes[cdx].prev; 
	}
	classes[cdx].next = firstFreeClass;
	firstFreeClass = cdx;
      } else {
	classes[cdx].firstItem = items[idx].next;
	items[items[idx].next].prev = items[idx].prev;
	items[items[idx].prev].next = items[idx].next;
      }
      items[idx].next = firstFreeItem;
      firstFreeItem = idx;
	
    }    

    
    /// \brief Removes the component of the given element from the structure.
    ///
    /// Removes the component of the given element from the structure.
    ///
    /// \warning It is an error to give an element which is not in the
    /// structure.
    void eraseClass(int cdx) {
      int idx = classes[cdx].firstItem;
      items[items[idx].prev].next = firstFreeItem;
      firstFreeItem = idx;

      if (classes[cdx].prev != -1) {
	classes[classes[cdx].prev].next = classes[cdx].next; 
      } else {
	firstClass = classes[cdx].next;
      }
      if (classes[cdx].next != -1) {
	classes[classes[cdx].next].prev = classes[cdx].prev; 
      }
      classes[cdx].next = firstFreeClass;
      firstFreeClass = cdx;
    }

    /// \brief Lemon style iterator for the classes.
    ///
    /// ClassIt is a lemon style iterator for the components. It iterates
    /// on the ids of classes.
    class ClassIt {
    public:
      /// \brief Constructor of the iterator
      ///
      /// Constructor of the iterator
      ClassIt(const ExtendFindEnum& ufe) : extendFind(&ufe) {
        cdx = extendFind->firstClass;
      }

      /// \brief Constructor to get invalid iterator
      ///
      /// Constructor to get invalid iterator
      ClassIt(Invalid) : extendFind(0), cdx(-1) {}
      
      /// \brief Increment operator
      ///
      /// It steps to the next representant item.
      ClassIt& operator++() {
        cdx = extendFind->classes[cdx].next;
        return *this;
      }
      
      /// \brief Conversion operator
      ///
      /// It converts the iterator to the current class id.
      operator int() const {
        return cdx;
      }

      /// \brief Equality operator
      ///
      /// Equality operator
      bool operator==(const ClassIt& i) { 
        return i.cdx == cdx;
      }

      /// \brief Inequality operator
      ///
      /// Inequality operator
      bool operator!=(const ClassIt& i) { 
        return i.cdx != cdx;
      }
      
    private:
      const ExtendFindEnum* extendFind;
      int cdx;
    };

    /// \brief Lemon style iterator for the items of a component.
    ///
    /// ClassIt is a lemon style iterator for the components. It iterates
    /// on the items of a class. By example if you want to iterate on
    /// each items of each classes then you may write the next code.
    ///\code
    /// for (ClassIt cit(ufe); cit != INVALID; ++cit) {
    ///   std::cout << "Class: ";
    ///   for (ItemIt iit(ufe, cit); iit != INVALID; ++iit) {
    ///     std::cout << toString(iit) << ' ' << std::endl;
    ///   }
    ///   std::cout << std::endl;
    /// }
    ///\endcode
    class ItemIt {
    public:
      /// \brief Constructor of the iterator
      ///
      /// Constructor of the iterator. The iterator iterates
      /// on the class of the \c item.
      ItemIt(const ExtendFindEnum& ufe, int cls) : extendFind(&ufe) {
        fdx = idx = extendFind->classes[cls].firstItem;
      }

      /// \brief Constructor to get invalid iterator
      ///
      /// Constructor to get invalid iterator
      ItemIt(Invalid) : extendFind(0), idx(-1) {}
      
      /// \brief Increment operator
      ///
      /// It steps to the next item in the class.
      ItemIt& operator++() {
        idx = extendFind->items[idx].next;
	if (fdx == idx) idx = -1;
        return *this;
      }
      
      /// \brief Conversion operator
      ///
      /// It converts the iterator to the current item.
      operator const Item&() const {
        return extendFind->items[idx].item;
      }

      /// \brief Equality operator
      ///
      /// Equality operator
      bool operator==(const ItemIt& i) { 
        return i.idx == idx;
      }

      /// \brief Inequality operator
      ///
      /// Inequality operator
      bool operator!=(const ItemIt& i) { 
        return i.idx != idx;
      }
      
    private:
      const ExtendFindEnum* extendFind;
      int idx, fdx;
    };

  };

  //! @}

} //namespace lemon

#endif //LEMON_UNION_FIND_H