/*
  This file is part of LilyPond, the GNU music typesetter.

  Copyright (C) 2006--2009 Joe Neeman <joeneeman@gmail.com>

  LilyPond 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.

  LilyPond 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 LilyPond.  If not, see <http://www.gnu.org/licenses/>.
*/

#include "constrained-breaking.hh"

#include "international.hh"
#include "main.hh"
#include "output-def.hh"
#include "page-layout-problem.hh"
#include "paper-column.hh"
#include "paper-score.hh"
#include "simple-spacer.hh"
#include "system.hh"
#include "warn.hh"

/*
  We use the following optimal substructure. Let W (A) be our weight function.

  Let A_{k, n} = (a_{k, n, 1}, ... a_{k, n, k}) be the optimal set of line breaks
  for k systems and n potential breakpoints. a_{k, n, k} = n (it is the end of
  the piece)

  Then A_{k+1, m} is contructed from
  min_ {k < j < m} ( W (A_{k, j} :: m) )
  where by A::m we denote appending m to the list A

  Indices in the code:

  The above algorithm makes it easy to end at a point before the end of the
  score (just find A_{k, m} for some m < breaks_.size () - 1). However, we must
  add information for starting at a point after the beginning. One constructor
  allows the specification of a list of starting columns, start_. We then have
  start_.size () different solution arrays. state_[i] is the array for the
  solution starting at column number start_[i].

  The indices "start" and "end" refer to the index in the start_ array of the
  desired starting and ending columns.

  each solution array looks like
   a_{1,1,1} a_{2,1,2} a_{3,1,3} . . .
       X     a_{2,2,2} a_{3,2,3} . . .
       X         X     a_{3,3,3} . . .
       .         .         .     .
       .         .         .       .
  where the X's mark invalid solutions (can't have more systems than
  breakpoints). Note that each value is of the form a_{x, n, x}. This is because
  a breakpoint of the form a_{x, n, x-1} will also be called a_{x-1, m, x-1} for
  some m < n. Each cell in the array stores the value of its m (ie. the
  ending breakpoint of the previous line) as "prev_".

  For finding A_{sys, brk}, let "me" be the (sys_count, brk) cell in our
  solution array (state_[start][sys * rank + brk]).

  Then A_{sys, brk} = A_{sys - 1, me.prev_} :: me
*/

/*
  start and sys here are indexed from 0.
  brk is indexed from starting_breakpoints_[start]
  (for brk, starting_breakpoints_[start] is the beginning
  of the piece; the smallest value we should ever see here is
  starting_breakpoints_[start] + 1) */
bool
Constrained_breaking::calc_subproblem (vsize start, vsize sys, vsize brk)
{
  assert (sys < systems_);
  assert (start < start_.size ());
  assert (brk < breaks_.size ());

  bool found_something = false;
  vsize start_col = starting_breakpoints_[start];
  Matrix<Constrained_break_node> &st = state_[start];
  vsize max_index = brk - start_col;
  for (vsize j=max_index; j-- > sys;)
    {
      if (0 == sys && j > 0)
        continue; /* the first line cannot have its first break after the beginning */

      Line_details const &cur = lines_.at (brk, j + start_col);
      if (isinf (cur.force_))
	break;

      Real prev_f = 0;
      Real prev_dem = 0;

      if (sys > 0)
        {
          prev_f = st.at (j, sys-1).details_.force_;
          prev_dem = st.at (j, sys-1).demerits_;
        }
      if (isinf (prev_dem))
        continue;

      Real dem = combine_demerits (cur.force_, prev_f) + prev_dem + cur.break_penalty_;
      Constrained_break_node &n = st.at (max_index, sys);
      if (dem < n.demerits_)
        {
          found_something = true;
          n.demerits_ = dem;
          n.details_ = cur;
          n.prev_ = j;
        }
    }
  return found_something;
}


Column_x_positions
Constrained_breaking::space_line (vsize i, vsize j)
{
  bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
  bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
  Column_x_positions col;

  vector<Grob*> line (all_.begin () + breaks_[i],
		      all_.begin () + breaks_[j] + 1);
  Interval line_dims = line_dimensions_int (pscore_->layout (), i);
  bool last = j == breaks_.size () - 1;
  bool ragged = ragged_right || (last && ragged_last);

  /* As a special case, if there is only one line in the score and ragged-right
     hasn't been specifically forbidden and the line is stretched, use
     ragged spacing. */
  if (last && i == 0
      && lines_.at (i, j).force_ >= 0
      && !scm_is_bool (pscore_->layout ()->c_variable ("ragged-right"))
      && !scm_is_bool (pscore_->layout ()->c_variable ("ragged-last")))
    ragged = true;

  return get_line_configuration (line, line_dims[RIGHT] - line_dims[LEFT], line_dims[LEFT], ragged);
}

void
Constrained_breaking::resize (vsize systems)
{
  systems_ = systems;

  if (pscore_ && systems_ > valid_systems_)
    {
      for (vsize i = 0; i < state_.size (); i++)
        state_[i].resize (breaks_.size () - starting_breakpoints_[i], systems_, Constrained_break_node ());

      /* fill out the matrices */
      for (vsize i = 0; i < state_.size (); i++)
        for (vsize j = valid_systems_; j < systems_; j++)
          for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
            if (!calc_subproblem (i, j, k))
              break; /* if we couldn't break this, it is too cramped already */
      valid_systems_ = systems_;
    }
}

vector<Column_x_positions>
Constrained_breaking::solve (vsize start, vsize end, vsize sys_count)
{
  vsize start_brk = starting_breakpoints_[start];
  vsize end_brk = prepare_solution (start, end, sys_count);

  Matrix<Constrained_break_node> const &st = state_[start];
  vector<Column_x_positions> ret;

  /* find the first solution that satisfies constraints */
  for (vsize sys = sys_count-1; sys != VPOS; sys--)
    {
      for (vsize brk = end_brk; brk != VPOS; brk--)
        {
          if (!isinf (st.at (brk, sys).details_.force_))
            {
              if (brk != end_brk)
                {
		  brk = st.at (brk, sys).prev_;
		  sys--;
                  warning (_ ("cannot find line breaking that satisfies constraints"));
                  ret.push_back (space_line (brk, end_brk));
                }

              /* build up the good part of the solution */
              for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
                {
		  vsize prev_brk = st.at (brk, cur_sys).prev_;
                  assert (brk != VPOS);
                  ret.push_back (space_line (prev_brk + start_brk, brk + start_brk));
                  brk = prev_brk;
                }
              reverse (ret);
              return ret;
            }
        }
    }
  /* if we get to here, just put everything on one line */
  warning (_ ("cannot find line breaking that satisfies constraints"));
  ret.push_back (space_line (0, end_brk));
  return ret;
}

vector<Column_x_positions>
Constrained_breaking::best_solution (vsize start, vsize end)
{
  vsize min_systems = min_system_count (start, end);
  vsize max_systems = max_system_count (start, end);
  Real best_demerits = infinity_f;
  vector<Column_x_positions> best_so_far;

  for (vsize i = min_systems; i <= max_systems; i++)
    {
      vsize brk = prepare_solution (start, end, i);
      Real dem = state_[start].at (brk, i-1).demerits_;

      if (dem < best_demerits)
	{
	  best_demerits = dem;
	  best_so_far = solve (start, end, i);
	}
      else
	{
	  vector<Column_x_positions> cur = solve (start, end, i);
	  bool too_many_lines = true;
	  
	  for (vsize j = 0; j < cur.size (); j++)
	    if (cur[j].force_ < 0)
	      {
		too_many_lines = false;
		break;
	      }
	  if (too_many_lines)
	    return best_so_far;
	}
    }
  if (best_so_far.size ())
    return best_so_far;
  return solve (start, end, max_systems);
}

std::vector<Line_details>
Constrained_breaking::line_details (vsize start, vsize end, vsize sys_count)
{
  vsize end_brk = prepare_solution (start, end, sys_count);
  Matrix<Constrained_break_node> const &st = state_[start];
  vector<Line_details> ret;

  /* This loop structure is C&Ped from solve(). */
  /* find the first solution that satisfies constraints */
  for (vsize sys = sys_count-1; sys != VPOS; sys--)
    {
      for (vsize brk = end_brk; brk != VPOS; brk--)
        {
          if (!isinf (st.at (brk, sys).details_.force_))
            {
              if (brk != end_brk)
		{
		  /*
		    During initialize(), we only fill out a
		    Line_details for lines that are valid (ie. not too
		    long), otherwise line breaking becomes O(n^3).
		    In case sys_count is such that no valid solution
		    is found, we need to fill in the Line_details.
		  */
		  Line_details details;
		  brk = st.at (brk, sys).prev_;
		  sys--;
		  fill_line_details (&details, brk, end_brk);
		  ret.push_back (details);
		}

              /* build up the good part of the solution */
              for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
                {
		  vsize prev_brk = st.at (brk, cur_sys).prev_;
                  assert (brk != VPOS);
                  ret.push_back (st.at (brk, cur_sys).details_);
                  brk = prev_brk;
                }
              reverse (ret);
              return ret;
            }
        }
    }

  /* if we get to here, just put everything on one line */
  Line_details details;
  fill_line_details (&details, 0, end_brk);
  ret.push_back (details);
  return ret;
}

int
Constrained_breaking::min_system_count (vsize start, vsize end)
{
  vsize sys_count;
  vsize brk = prepare_solution (start, end, 1);
  vsize rank = breaks_.size () - starting_breakpoints_[start];
  Matrix<Constrained_break_node> const &st = state_[start];

  /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
  for (sys_count = 0; sys_count < rank; sys_count++)
    {
      if (sys_count >= valid_systems_)
        {
          resize (sys_count + 3);
        }
      if (!isinf (st.at (brk, sys_count).details_.force_))
        return sys_count + 1;
    }
  /* no possible breaks satisfy constraints */
  return 1;
}

int
Constrained_breaking::max_system_count (vsize start, vsize end)
{
  vsize brk = (end >= start_.size ()) ? breaks_.size () - 1 : starting_breakpoints_[end];
  return brk - starting_breakpoints_[start];
}

vsize
Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count)
{
  assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
  assert (start < end);

  resize (sys_count);
  if (end == start_.size ())
    end = VPOS;

  vsize brk;
  brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
  brk -= starting_breakpoints_[start];
  return brk;
}

Constrained_breaking::Constrained_breaking (Paper_score *ps)
{
  valid_systems_ = systems_ = 0;
  start_.push_back (0);
  pscore_ = ps;
  initialize ();
}

Constrained_breaking::Constrained_breaking (Paper_score *ps, vector<vsize> const &start)
  : start_ (start)
{
  valid_systems_ = systems_ = 0;
  pscore_ = ps;
  initialize ();
}

static SCM
min_permission (SCM perm1, SCM perm2)
{
  if (perm1 == ly_symbol2scm ("force"))
    return perm2;
  if (perm1 == ly_symbol2scm ("allow")
     && perm2 != ly_symbol2scm ("force"))
    return perm2;
  return SCM_EOL;
}

/* find the forces for all possible lines and cache ragged_ and ragged_right_ */
void
Constrained_breaking::initialize ()
{
  if (!pscore_)
    return;

  ragged_right_ = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
  ragged_last_ = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
  /* NOTE: currently, we aren't using the space_ field of a
     Line_details for anything.  That's because the approximations
     used for scoring a page configuration don't actually space things
     properly (for speed reasong) using springs anchored at the staff
     refpoints.  Rather, the "space" is placed between the extent
     boxes.  To get a good result, therefore, the "space" value for
     page breaking needs to be much smaller than the "space" value for
     page layout.  Currently, we just make it zero always.
  */
  between_system_space_ = 0;
  between_system_padding_ = 0;
  before_title_padding_ = 0;

  Output_def *l = pscore_->layout ();

  SCM spacing_spec = l->c_variable ("between-system-spacing");
  SCM title_spec = l->c_variable ("before-title-spacing");
  SCM page_breaking_spacing_spec = l->c_variable ("page-breaking-between-system-spacing");
  Page_layout_problem::read_spacing_spec (spacing_spec,
					  &between_system_padding_,
					  ly_symbol2scm ("padding"));
  Page_layout_problem::read_spacing_spec (page_breaking_spacing_spec,
					  &between_system_padding_,
					  ly_symbol2scm ("padding"));
  Page_layout_problem::read_spacing_spec (title_spec,
					  &before_title_padding_,
					  ly_symbol2scm ("padding"));

  Interval first_line = line_dimensions_int (pscore_->layout (), 0);
  Interval other_lines = line_dimensions_int (pscore_->layout (), 1);
  /* do all the rod/spring problems */
  breaks_ = pscore_->find_break_indices ();
  all_ = pscore_->root_system ()->used_columns ();
  lines_.resize (breaks_.size (), breaks_.size (), Line_details ());
  vector<Real> forces = get_line_forces (all_,
					 other_lines.length (),
					 other_lines.length () - first_line.length (),
					 ragged_right_);
  for (vsize i = 0; i + 1 < breaks_.size (); i++)
    {
      for (vsize j = i + 1; j < breaks_.size (); j++)
	{
	  bool last = j == breaks_.size () - 1;
	  bool ragged = ragged_right_ || (last && ragged_last_);
	  Line_details &line = lines_.at (j, i);

	  line.force_ = forces[i*breaks_.size () + j];
	  if (ragged && last && !isinf (line.force_))
	    line.force_ = (line.force_ < 0 && j > i + 1) ? infinity_f : 0;
	  if (isinf (line.force_))
	    break;

	  fill_line_details (&line, i, j);
	}
    }

  /* work out all the starting indices */
  for (vsize i = 0; i < start_.size (); i++)
    {
      vsize j;
      for (j = 0; j + 1 < breaks_.size () && breaks_[j] < start_[i]; j++)
	;
      starting_breakpoints_.push_back (j);
      start_[i] = breaks_[j];
    }
  state_.resize (start_.size ());
}

/*
  Fills out all of the information contained in a Line_details,
  except for information about horizontal spacing.
*/
void
Constrained_breaking::fill_line_details (Line_details *const out, vsize start, vsize end)
{
  int start_rank = Paper_column::get_rank (all_[breaks_[start]]);
  int end_rank = Paper_column::get_rank (all_[breaks_[end]]);
  System *sys = pscore_->root_system ();
  Interval extent = sys->pure_height (sys, start_rank, end_rank);

  Grob *c = all_[breaks_[end]];
  out->last_column_ = c;
  out->break_penalty_ = robust_scm2double (c->get_property ("line-break-penalty"), 0);
  out->page_penalty_ = robust_scm2double (c->get_property ("page-break-penalty"), 0);
  out->turn_penalty_ = robust_scm2double (c->get_property ("page-turn-penalty"), 0);
  out->break_permission_ = c->get_property ("line-break-permission");
  out->page_permission_ = c->get_property ("page-break-permission");
  out->turn_permission_ = c->get_property ("page-turn-permission");

  /* turn permission should always be stricter than page permission
     and page permission should always be stricter than line permission */
  out->page_permission_ = min_permission (out->break_permission_,
					  out->page_permission_);
  out->turn_permission_ = min_permission (out->page_permission_,
					  out->turn_permission_);

  // TODO: see the hack regarding begin_of_line and
  // rest_of_line extents in align-interface.  Perhaps we
  // should do the same thing here so that the effect extends
  // between systems as well as within systems.  It isn't as
  // crucial here, however, because the effect is largest when
  // dealing with large systems.
  out->extent_ = (extent.is_empty ()
		  || isnan (extent[LEFT])
		  || isnan (extent[RIGHT]))
    ? Interval (0, 0) : extent;
  out->padding_ = between_system_padding_;
  out->title_padding_ = before_title_padding_;
  out->space_ = between_system_space_;
  out->inverse_hooke_ = extent.length () + between_system_space_;
}

Real
Constrained_breaking::combine_demerits (Real force, Real prev_force)
{
  if (ragged_right_)
    return force * force;

  return force * force + (prev_force - force) * (prev_force - force);
}

Line_details::Line_details (Prob *pb, Output_def *paper)
{
  SCM spec = paper->c_variable ("after-title-spacing");
  SCM title_spec = paper->c_variable ("between-title-spacing");
  padding_ = 0;
  title_padding_ = 0;
  Page_layout_problem::read_spacing_spec (spec, &padding_, ly_symbol2scm ("padding"));
  Page_layout_problem::read_spacing_spec (title_spec, &title_padding_, ly_symbol2scm ("padding"));

  last_column_ = 0;
  force_ = 0;
  extent_ = unsmob_stencil (pb->get_property ("stencil")) ->extent (Y_AXIS);
  bottom_padding_ = 0;
  space_ = robust_scm2double (pb->get_property ("next-space"), 1.0);
  inverse_hooke_ = 1.0;
  break_permission_ = ly_symbol2scm ("allow");
  page_permission_ = pb->get_property ("page-break-permission");
  turn_permission_ = pb->get_property ("page-turn-permission");
  break_penalty_ = 0;
  page_penalty_ = robust_scm2double (pb->get_property ("page-break-penalty"), 0);
  turn_penalty_ = robust_scm2double (pb->get_property ("page-turn-penalty"), 0);
  title_ = to_boolean (pb->get_property ("is-title"));
  compressed_lines_count_ = 1;
  compressed_nontitle_lines_count_ = title_ ? 0 : 1;
}
