/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
 *  Main authors:
 *     Guido Tack <tack@gecode.org>
 *
 *  Copyright:
 *     Guido Tack, 2011
 *
 *  Last modified:
 *     $Date: 2011-08-25 00:34:16 +1000 (Thu, 25 Aug 2011) $ by $Author: tack $
 *     $Revision: 12346 $
 *
 *  This file is part of Gecode, the generic constraint
 *  development environment:
 *     http://www.gecode.org
 *
 *  Permission is hereby granted, free of charge, to any person obtaining
 *  a copy of this software and associated documentation files (the
 *  "Software"), to deal in the Software without restriction, including
 *  without limitation the rights to use, copy, modify, merge, publish,
 *  distribute, sublicense, and/or sell copies of the Software, and to
 *  permit persons to whom the Software is furnished to do so, subject to
 *  the following conditions:
 *
 *  The above copyright notice and this permission notice shall be
 *  included in all copies or substantial portions of the Software.
 *
 *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
 *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
 *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
 *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 */

namespace Gecode { namespace Set { namespace Rel {

  /**
   * \brief Representation of the characteristic functions of two sets
   */
  class CharacteristicSets {
  protected:
    /// Size of the combined upper bounds
    unsigned int xsize;
    /// Storage for the characteristic functions
    Support::BitSetBase b;
    /// Elements in the combined upper bounds
    int* ub;
    /// Whether lower bound of x was updated
    bool xlm;
    /// Whether upper bound of x was updated
    bool xum;
    /// Whether lower bound of y was updated
    bool ylm;
    /// Whether upper bound of y was updated
    bool yum;
    /// Set bit \a i to value \a j
    void set(int i, bool j) {
      if (j)
        b.set(i);
      else
        b.clear(i);
    }
    
    /// \brief Value iterator for characteristic function
    class CSIter {
    public:
      /// Pointer to the underlying set
      CharacteristicSets* cs;
      /// Current position
      unsigned int i;
      /// Offset from start of bitset
      int xoff;
      /// Offset for each element (0=lower bound, 1=upper bound)
      int yoff;
      /// Move iterator to next element
      void operator++ (void) {
        i++;
        while (i<cs->xsize && !cs->b.get(xoff+2*i+yoff))
          i++;
      }
      /// Default constructor
      CSIter(void) {}
      /// Constructor
      CSIter(CharacteristicSets& cs0, int xoff0, int yoff0)
        : cs(&cs0), i(-1), xoff(xoff0), yoff(yoff0) {
        ++(*this);
      }
      /// Test if iterator is finished
      bool operator() (void) const { return i<cs->xsize; }
      /// Value of current iterator position
      int val(void) const { return cs->ub[i]; }
    };
    
  public:
    /// Constructor
    template<class View0, class View1>
    CharacteristicSets(Region& re, View0 x, View1 y);
    
    /// Return minimum of element \a i for variable x
    bool xmin(int i) const { return b.get(2*i); }
    /// Return maximum of element \a i for variable x
    bool xmax(int i) const { return b.get(2*i+1); }
    /// Return minimum of element \a i for variable y
    bool ymin(int i) const { return b.get(2*xsize+2*i); }
    /// Return maximum of element \a i for variable y
    bool ymax(int i) const { return b.get(2*xsize+2*i+1); }

    /// Set minimum of element \a i for variable x to \a j
    void xmin(int i, bool j) { set(2*i,j); }
    /// Set maximum of element \a i for variable x to \a j
    void xmax(int i, bool j) { set(2*i+1,j); }
    /// Set minimum of element \a i for variable y to \a j
    void ymin(int i, bool j) { set(2*xsize+2*i,j); }
    /// Set maximum of element \a i for variable y to \a j
    void ymax(int i, bool j) { set(2*xsize+2*i+1,j); }

    /// Update upper bound of \f$x_i\f$ to \a j
    ModEvent xlq(int i, bool j) {
      if (!j) {
        if (xmin(i)) return ME_SET_FAILED;
        if (xmax(i)) {
          xmax(i,false);
          xum=true;
        }
      }
      return ME_SET_NONE;
    }
    /// Update lower bound of \f$x_i\f$ to \a j
    ModEvent xgq(int i, bool j) {
      if (j) {
        if (!xmax(i)) return ME_SET_FAILED;
        if (!xmin(i)) {
          xmin(i,true);
          xlm=true;
        }
      }
      return ME_SET_NONE;
    }
    /// Update upper bound of \f$y_i\f$ to \a j
    ModEvent ylq(int i, bool j) {
      if (!j) {
        if (ymin(i)) return ME_SET_FAILED;
        if (ymax(i)) {
          ymax(i,false);
          yum=true;
        }
      }
      return ME_SET_NONE;
    }
    /// Update lower bound of \f$y_i\f$ to \a j
    ModEvent ygq(int i, bool j) {
      if (j) {
        if (!ymax(i)) return ME_SET_FAILED;
        if (!ymin(i)) {
          ymin(i,true);
          ylm=true;
        }
      }
      return ME_SET_NONE;
    }

    /// Return size of combined upper bounds
    int size(void) const { return xsize; }
    
    /// Prune \a x and \a y using computed bounds
    template<class View0, class View1>
    ExecStatus prune(Space& home, View0 x, View1 y) {
      if (xlm) {
        CSIter i(*this,0,0);
        Iter::Values::ToRanges<CSIter> ir(i);
        GECODE_ME_CHECK(x.includeI(home,ir));
      }
      if (xum) {
        CSIter i(*this,0,1);
        Iter::Values::ToRanges<CSIter> ir(i);
        GECODE_ME_CHECK(x.intersectI(home,ir));
      }
      if (ylm) {
        CSIter i(*this,2*xsize,0);
        Iter::Values::ToRanges<CSIter> ir(i);
        GECODE_ME_CHECK(y.includeI(home,ir));
      }
      if (yum) {
        CSIter i(*this,2*xsize,1);
        Iter::Values::ToRanges<CSIter> ir(i);
        GECODE_ME_CHECK(y.intersectI(home,ir));
      }
      return ES_OK;
    }
    
  };

  template<class View0, class View1>
  CharacteristicSets::CharacteristicSets(Region& re,View0 x, View1 y)
    : xlm(false), xum(false), ylm(false), yum(false) {
    LubRanges<View0> xlub(x);
    LubRanges<View1> ylub(y);
    Iter::Ranges::Union<LubRanges<View0>,LubRanges<View1> > xylub(xlub,ylub);
    Iter::Ranges::Cache xylubc(re,xylub);
    xsize = Iter::Ranges::size(xylubc);
    b.init(re,4*xsize);
    ub = re.alloc<int>(xsize);
    xylubc.reset();
    Iter::Ranges::ToValues<Iter::Ranges::Cache> xylubv(xylubc);
    LubRanges<View0> xur(x);
    GlbRanges<View0> xlr(x);
    LubRanges<View1> yur(y);
    GlbRanges<View1> ylr(y);
    Iter::Ranges::ToValues<LubRanges<View0> > xuv(xur);
    Iter::Ranges::ToValues<GlbRanges<View0> > xlv(xlr);
    Iter::Ranges::ToValues<LubRanges<View1> > yuv(yur);
    Iter::Ranges::ToValues<GlbRanges<View1> > ylv(ylr);
    for (int i=0; xylubv(); ++xylubv, ++i) {
      ub[i] = xylubv.val();
      if (xlv() && xylubv.val()==xlv.val()) {
        b.set(2*i);
        ++xlv;
      }
      if (xuv() && xylubv.val()==xuv.val()) {
        b.set(2*i+1);
        ++xuv;
      }
      if (ylv() && xylubv.val()==ylv.val()) {
        b.set(2*xsize+2*i);
        ++ylv;
      }
      if (yuv() && xylubv.val()==yuv.val()) {
        b.set(2*xsize+2*i+1);
        ++yuv;
      }
    }
  }

  template<class View0, class View1, bool strict>
  forceinline
  Lq<View0,View1,strict>::Lq(Home home, View0 x, View1 y)
    : MixBinaryPropagator<View0,PC_SET_ANY,View1,PC_SET_ANY>(home,x,y) {}

  template<class View0, class View1, bool strict>
  forceinline
  Lq<View0,View1,strict>::Lq(Space& home, bool share, Lq& p)
    : MixBinaryPropagator<View0,PC_SET_ANY,View1,PC_SET_ANY>(home,share,p) {}

  template<class View0, class View1, bool strict>
  ExecStatus
  Lq<View0,View1,strict>::post(Home home, View0 x, View1 y) {
    if (strict)
      GECODE_ME_CHECK(y.cardMin(home,1));
    (void) new (home) Lq(home,x,y);
    return ES_OK;
  }

  template<class View0, class View1, bool strict>
  Actor*
  Lq<View0,View1,strict>::copy(Space& home, bool share) {
    return new (home) Lq(home,share,*this);
  }

  template<class View0, class View1, bool strict>
  ExecStatus
  Lq<View0,View1,strict>::propagate(Space& home, const ModEventDelta&) {
    if ( (!strict) && x1.cardMax()==0) {
      GECODE_ME_CHECK(x0.cardMax(home,0));
    }

    if (x0.cardMax()==0) {
      return home.ES_SUBSUMED(*this);
    }

    if (x0.glbMin() < x1.lubMin())
      return ES_FAILED;
    if (x1.glbMin() < x0.lubMin())
      return home.ES_SUBSUMED(*this);
    
    bool assigned = x0.assigned() && x1.assigned();
    
    Region re(home);
    CharacteristicSets cs(re,x0,x1);

    /*
     * State 1
     *
     */
    int i=0;
    int firsti=0;
    int n=cs.size();
    while ((i<n) && cs.xmin(i) == cs.ymax(i)) {
      // case: =, >=
      GECODE_ME_CHECK(cs.xlq(i,cs.ymax(i)));
      GECODE_ME_CHECK(cs.ygq(i,cs.xmin(i)));
      i++;
    }
    
    if (i == n) {// case: $
      if (strict) {
        return ES_FAILED;
      } else {
        GECODE_ES_CHECK(cs.prune(home,x0,x1));
        return home.ES_SUBSUMED(*this);
      }
    }
    
    // Possible cases left: <, <=, > (yields failure), ?
    GECODE_ME_CHECK(cs.xlq(i,cs.ymax(i)));
    GECODE_ME_CHECK(cs.ygq(i,cs.xmin(i)));

    if (cs.xmax(i) < cs.ymin(i)) { // case: < (after tell)
      GECODE_ES_CHECK(cs.prune(home,x0,x1));
      return home.ES_SUBSUMED(*this);
    }

    firsti=i;

    /*
     * State 2
     *   prefix: (?|<=)
     *
     */
    i++;

    while ((i < n) &&
           (cs.xmin(i) == cs.ymax(i)) &&
           (cs.xmax(i) == cs.ymin(i))) { // case: =
      i++;
    }

    if (i == n) { // case: $
      if (strict)
        goto rewrite_le;
      else
        goto rewrite_lq;
    }

    if (cs.xmax(i) < cs.ymin(i)) // case: <
      goto rewrite_lq;

    if (cs.xmin(i) > cs.ymax(i)) // case: >
      goto rewrite_le;
    
    if (cs.xmax(i) <= cs.ymin(i)) {
      // case: <= (invariant: not =, <)
      /*
       * State 3
       *   prefix: (?|<=),<=
       *
       */
      i++;

      while ((i < n) && (cs.xmax(i) == cs.ymin(i))) {// case: <=, =
        i++;
      }

      if (i == n) { // case: $
        if (strict) {
          GECODE_ES_CHECK(cs.prune(home,x0,x1));
          return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
        } else {
          goto rewrite_lq;
        }
      }

      if (cs.xmax(i) < cs.ymin(i)) // case: <
        goto rewrite_lq;

      GECODE_ES_CHECK(cs.prune(home,x0,x1));
      return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
    }

    if (cs.xmin(i) >= cs.ymax(i)) {
      // case: >= (invariant: not =, >)
      /*
       * State 4
       *   prefix: (?|<=) >=
       *
       */
      i++;

      while ((i < n) && (cs.xmin(i) == cs.ymax(i))) {
        // case: >=, =
        i++;
      }

      if (i == n) { // case: $
        if (strict) {
          goto rewrite_le;
        } else {
          GECODE_ES_CHECK(cs.prune(home,x0,x1));
          return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
        }
      }

      if (cs.xmin(i) > cs.ymax(i)) // case: >
        goto rewrite_le;

      GECODE_ES_CHECK(cs.prune(home,x0,x1));
      return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
    }    

    GECODE_ES_CHECK(cs.prune(home,x0,x1));
    return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;

  rewrite_le:
    GECODE_ME_CHECK(cs.xlq(firsti,false));
    GECODE_ME_CHECK(cs.ygq(firsti,true));
    GECODE_ES_CHECK(cs.prune(home,x0,x1));
    return home.ES_SUBSUMED(*this);
  rewrite_lq:
    GECODE_ES_CHECK(cs.prune(home,x0,x1));
    return assigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
  }

}}}

// STATISTICS: set-prop