+/*
+ page-spacing.cc - implement routines for spacing
+ systems vertically on pages
+
+ source file of the GNU LilyPond music typesetter
+
+ (c) 2006 Joe Neeman <joeneeman@gmail.com>
+*/
+
+#include "page-spacing.hh"
+#include "matrix.hh"
+
+/*
+ A much simplified rods-and-springs problem.
+ */
+struct Page_spacing
+{
+ 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 ();
+ }
+
+ void calc_force ();
+
+ void append_system (const Line_details &line);
+ void prepend_system (const Line_details &line);
+ void clear ();
+};
+
+void
+Page_spacing::calc_force ()
+{
+ 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_;
+}
+
+void
+Page_spacing::append_system (const Line_details &line)
+{
+ rod_height_ += last_line_.padding_;
+
+ rod_height_ += line.extent_.length ();
+ spring_len_ += line.space_;
+ inverse_spring_k_ += line.inverse_hooke_;
+
+ last_line_ = line;
+
+ calc_force ();
+}
+
+void
+Page_spacing::prepend_system (const Line_details &line)
+{
+ if (rod_height_)
+ rod_height_ += line.padding_;
+ else
+ last_line_ = line;
+
+ rod_height_ += line.extent_.length ();
+ spring_len_ += line.space_;
+ inverse_spring_k_ += line.inverse_hooke_;
+
+ calc_force ();
+}
+
+void
+Page_spacing::clear ()
+{
+ force_ = rod_height_ = spring_len_ = 0;
+ inverse_spring_k_ = 0;
+}
+
+/* for each forbidden page break, merge the systems around it into one system. */
+static vector<Line_details>
+compress_lines (const vector<Line_details> &orig)
+{
+ vector<Line_details> ret;
+
+ for (vsize i = 0; i < orig.size (); i++)
+ {
+ if (i < orig.size () - 1 && orig[i].page_permission_ == SCM_EOL)
+ {
+ Line_details compressed = orig[i+1];
+ compressed.extent_[DOWN] = orig[i].extent_[DOWN];
+ compressed.extent_[UP] = orig[i].extent_[UP] + orig[i+1].extent_.length () + orig[i].padding_;
+ compressed.space_ += orig[i].space_;
+ compressed.inverse_hooke_ += orig[i].inverse_hooke_;
+
+ /* we don't need the force_ field for the vertical spacing,
+ so we use force_ = -1 to signal that the line was compressed
+ (and force_ = +1 otherwise).
+ This makes uncompression much easier. */
+ compressed.force_ = -1;
+ ret.push_back (compressed);
+ i++;
+ }
+ else
+ {
+ ret.push_back (orig[i]);
+ ret.back ().force_ = 1;
+ }
+ }
+ return ret;
+}
+
+/* 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)
+{
+ vector<vsize> ret;
+ vsize start_sys = 0;
+
+ for (vsize i = 0; i < systems_per_page.size (); i++)
+ {
+ int compressed_count = 0;
+ for (vsize j = start_sys; j < start_sys + systems_per_page[i]; j++)
+ if (compressed[j].force_ < 0)
+ compressed_count++;
+
+ ret.push_back (systems_per_page[i] + compressed_count);
+ start_sys += systems_per_page[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)
+{
+ 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 (space.force_);
+ ret.penalty_ = lines.back ().page_penalty_ + lines.back ().turn_penalty_;
+ ret.demerits_ = ret.force_.back () * ret.force_.back () + ret.penalty_;
+
+ return ret;
+}
+
+static Spacing_result
+space_systems_on_2_pages (vector<Line_details> const &lines, Real page_height)
+{
+ /* 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);
+ Spacing_result p2 = space_systems_on_1_page (lines2, page_height);
+
+ 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++)
+ {
+ page1.append_system (lines[i]);
+ page2.prepend_system (lines[lines.size () - 1 - i]);
+ page1_force[i] = page1.force_;
+ 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;
+ }
+ }
+
+ 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;
+
+ return ret;
+}
+
+/* for page_count > 2, we use a dynamic algorithm similar to
+ constrained-breaking -- we have a class that stores the intermediate
+ calculations so they can be reused for querying different page counts.
+*/
+
+class Page_spacer
+{
+public:
+ Page_spacer (vector<Line_details> const &lines, Real page_height);
+ Spacing_result solve (vsize page_count);
+
+private:
+ struct Page_spacing_node
+ {
+ Page_spacing_node ()
+ {
+ demerits_ = infinity_f;
+ force_ = infinity_f;
+ penalty_ = infinity_f;
+ prev_ = VPOS;
+ }
+
+ Real demerits_;
+ Real force_;
+ Real penalty_;
+ vsize prev_;
+ };
+
+ Real page_height_;
+ vector<Line_details> lines_;
+ Matrix<Page_spacing_node> state_;
+ vsize max_page_count_;
+
+ void resize (vsize page_count);
+ bool calc_subproblem (vsize page, vsize lines);
+};
+
+Page_spacer::Page_spacer (vector<Line_details> const &lines, Real page_height)
+ : lines_ (lines)
+{
+ page_height_ = page_height;
+ max_page_count_ = 0;
+}
+
+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);
+
+ vsize system = lines_.size () - 1;
+
+ ret.penalty_ = state_.at (system, page_count-1).penalty_
+ + lines_.back ().page_penalty_ + lines_.back ().turn_penalty_;
+
+ for (vsize p = page_count; p--;)
+ {
+ assert (system != VPOS);
+
+ Page_spacing_node const &ps = state_.at (system, p);
+ ret.force_[p] = ps.force_;
+ ret.demerits_ += ps.force_ * ps.force_;
+ if (p == 0)
+ ret.systems_per_page_[p] = system + 1;
+ else
+ ret.systems_per_page_[p] = system - ps.prev_;
+ system = ps.prev_;
+ }
+ ret.demerits_ += ret.penalty_;
+ return ret;
+}
+
+void
+Page_spacer::resize (vsize page_count)
+{
+ assert (page_count > 0);
+
+ if (max_page_count_ >= page_count)
+ return;
+
+ state_.resize (lines_.size (), page_count, Page_spacing_node ());
+ for (vsize page = max_page_count_; page < page_count; page++)
+ for (vsize line = page; line < lines_.size (); line++)
+ if (!calc_subproblem (page, line))
+ break;
+
+ max_page_count_ = page_count;
+}
+
+bool
+Page_spacer::calc_subproblem (vsize page, vsize line)
+{
+ Page_spacing space (page_height_);
+ Page_spacing_node &cur = state_.at (line, page);
+
+ for (vsize page_start = line+1; page_start > page && page_start--;)
+ {
+ Page_spacing_node const *prev = page > 0 ? &state_.at (page_start-1, page-1) : 0;
+
+ space.prepend_system (lines_[page_start]);
+ if (isinf (space.force_))
+ break;
+
+ if (page == 0 && page_start > 0)
+ continue;
+
+ 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_)
+ {
+ cur.demerits_ = dem;
+ cur.force_ = space.force_;
+ cur.penalty_ = penalty + (prev ? prev->penalty_ : 0);
+ cur.prev_ = page_start - 1;
+ }
+ }
+ return !isinf (cur.demerits_);
+}
+
+static vsize
+min_page_count (vector<Line_details> const &lines, Real page_height)
+{
+ vsize ret = 1;
+ Real cur_rod_height = 0;
+
+ for (vsize i = 0; i < lines.size (); i++)
+ {
+ Real next_height = cur_rod_height + lines[i].extent_.length ()
+ + ((i > 0 && cur_rod_height > 0) ? lines[i-1].padding_: 0);
+
+ if ((next_height > page_height && cur_rod_height > 0)
+ || (i > 0 && lines[i-1].page_permission_ == ly_symbol2scm ("force")))
+ {
+ ret++;
+ cur_rod_height = lines[i].extent_.length ();
+ }
+ else
+ cur_rod_height = next_height;
+ }
+ return ret;
+}
+
+Spacing_result
+space_systems_on_min_pages (vector<Line_details> const &lines,
+ Real page_height,
+ Real odd_pages_penalty)
+{
+ vector<Line_details> compressed_lines = compress_lines (lines);
+ vsize min_p_count = min_page_count (compressed_lines, page_height);
+ Spacing_result ret;
+
+ if (min_p_count == 1)
+ {
+ Spacing_result candidate1 = space_systems_on_1_page (compressed_lines, page_height);
+ candidate1.force_.back () += odd_pages_penalty;
+ candidate1.demerits_ += odd_pages_penalty;
+ if (compressed_lines.size () == 1)
+ ret = candidate1;
+ else
+ {
+ Spacing_result candidate2 = space_systems_on_2_pages (compressed_lines, page_height);
+ ret = (candidate1.demerits_ < candidate2.demerits_) ?
+ candidate1 : candidate2;
+ }
+ }
+ else if (min_p_count == 2)
+ ret = space_systems_on_2_pages (compressed_lines, page_height);
+ else
+ {
+ Page_spacer ps (compressed_lines, page_height);
+ Spacing_result candidate1 = ps.solve (min_p_count);
+ if (min_p_count % 2 == 0)
+ ret = candidate1;
+ else
+ {
+ candidate1.force_.back () += odd_pages_penalty;
+ candidate1.demerits_ += odd_pages_penalty;
+
+ if (min_p_count == compressed_lines.size ())
+ ret = candidate1;
+ else
+ {
+ Spacing_result candidate2 = ps.solve (min_p_count + 1);
+ ret = (candidate1.demerits_ < candidate2.demerits_) ?
+ candidate1 : candidate2;
+ }
+ }
+ }
+ ret.systems_per_page_ = uncompress_solution (ret.systems_per_page_, compressed_lines);
+ return ret;
+}
+
+Spacing_result
+space_systems_on_best_pages (vector<Line_details> const &lines,
+ Real page_height,
+ Real odd_pages_penalty)
+{
+ vector<Line_details> compressed_lines = compress_lines (lines);
+ vsize min_p_count = min_page_count (compressed_lines, page_height);
+
+ Page_spacer ps (compressed_lines, page_height);
+ Spacing_result best = ps.solve (min_p_count);
+ 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;
+}