// -*- c++ -*- //

#ifndef HUGO_UNION_FIND_H

#define HUGO_UNION_FIND_H

#include <vector>

#include <list>

#include <utility>

#include <algorithm>

#include <invalid.h>

namespace hugo {

  template <typename T, typename TIntMap>

  class UnionFind {

  public:

    typedef T ElementType;

    typedef std::pair<int,int> PairType;

  private:

    std::vector<PairType> data;

    TIntMap& map;

  public:

    UnionFind(TIntMap& m) : map(m) {}

    int find(T a)

    {

      int comp0 = map[a];

      if (comp0 < 0) {

	return insert(a);

      }

      int comp = comp0;

      int next;

      while ( (next = data[comp].first) != comp) {

	comp = next;

      }

      while ( (next = data[comp0].first) != comp) {

	data[comp0].first = comp;

	comp0 = next;

      }

      return comp;

    }

    int insert(T a)

    {

      int n = data.size();

      data.push_back(std::make_pair(n, 1));

      map.set(a,n);

      return n;

    }

    bool join(T a, T b)

    {

      int ca = find(a);

      int cb = find(b);

      if ( ca == cb ) 

	return false;

      if ( data[ca].second > data[cb].second ) {

	data[cb].first = ca;

	data[ca].second += data[cb].second;

      }

      else {

	data[ca].first = cb;

	data[cb].second += data[ca].second;

      }

      return true;

    }

    int size(T a)

    {

      int ca = find(a);

      return data[ca].second;

    }

  };

  /*******************************************************/

  template <typename T>

  struct UnionFindEnumItem {

    typedef std::list<UnionFindEnumItem> ItemList;

    typedef std::list<ItemList> ClassList;

    typedef typename ItemList::iterator IIter;

    typedef typename ClassList::iterator CIter;

    T me;

    IIter parent;

    int size;

    CIter my_class;

    UnionFindEnumItem() {}

    UnionFindEnumItem(const T &_me, CIter _my_class): 

      me(_me), size(1), my_class(_my_class) {}

  };

  template <typename T, template <typename Item> class Map>

  class UnionFindEnum {

    typedef std::list<UnionFindEnumItem<T> > ItemList;

    typedef std::list<ItemList> ClassList;

    typedef typename ItemList::iterator IIter;

    typedef typename ItemList::const_iterator IcIter;

    typedef typename ClassList::iterator CIter;

    typedef typename ClassList::const_iterator CcIter;

  public:

    typedef T ElementType;

    typedef UnionFindEnumItem<T> ItemType;

    typedef Map< IIter > MapType;

  private:

    MapType& m;

    ClassList classes;

    //    IIter where(const T &a) { return m[a]; }

    //    IIter parent(IIter a) { return a->parent; }

    //    P sibling(P a) { return &m[a->sibling]; }

    IIter _find(IIter a) const {

      IIter comp = a;

      IIter next;

      while( (next = comp->parent) != comp ) {

	comp = next;

      }

      IIter comp1 = a;

      while( (next = comp1->parent) != comp ) {

	comp1->parent = comp->parent;

	comp1 = next;

      }

      return comp;

    }

  public:

    UnionFindEnum(MapType& _m) : m(_m) {}

    void insert(const T &a)

    {

      classes.push_back(ItemList());

      CIter aclass = classes.end();

      --aclass;

      ItemList &alist = *aclass;

      alist.push_back(ItemType(a, aclass));

      IIter ai = alist.begin();

      ai->parent = ai;

      m.set(a, ai);

    }

    T find(const T &a) const {

      return _find(m[a])->me;

    }

    bool join(T a, T b) {

      IIter ca = _find(m[a]);

      IIter cb = _find(m[b]);

      if ( ca == cb ) {

	return false;

      }

      if ( ca->size > cb->size ) {

	cb->parent = ca->parent;

	ca->size += cb->size;

	ItemList &alist = *ca->my_class;

	alist.splice(alist.end(),*cb->my_class);

	classes.erase(cb->my_class);

	cb->my_class = 0;

      }

      else {

	ca->parent = cb->parent;

	cb->size += ca->size;

	ItemList &blist = *cb->my_class;

	blist.splice(blist.end(),*ca->my_class);

	classes.erase(ca->my_class);

	ca->my_class = 0;

      }

      return true;

    }

    int size(const T &a) const {

      return _find(m[a])->size;

    }

    void split(const T &a) {

      IIter ca = _find(m[a]);

      if ( ca->size == 1 )

	return;

      CIter aclass = ca->my_class;

      for(IIter curr = ca; ++curr != aclass->end(); curr=ca) {

	classes.push_back(ItemList());

	CIter nl = --classes.end();

	nl->splice(nl->end(), *aclass, curr);

	curr->size=1;

	curr->parent=curr;

	curr->my_class = nl;

      }

      ca->size=1;

      return;

    }

    void erase(const T &a) {

      IIter ma = m[a];

      if (ma == 0) return;

      IIter la = _find(ma);

      if (la == ma) {

	if (ma -> size == 1){

	  classes.erase(ma->my_class);

	  m.set(a,0);

	  return;

	}

	++la;

	la->size = ma->size - 1; 

	la->my_class = ma->my_class;	

      }

      for (IIter i = la; i != la->my_class->end(); ++i) {

	i->parent = la;

      }

      la->my_class->erase(ma);

      m.set(a,0);

    }

    void eraseClass(const T &a) {

      IIter ma = m[a];

      if (ma == 0) return;

#     ifdef DEBUG

      CIter c = _find(ma)->my_class;

      for (IIter i=c->begin(); i!=c->end(); ++i)

	m.set(i->me, 0);

#     endif

      classes.erase(_find(ma)->my_class);

    }

    class ClassIt {

      friend class UnionFindEnum;

      CcIter i;

    public:

      ClassIt(Invalid): i(0) {}

      ClassIt() {}

      operator const T& () const { 

	ItemList const &ll = *i;

	return (ll.begin())->me; }

      bool operator == (ClassIt it) const {

	return (i == it.i);

      }

      bool operator != (ClassIt it) const {

	return (i != it.i);

      }

      bool operator < (ClassIt it) const {

	return (i < it.i);

      }

      bool valid() const { return i != 0; }

    private:

      void first(const ClassList &l) { i = l.begin(); validate(l); }

      void next(const ClassList &l) {

	++i; 

	validate(l);

      }

      void validate(const ClassList &l) {

	if ( i == l.end() ) 

	  i = 0;

      }

    };

    ClassIt& first(ClassIt& it) const {

      it.first(classes);

      return it;

    }

    bool valid(ClassIt const &it) const {

      return it.valid(); 

    }

    ClassIt& next(ClassIt& it) const {

      it.next(classes);

      return it;

    }

    class ItemIt {

      friend class UnionFindEnum;

      IcIter i;

      const ItemList *l;

    public:

      ItemIt(Invalid): i(0) {}

      ItemIt() {}

      operator const T& () const { return i->me; }

      bool operator == (ItemIt it) const {

	return (i == it.i);

      }

      bool operator != (ItemIt it) const {

	return (i != it.i);

      }

      bool operator < (ItemIt it) const {

	return (i < it.i);

      }

      bool valid() const { return i != 0; }

    private:

      void first(const ItemList &il) { l=&il; i = l->begin(); validate(); }

      void next() {

	++i; 

	validate();

      }

      void validate() {

	if ( i == l->end() ) 

	  i = 0;

      }

    };

    ItemIt& first(ItemIt& it, const T& a) const {

      it.first( * _find(m[a])->my_class );

      return it;

    }

    bool valid(ItemIt const &it) const {

      return it.valid(); 

    }

    ItemIt& next(ItemIt& it) const {

      it.next();

      return it;

    }

  };

} //namespace hugo

#endif //HUGO_UNION_FIND_H