/* Constraint_System class declaration.
   Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
   Copyright (C) 2010-2012 BUGSENG srl (http://bugseng.com)

This file is part of the Parma Polyhedra Library (PPL).

The PPL is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The PPL is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.

For the most up-to-date information see the Parma Polyhedra Library
site: http://bugseng.com/products/ppl/ . */

#ifndef PPL_Constraint_System_defs_hh
#define PPL_Constraint_System_defs_hh 1

#include "Constraint_System.types.hh"
#include "Linear_Expression.types.hh"
#include "Linear_System.defs.hh"
#include "Generator.types.hh"
#include "Polyhedron.types.hh"
#include "Constraint.types.hh"
#include "Congruence_System.types.hh"
#include <iterator>
#include <iosfwd>

namespace Parma_Polyhedra_Library {

namespace IO_Operators {

//! Output operator.
/*!
  \relates Parma_Polyhedra_Library::Constraint_System
  Writes <CODE>true</CODE> if \p cs is empty.  Otherwise, writes on
  \p s the constraints of \p cs, all in one row and separated by ", ".
*/
std::ostream& operator<<(std::ostream& s, const Constraint_System& cs);

} // namespace IO_Operators

//! Swaps \p x with \p y.
/*! \relates Constraint_System */
void swap(Constraint_System& x, Constraint_System& y);

// Put it in the namespace here to declare it friend later.
/*! \relates Polyhedron */
bool operator==(const Polyhedron& x, const Polyhedron& y);

} // namespace Parma_Polyhedra_Library

//! A system of constraints.
/*! \ingroup PPL_CXX_interface
    An object of the class Constraint_System is a system of constraints,
    i.e., a multiset of objects of the class Constraint.
    When inserting constraints in a system, space dimensions are
    automatically adjusted so that all the constraints in the system
    are defined on the same vector space.

    \par
    In all the examples it is assumed that variables
    <CODE>x</CODE> and <CODE>y</CODE> are defined as follows:
    \code
  Variable x(0);
  Variable y(1);
    \endcode

    \par Example 1
    The following code builds a system of constraints corresponding to
    a square in \f$\Rset^2\f$:
    \code
  Constraint_System cs;
  cs.insert(x >= 0);
  cs.insert(x <= 3);
  cs.insert(y >= 0);
  cs.insert(y <= 3);
    \endcode
    Note that:
    the constraint system is created with space dimension zero;
    the first and third constraint insertions increase the space
    dimension to \f$1\f$ and \f$2\f$, respectively.

    \par Example 2
    By adding four strict inequalities to the constraint system
    of the previous example, we can remove just the four
    vertices from the square defined above.
    \code
  cs.insert(x + y > 0);
  cs.insert(x + y < 6);
  cs.insert(x - y < 3);
  cs.insert(y - x < 3);
    \endcode

    \par Example 3
    The following code builds a system of constraints corresponding to
    a half-strip in \f$\Rset^2\f$:
    \code
  Constraint_System cs;
  cs.insert(x >= 0);
  cs.insert(x - y <= 0);
  cs.insert(x - y + 1 >= 0);
    \endcode

    \note
    After inserting a multiset of constraints in a constraint system,
    there are no guarantees that an <EM>exact</EM> copy of them
    can be retrieved:
    in general, only an <EM>equivalent</EM> constraint system
    will be available, where original constraints may have been
    reordered, removed (if they are trivial, duplicate or
    implied by other constraints), linearly combined, etc.
*/
class Parma_Polyhedra_Library::Constraint_System : private Linear_System {
public:
  //! Default constructor: builds an empty system of constraints.
  Constraint_System();

  //! Builds the singleton system containing only constraint \p c.
  explicit Constraint_System(const Constraint& c);

  //! Builds a system containing copies of any equalities in \p cgs.
  explicit Constraint_System(const Congruence_System& cgs);

  //! Ordinary copy constructor.
  Constraint_System(const Constraint_System& cs);

  //! Destructor.
  ~Constraint_System();

  //! Assignment operator.
  Constraint_System& operator=(const Constraint_System& y);

  //! Returns the maximum space dimension a Constraint_System can handle.
  static dimension_type max_space_dimension();

  //! Returns the dimension of the vector space enclosing \p *this.
  dimension_type space_dimension() const;

  /*! \brief
    Returns <CODE>true</CODE> if and only if \p *this
    contains one or more equality constraints.
  */
  bool has_equalities() const;

  /*! \brief
    Returns <CODE>true</CODE> if and only if \p *this
    contains one or more strict inequality constraints.
  */
  bool has_strict_inequalities() const;

  /*! \brief
    Removes all the constraints from the constraint system
    and sets its space dimension to 0.
  */
  void clear();

  /*! \brief
    Inserts in \p *this a copy of the constraint \p c,
    increasing the number of space dimensions if needed.
  */
  void insert(const Constraint& c);

  //! Initializes the class.
  static void initialize();

  //! Finalizes the class.
  static void finalize();

  /*! \brief
    Returns the singleton system containing only Constraint::zero_dim_false().
  */
  static const Constraint_System& zero_dim_empty();

  //! An iterator over a system of constraints.
  /*! \ingroup PPL_CXX_interface
    A const_iterator is used to provide read-only access
    to each constraint contained in a Constraint_System object.

    \par Example
    The following code prints the system of constraints
    defining the polyhedron <CODE>ph</CODE>:
    \code
  const Constraint_System& cs = ph.constraints();
  for (Constraint_System::const_iterator i = cs.begin(),
         cs_end = cs.end(); i != cs_end; ++i)
    cout << *i << endl;
    \endcode
  */
  class const_iterator
    : public std::iterator<std::forward_iterator_tag,
			   Constraint,
			   ptrdiff_t,
			   const Constraint*,
			   const Constraint&> {
  public:
    //! Default constructor.
    const_iterator();

    //! Ordinary copy constructor.
    const_iterator(const const_iterator& y);

    //! Destructor.
    ~const_iterator();

    //! Assignment operator.
    const_iterator& operator=(const const_iterator& y);

    //! Dereference operator.
    const Constraint& operator*() const;

    //! Indirect member selector.
    const Constraint* operator->() const;

    //! Prefix increment operator.
    const_iterator& operator++();

    //! Postfix increment operator.
    const_iterator operator++(int);

    /*! \brief
      Returns <CODE>true</CODE> if and only if
      \p *this and \p y are identical.
    */
    bool operator==(const const_iterator& y) const;

    /*! \brief
      Returns <CODE>true</CODE> if and only if
      \p *this and \p y are different.
    */
    bool operator!=(const const_iterator& y) const;

  private:
    friend class Constraint_System;

    //! The const iterator over the matrix of constraints.
    Linear_System::const_iterator i;

    //! A const pointer to the matrix of constraints.
    const Linear_System* csp;

    //! Constructor.
    const_iterator(const Linear_System::const_iterator& iter,
		   const Constraint_System& cs);

    //! \p *this skips to the next non-trivial constraint.
    void skip_forward();
  };

  //! Returns <CODE>true</CODE> if and only if \p *this has no constraints.
  bool empty() const;

  /*! \brief
    Returns the const_iterator pointing to the first constraint,
    if \p *this is not empty;
    otherwise, returns the past-the-end const_iterator.
  */
  const_iterator begin() const;

  //! Returns the past-the-end const_iterator.
  const_iterator end() const;

  //! Checks if all the invariants are satisfied.
#ifdef PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
  /*!
    Returns <CODE>true</CODE> if and only if \p *this is a valid
    Linear_System and each row in the system is a valid Constraint.
  */
#endif // defined(PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS)
  bool OK() const;

  PPL_OUTPUT_DECLARATIONS

  /*! \brief
    Loads from \p s an ASCII representation (as produced by
    ascii_dump(std::ostream&) const) and sets \p *this accordingly.
    Returns <CODE>true</CODE> if successful, <CODE>false</CODE> otherwise.
  */
  bool ascii_load(std::istream& s);

  //! Returns the total size in bytes of the memory occupied by \p *this.
  memory_size_type total_memory_in_bytes() const;

  //! Returns the size in bytes of the memory managed by \p *this.
  memory_size_type external_memory_in_bytes() const;

  //! Swaps \p *this with \p y.
  void m_swap(Constraint_System& y);

private:
  /*! \brief
    Holds (between class initialization and finalization) a pointer to
    the singleton system containing only Constraint::zero_dim_false().
  */
  static const Constraint_System* zero_dim_empty_p;

  friend class const_iterator;
  friend class Parma_Polyhedra_Library::Polyhedron;

  friend bool operator==(const Polyhedron& x, const Polyhedron& y);

  //! Builds an empty system of constraints having the specified topology.
  explicit Constraint_System(Topology topol);

  /*! \brief
    Builds a system of \p n_rows constraints on a \p n_columns - 1
    dimensional space (including the \f$\epsilon\f$ dimension, if
    \p topol is <CODE>NOT_NECESSARILY_CLOSED</CODE>).
  */
  Constraint_System(Topology topol,
		    dimension_type n_rows, dimension_type n_columns);

  /*! \brief
    Adjusts \p *this so that it matches \p new_topology and
    \p new_space_dim (adding or removing columns if needed).
    Returns <CODE>false</CODE> if and only if \p topol is
    equal to <CODE>NECESSARILY_CLOSED</CODE> and \p *this
    contains strict inequalities.
  */
  bool adjust_topology_and_space_dimension(Topology new_topology,
					   dimension_type new_space_dim);

  //! Returns the \p k- th constraint of the system.
  Constraint& operator[](dimension_type k);

  //! Returns a constant reference to the \p k- th constraint of the system.
  const Constraint& operator[](dimension_type k) const;

  //! Returns <CODE>true</CODE> if \p g satisfies all the constraints.
  bool satisfies_all_constraints(const Generator& g) const;

  //! Substitutes a given column of coefficients by a given affine expression.
  /*!
    \param v
    Index of the column to which the affine transformation is substituted.

    \param expr
    The numerator of the affine transformation:
    \f$\sum_{i = 0}^{n - 1} a_i x_i + b\f$;

    \param denominator
    The denominator of the affine transformation.

    We want to allow affine transformations
    (see Section \ref Images_and_Preimages_of_Affine_Transfer_Relations)
    having any rational coefficients. Since the coefficients of the
    constraints are integers we must also provide an integer \p
    denominator that will be used as denominator of the affine
    transformation.
    The denominator is required to be a positive integer.

    The affine transformation substitutes the matrix of constraints
    by a new matrix whose elements \f${a'}_{ij}\f$ are built from
    the old one \f$a_{ij}\f$ as follows:
    \f[
      {a'}_{ij} =
        \begin{cases}
          a_{ij} * \mathrm{denominator} + a_{iv} * \mathrm{expr}[j]
            \quad \text{for } j \neq v; \\
          \mathrm{expr}[v] * a_{iv}
            \quad \text{for } j = v.
        \end{cases}
    \f]

    \p expr is a constant parameter and unaltered by this computation.
  */
  void affine_preimage(dimension_type v,
		       const Linear_Expression& expr,
		       Coefficient_traits::const_reference denominator);

  //! Returns the number of equality constraints.
  dimension_type num_equalities() const;

  //! Returns the number of inequality constraints.
  dimension_type num_inequalities() const;

  /*! \brief
    Applies Gaussian elimination and back-substitution so as
    to provide a partial simplification of the system of constraints.

    It is assumed that the system has no pending constraints.
  */
  void simplify();

  /*! \brief
    Inserts in \p *this a copy of the constraint \p c,
    increasing the number of space dimensions if needed.
    It is a pending constraint.
  */
  void insert_pending(const Constraint& c);

  //! Adds low-level constraints to the constraint system.
  void add_low_level_constraints();
};

namespace Parma_Polyhedra_Library {

namespace Implementation {

#ifdef PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
//! Helper returning number of constraints in system.
#endif // defined(PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS)
dimension_type
num_constraints(const Constraint_System& cs);

} // namespace Implementation

} // namespace Parma_Polyhedra_Library

// Constraint_System.inlines.hh is not included here on purpose.

#endif // !defined(PPL_Constraint_System_defs_hh)
