/*
- page-spacing.cc - implement routines for spacing
- systems vertically on pages
+ This file is part of LilyPond, the GNU music typesetter.
- source file of the GNU LilyPond music typesetter
+ Copyright (C) 2006--2012 Joe Neeman <joeneeman@gmail.com>
- (c) 2006--2007 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 "page-spacing.hh"
+#include "international.hh"
#include "matrix.hh"
+#include "page-breaking.hh"
#include "warn.hh"
-/*
- A much simplified rods-and-springs problem.
- */
-struct Page_spacing
+void
+Page_spacing::calc_force ()
{
- Real force_;
- Real page_height_;
- Real rod_height_;
- Real spring_len_;
- Real inverse_spring_k_;
-
- Line_details last_line_;
-
- Page_spacing (Real page_height)
- {
- page_height_ = page_height;
- clear ();
- }
+ Real height = page_height_
+ - breaker_->min_whitespace_at_top_of_page (first_line_)
+ - breaker_->min_whitespace_at_bottom_of_page (last_line_);
- void calc_force ();
-
- void append_system (const Line_details &line);
- void prepend_system (const Line_details &line);
- void clear ();
-};
+ if (rod_height_ + last_line_.bottom_padding_ >= height)
+ force_ = -infinity_f;
+ else
+ force_ = (height - rod_height_ - last_line_.bottom_padding_ - spring_len_)
+ / max (0.1, inverse_spring_k_);
+}
void
-Page_spacing::calc_force ()
+Page_spacing::resize (Real new_height)
{
- if (rod_height_ + last_line_.bottom_padding_ >= page_height_ || !inverse_spring_k_)
- force_ = infinity_f;
- else
- force_ = (page_height_ - rod_height_ - last_line_.bottom_padding_ - spring_len_) / inverse_spring_k_;
+ page_height_ = new_height;
+ calc_force ();
}
void
Page_spacing::append_system (const Line_details &line)
{
- rod_height_ += last_line_.padding_;
+ if (rod_height_)
+ {
+ rod_height_ += line.tallness_;
+ spring_len_ += last_line_.spring_length (line);
+
+ }
+ else
+ {
+ rod_height_ += line.full_height ();
+ first_line_ = line;
+ }
- rod_height_ += line.extent_.length ();
- spring_len_ += line.space_;
+ rod_height_ += account_for_footnotes (line);
inverse_spring_k_ += line.inverse_hooke_;
last_line_ = line;
calc_force ();
}
+Real
+Page_spacing::account_for_footnotes (Line_details const &line)
+{
+ Real footnote_height = 0.0;
+ Real in_note_height = 0.0;
+ bool has_in_notes = false;
+ for (vsize i = 0; i < line.in_note_heights_.size (); i++)
+ {
+ in_note_height += (has_in_notes
+ ? 0.0
+ : breaker_->in_note_padding ());
+ has_in_notes = true;
+ in_note_height += line.in_note_heights_[i];
+ }
+
+ for (vsize i = 0; i < line.footnote_heights_.size (); i++)
+ {
+ footnote_height += (has_footnotes_
+ ? 0.0
+ : (breaker_->footnote_separator_stencil_height ()
+ + breaker_->footnote_padding ()
+ + breaker_->footnote_number_raise ()));
+
+ has_footnotes_ = true;
+ footnote_height += line.footnote_heights_[i];
+ footnote_height += breaker_->footnote_padding ();
+ }
+
+ return (in_note_height
+ - (has_in_notes
+ ? breaker_->in_note_padding ()
+ : 0.0))
+ +
+ (footnote_height
+ + (has_footnotes_
+ ? - breaker_->footnote_padding () + breaker_->footnote_footer_padding ()
+ : 0.0));
+}
+
void
Page_spacing::prepend_system (const Line_details &line)
{
if (rod_height_)
- rod_height_ += line.padding_;
+ spring_len_ += line.spring_length (first_line_);
else
last_line_ = line;
- rod_height_ += line.extent_.length ();
- spring_len_ += line.space_;
+ rod_height_ -= first_line_.full_height ();
+ rod_height_ += first_line_.tallness_;
+ rod_height_ += line.full_height ();
+ rod_height_ += account_for_footnotes (line);
inverse_spring_k_ += line.inverse_hooke_;
+ first_line_ = line;
+
calc_force ();
}
{
force_ = rod_height_ = spring_len_ = 0;
inverse_spring_k_ = 0;
+ has_footnotes_ = false;
}
-/* for each forbidden page break, merge the systems around it into one system. */
-static vector<Line_details>
-compress_lines (const vector<Line_details> &orig)
+Page_spacer::Page_spacer (vector<Line_details> const &lines, vsize first_page_num, Page_breaking const *breaker)
+ : lines_ (lines)
{
- vector<Line_details> ret;
-
- for (vsize i = 0; i < orig.size (); i++)
- {
- if (ret.size () && ret.back ().page_permission_ == SCM_EOL)
- {
- Line_details const &old = ret.back ();
- Line_details compressed = orig[i];
- compressed.extent_[DOWN] = old.extent_[DOWN];
- compressed.extent_[UP] = old.extent_[UP] + orig[i].extent_.length () + old.padding_;
- compressed.space_ += old.space_;
- compressed.inverse_hooke_ += old.inverse_hooke_;
-
- /* we don't need the force_ field for the vertical spacing,
- so we use force_ = n to signal that the line was compressed,
- reducing the number of lines by n (and force_ = 0 otherwise).
- This makes uncompression much easier. */
- compressed.force_ = old.force_ + 1;
- ret.back () = compressed;
- }
- else
- {
- ret.push_back (orig[i]);
- ret.back ().force_ = 0;
- }
- }
- return ret;
+ first_page_num_ = first_page_num;
+ breaker_ = breaker;
+ max_page_count_ = 0;
+ ragged_ = breaker->ragged ();
+ ragged_last_ = breaker->is_last () && breaker->ragged_last ();
}
-/* translate the number of systems-per-page into something meaningful for
- the uncompressed lines.
-*/
-static vector<vsize>
-uncompress_solution (vector<vsize> const &systems_per_page,
- vector<Line_details> const &compressed)
+Page_spacing_result
+Page_spacer::solve ()
{
- vector<vsize> ret;
- vsize start_sys = 0;
-
- for (vsize i = 0; i < systems_per_page.size (); i++)
+ if (simple_state_.empty ())
{
- int compressed_count = 0;
- for (vsize j = start_sys; j < start_sys + systems_per_page[i]; j++)
- compressed_count += (int)compressed[j].force_;
-
- ret.push_back (systems_per_page[i] + compressed_count);
- start_sys += systems_per_page[i];
+ simple_state_.resize (lines_.size ());
+ for (vsize i = 0; i < lines_.size (); ++i)
+ calc_subproblem (VPOS, i);
}
- return ret;
-}
-
-/* the cases for page_count = 1 or 2 can be done in O(n) time. Since they
- are by far the most common cases, we have special functions for them */
-static Spacing_result
-space_systems_on_1_page (vector<Line_details> const &lines, Real page_height, bool ragged)
-{
- Page_spacing space (page_height);
- Spacing_result ret;
-
- for (vsize i = 0; i < lines.size (); i++)
- space.append_system (lines[i]);
- ret.systems_per_page_.push_back (lines.size ());
- ret.force_.push_back (ragged ? min (space.force_, 0.0) : space.force_);
- ret.penalty_ = lines.back ().page_penalty_ + lines.back ().turn_penalty_;
- ret.demerits_ = ret.force_.back () * ret.force_.back () + ret.penalty_;
+ Page_spacing_result ret;
+ if (simple_state_.empty ())
+ return ret;
- return ret;
-}
+ ret.penalty_ = simple_state_.back ().penalty_
+ + lines_.back ().page_penalty_ + lines_.back ().turn_penalty_;
+ ret.system_count_status_ = simple_state_.back ().system_count_status_;
-static Spacing_result
-space_systems_on_2_pages (vector<Line_details> const &lines,
- Real page_height,
- bool ragged,
- bool ragged_last)
-{
- /* if there is a forced break, this reduces to 2 1-page problems */
- for (vsize i = 0; i < lines.size () - 1; i++)
- if (lines[i].page_permission_ == ly_symbol2scm ("force"))
- {
- vector<Line_details> lines1 (lines.begin (), lines.begin () + i + 1);
- vector<Line_details> lines2 (lines.begin () + i + 1, lines.end ());
- Spacing_result p1 = space_systems_on_1_page (lines1, page_height, ragged);
- Spacing_result p2 = space_systems_on_1_page (lines2, page_height, ragged || ragged_last);
-
- p1.systems_per_page_.push_back (p2.systems_per_page_[0]);
- p1.force_.push_back (p2.force_[0]);
- p1.penalty_ += p2.penalty_ - lines[i].turn_penalty_;
- p1.demerits_ += p2.demerits_ - lines[i].turn_penalty_;
- return p1;
- }
-
- vector<Real> page1_force;
- vector<Real> page2_force;
- Page_spacing page1 (page_height);
- Page_spacing page2 (page_height);
-
- page1_force.resize (lines.size () - 1, infinity_f);
- page2_force.resize (lines.size () - 1, infinity_f);
-
- for (vsize i = 0; i < page1_force.size (); i++)
+ vsize system = lines_.size () - 1;
+ while (system != VPOS)
{
- page1.append_system (lines[i]);
- page2.prepend_system (lines[lines.size () - 1 - i]);
- page1_force[i] = (ragged && page1.force_ < 0 && i > 0) ? infinity_f : page1.force_;
+ Page_spacing_node const &cur = simple_state_[system];
+ vsize system_count = (cur.prev_ == VPOS) ? system + 1 : system - cur.prev_;
- if (ragged || ragged_last)
- page2_force[page2_force.size () - 1 - i] =
- (page2.force_ < 0 && i < page1_force.size () - 1) ? infinity_f : 0;
- else
- page2_force[page2_force.size () - 1 - i] = page2.force_;
- }
-
- vsize best_sys_count = 1;
- Real best_demerits = infinity_f;
- for (vsize i = 0; i < page1_force.size (); i++)
- {
- Real dem = page1_force[i] * page1_force[i]
- + page2_force[i] * page2_force[i]
- + lines[i+1].page_penalty_
- + lines.back ().page_penalty_ + lines.back ().turn_penalty_;
- if (dem < best_demerits)
- {
- best_demerits = dem;
- best_sys_count = i+1;
- }
+ ret.force_.push_back (cur.force_);
+ ret.systems_per_page_.push_back (system_count);
+ ret.demerits_ += cur.force_ * cur.force_;
+ system = cur.prev_;
}
- Spacing_result ret;
- ret.systems_per_page_.push_back (best_sys_count);
- ret.systems_per_page_.push_back (lines.size () - best_sys_count);
- ret.force_.push_back (page1_force[best_sys_count-1]);
- ret.force_.push_back (page2_force[best_sys_count-1]);
- ret.penalty_ = lines[best_sys_count-1].page_penalty_
- + lines.back ().page_penalty_
- + lines.back ().turn_penalty_;
- ret.demerits_ = best_demerits;
-
+ reverse (ret.force_);
+ reverse (ret.systems_per_page_);
return ret;
}
-Page_spacer::Page_spacer (vector<Line_details> const &lines, Real page_height, bool ragged, bool ragged_last)
- : lines_ (lines)
-{
- page_height_ = page_height;
- max_page_count_ = 0;
- ragged_ = ragged;
- ragged_last_ = ragged_last;
-}
-
-Spacing_result
+Page_spacing_result
Page_spacer::solve (vsize page_count)
{
if (page_count > max_page_count_)
resize (page_count);
- Spacing_result ret;
- ret.force_.resize (page_count);
- ret.systems_per_page_.resize (page_count);
+ Page_spacing_result ret;
vsize system = lines_.size () - 1;
+ vsize extra_systems = 0;
+ vsize extra_pages = 0;
- if (isinf (state_.at (system, page_count-1).demerits_))
+ if (isinf (state_.at (system, page_count - 1).demerits_))
{
programming_error ("tried to space systems on a bad number of pages");
- return Spacing_result (); /* bad number of pages */
+ /* Usually, this means that we tried to cram too many systems into
+ to few pages. To avoid crashing, we look for the largest number of
+ systems that we can fit properly onto the right number of pages.
+ All the systems that don't fit get tacked onto the last page.
+ */
+ vsize i;
+ for (i = system; isinf (state_.at (i, page_count - 1).demerits_) && i; i--)
+ ;
+
+ if (i)
+ {
+ extra_systems = system - i;
+ system = i;
+ }
+ else
+ {
+ /* try chopping off pages from the end */
+ vsize j;
+ for (j = page_count; j && isinf (state_.at (system, j - 1).demerits_); j--)
+ ;
+
+ if (j)
+ {
+ extra_pages = page_count - j;
+ page_count = j;
+ }
+ else
+ return Page_spacing_result (); /* couldn't salvage it -- probably going to crash */
+ }
}
- ret.penalty_ = state_.at (system, page_count-1).penalty_
- + lines_.back ().page_penalty_ + lines_.back ().turn_penalty_;
+ ret.force_.resize (page_count);
+ ret.systems_per_page_.resize (page_count);
+ ret.system_count_status_ = state_.at (system, page_count - 1).system_count_status_;
+ ret.penalty_ = state_.at (system, page_count - 1).penalty_
+ + lines_.back ().page_penalty_ + lines_.back ().turn_penalty_;
ret.demerits_ = 0;
for (vsize p = page_count; p--;)
ret.force_[p] = ps.force_;
ret.demerits_ += ps.force_ * ps.force_;
if (p == 0)
- ret.systems_per_page_[p] = system + 1;
+ ret.systems_per_page_[p] = system + 1;
else
- ret.systems_per_page_[p] = system - ps.prev_;
+ ret.systems_per_page_[p] = system - ps.prev_;
system = ps.prev_;
}
- ret.demerits_ += ret.penalty_;
+
+ if (extra_systems)
+ {
+ ret.systems_per_page_.back () += extra_systems;
+ ret.force_.back () = BAD_SPACING_PENALTY;
+ }
+ if (extra_pages)
+ {
+ ret.force_.insert (ret.force_.end (), extra_pages, BAD_SPACING_PENALTY);
+ ret.systems_per_page_.insert (ret.systems_per_page_.end (), extra_pages, 0);
+ }
+
return ret;
}
for (vsize page = max_page_count_; page < page_count; page++)
for (vsize line = page; line < lines_.size (); line++)
if (!calc_subproblem (page, line))
- break;
+ break;
max_page_count_ = page_count;
}
+// Carries out one step in the dynamic programming algorithm for putting systems
+// on a fixed number of pages. One call to this routine calculates the best
+// configuration for putting lines 0 through LINE-1 on PAGE+1 pages, provided that
+// we have previously called calc_subproblem(page-1, k) for every k < LINE.
+//
+// This algorithm is similar to the constrained-breaking algorithm.
+//
+// If page == VPOS, we act on simple_state_ instead of state_. This is useful if
+// we don't want to constrain the number of pages that the solution has. In this
+// case, the algorithm looks more like the page-turn-page-breaking algorithm. But
+// the subproblems look similar for both, so we reuse this method.
bool
Page_spacer::calc_subproblem (vsize page, vsize line)
{
- Page_spacing space (page_height_);
- Page_spacing_node &cur = state_.at (line, page);
- bool ragged = ragged_ || (ragged_last_ && line == lines_.size () - 1);
-
- for (vsize page_start = line+1; page_start > page && page_start--;)
+ bool last = line == lines_.size () - 1;
+
+ // Note: if page == VPOS then we don't actually know yet which page number we're
+ // working on, so we have to recalculate the page height in the loop. Therefore
+ // our early-exit condition from the loop depends on paper_height rather than
+ // page_height (ie. we break only if we would overfill a page without margins
+ // or headers/footers). Otherwise, the algorithm would not be optimal:
+ // if our page has a very large header then perhaps
+ // we should look ahead a few systems in order to find the best solution. A
+ // good example of this is input/regression/page-spacing-tall-headfoot.ly
+ vsize page_num = page == VPOS ? 0 : page;
+ Real paper_height = breaker_->paper_height ();
+ Page_spacing space (breaker_->page_height (page_num + first_page_num_, last),
+ breaker_);
+ Page_spacing_node &cur = page == VPOS ? simple_state_[line] : state_.at (line, page);
+ bool ragged = ragged_ || (ragged_last_ && last);
+ int line_count = 0;
+
+ for (vsize page_start = line + 1; page_start > page_num && page_start--;)
{
- Page_spacing_node const *prev = page > 0 ? &state_.at (page_start-1, page-1) : 0;
+ Page_spacing_node const *prev = 0;
+
+ if (page == VPOS)
+ {
+ if (page_start > 0)
+ {
+ prev = &simple_state_[page_start - 1];
+ space.resize (breaker_->page_height (prev->page_ + 1, last));
+ }
+ else
+ space.resize (breaker_->page_height (first_page_num_, last));
+ }
+ else if (page > 0)
+ prev = &state_.at (page_start - 1, page - 1);
space.prepend_system (lines_[page_start]);
- if (page_start < line && (isinf (space.force_) || (space.force_ < 0 && ragged)))
- break;
+ bool overfull = (space.rod_height_ > paper_height
+ || (ragged_
+ && (space.rod_height_ + space.spring_len_ > paper_height)));
+ // This 'if' statement is a little hard to parse. It won't consider this configuration
+ // if it is overfull unless the current configuration is the first one with this start
+ // point. We also make an exception (and consider this configuration) if the previous
+ // configuration we tried had fewer lines than min-systems-per-page.
+ if (!breaker_->too_few_lines (line_count)
+ && page_start < line
+ && overfull)
+ break;
+
+ line_count += lines_[page_start].compressed_nontitle_lines_count_;
if (page > 0 || page_start == 0)
- {
- if (line == lines_.size () - 1 && ragged_last_ && space.force_ > 0)
- space.force_ = 0;
-
- /* we may have to deal with single lines that are taller than a page */
- if (isinf (space.force_) && page_start == line)
- space.force_ = -200000;
-
- Real dem = fabs (space.force_) + (prev ? prev->demerits_ : 0);
- Real penalty = 0;
- if (page_start > 0)
- penalty = lines_[page_start-1].page_penalty_
- + (page % 2 == 0) ? lines_[page_start-1].turn_penalty_ : 0;
-
- dem += penalty;
- if (dem < cur.demerits_ || page_start == line)
- {
- cur.demerits_ = dem;
- cur.force_ = space.force_;
- cur.penalty_ = penalty + (prev ? prev->penalty_ : 0);
- cur.prev_ = page_start - 1;
- }
- }
+ {
+ // If the last page is ragged, set its force to zero. This way, we will leave
+ // the last page half-empty rather than trying to balance things out
+ // (which only makes sense in non-ragged situations).
+ if (line == lines_.size () - 1 && ragged && last && space.force_ > 0)
+ space.force_ = 0;
+
+ Real demerits = space.force_ * space.force_;
+
+ // Clamp the demerits at BAD_SPACING_PENALTY, even if the page
+ // is overfull. This ensures that TERRIBLE_SPACING_PENALTY takes
+ // precedence over overfull pages.
+ demerits = min (demerits, BAD_SPACING_PENALTY);
+ demerits += (prev ? prev->demerits_ : 0);
+
+ Real penalty = breaker_->line_count_penalty (line_count);
+ if (page_start > 0)
+ penalty += lines_[page_start - 1].page_penalty_
+ + (page % 2 == 0) ? lines_[page_start - 1].turn_penalty_ : 0;
+
+ /* Deal with widow/orphan lines */
+ /* Last line of paragraph is first line on the new page */
+ if ((page_start > 0)
+ && (page_start < lines_.size ())
+ && (lines_[page_start].last_markup_line_))
+ penalty += breaker_->orphan_penalty ();
+ /* First line of paragraph is last line on the previous page */
+ if ((page_start > 0)
+ && (page_start < lines_.size ())
+ && (lines_[page_start - 1].first_markup_line_))
+ penalty += breaker_->orphan_penalty ();
+
+ demerits += penalty;
+ if (demerits < cur.demerits_ || page_start == line)
+ {
+ cur.demerits_ = demerits;
+ cur.force_ = space.force_;
+ cur.penalty_ = penalty + (prev ? prev->penalty_ : 0);
+ cur.system_count_status_ = breaker_->line_count_status (line_count)
+ | (prev ? prev->system_count_status_ : 0);
+ cur.prev_ = page_start - 1;
+ cur.page_ = prev ? prev->page_ + 1 : first_page_num_;
+ }
+ }
if (page_start > 0
- && lines_[page_start-1].page_permission_ == ly_symbol2scm ("force"))
- break;
+ && lines_[page_start - 1].page_permission_ == ly_symbol2scm ("force"))
+ break;
}
return !isinf (cur.demerits_);
}
-vsize
-min_page_count (vector<Line_details> const &uncompressed_lines,
- Real page_height, bool ragged, bool ragged_last)
-{
- vsize ret = 1;
- Real cur_rod_height = 0;
- vector<Line_details> lines = compress_lines (uncompressed_lines);
-
- assert (lines.size ());
- for (vsize i = lines.size (); i--;)
- {
- bool rag = ragged || (ragged_last && ret == 1);
- Real ext_len = lines[i].extent_.length ();
- Real next_height = cur_rod_height + ext_len
- + (rag ? lines[i].space_ : 0)
- + ((cur_rod_height > 0) ? lines[i].padding_: 0);
-
- if ((next_height > page_height && cur_rod_height > 0)
- || (i < lines.size () - 1 && lines[i].page_permission_ == ly_symbol2scm ("force")))
- {
- ret++;
- cur_rod_height = ext_len + (rag ? lines[i].space_ : 0);
- }
- else
- cur_rod_height = next_height;
- }
-
- return ret;
-}
-
-Spacing_result
-space_systems_on_n_pages (vector<Line_details> const &lines,
- vsize n,
- Real page_height,
- bool ragged,
- bool ragged_last)
-{
- vector<Line_details> compressed_lines = compress_lines (lines);
- Spacing_result ret;
- assert (n >= min_page_count (lines, page_height, ragged, ragged_last));
-
- if (n > compressed_lines.size ())
- return Spacing_result ();
- if (n == 1)
- ret = space_systems_on_1_page (compressed_lines, page_height, ragged || ragged_last);
- else if (n == 2)
- ret = space_systems_on_2_pages (compressed_lines, page_height, ragged, ragged_last);
-
- Page_spacer ps (compressed_lines, page_height, ragged, ragged_last);
- ret = ps.solve (n);
-
- ret.systems_per_page_ = uncompress_solution (ret.systems_per_page_, compressed_lines);
- return ret;
-}
-
-Spacing_result
-space_systems_on_n_or_one_more_pages (vector<Line_details> const &lines,
- vsize n,
- Real page_height,
- Real odd_pages_penalty,
- bool ragged,
- bool ragged_last)
-{
- Spacing_result n_res = space_systems_on_n_pages (lines, n, page_height, ragged, ragged_last);
- Spacing_result m_res = space_systems_on_n_pages (lines, n+1, page_height, ragged, ragged_last);
- n_res.demerits_ += odd_pages_penalty;
- n_res.force_.back () += odd_pages_penalty;
-
- if (n_res.demerits_ < m_res.demerits_)
- return n_res;
- return m_res;
-}
-
-Spacing_result
-space_systems_on_best_pages (vector<Line_details> const &lines,
- Real page_height,
- Real odd_pages_penalty,
- bool ragged,
- bool ragged_last)
-{
- vector<Line_details> compressed_lines = compress_lines (lines);
- vsize min_p_count = min_page_count (compressed_lines, page_height, ragged, ragged_last);
-
- Page_spacer ps (compressed_lines, page_height, ragged, ragged_last);
- Spacing_result best = ps.solve (min_p_count);
- best.force_.back () += (min_p_count % 2) ? odd_pages_penalty : 0;
- best.demerits_ += (min_p_count % 2) ? odd_pages_penalty : 0;
-
- for (vsize i = min_p_count+1; i <= compressed_lines.size (); i++)
- {
- Spacing_result cur = ps.solve (i);
- cur.demerits_ += (i % 2) ? odd_pages_penalty : 0;
- if (cur.demerits_ < best.demerits_)
- best = cur;
- }
-
- best.systems_per_page_ = uncompress_solution (best.systems_per_page_, compressed_lines);
- return best;
-}