2 constrained-breaking.cc -- implement a line breaker that
3 support limits on the number of systems
5 source file of the GNU LilyPond music typesetter
7 (c) 2006 Han-Wen Nienhuys <hanwen@xs4all.nl>
10 #include "constrained-breaking.hh"
12 #include "international.hh"
14 #include "output-def.hh"
15 #include "paper-column.hh"
16 #include "paper-score.hh"
17 #include "simple-spacer.hh"
22 We use the following optimal substructure. Let W(A) be our weight function.
24 Let A_{k,n} = (a_{k,n,1}, ... a_{k,n,k}) be the optimal set of line breaks
25 for k systems and n potential breakpoints. a_{k,n,k} = n (it is the end of
28 Then A_{k+1, m} is contructed from
29 min_ {k < j < m} ( W(A_{k,j} :: m) )
30 where by A::m we denote appending m to the list A
34 The above algorithm makes it easy to end at a point before the end of the
35 score (just find A_{k,m} for some m < breaks_.size () - 1). However, we must
36 add information for starting at a point after the beginning. One constructor
37 allows the specification of a list of starting columns, start_. We then have
38 start_.size () different solution arrays. state_[i] is the array for the
39 solution starting at column number start_[i].
41 The indicies "start" and "end" refer to the index in the start_ array of the
42 desired starting and ending columns.
44 each solution array looks like
45 a_{1,1,1} a_{2,1,2} a_{3,1,3} . . .
46 X a_{2,2,2} a_{3,2,3} . . .
50 where the X's mark invalid solutions (can't have more systems than
51 breakpoints). Note that each value is of the form a_{x,n,x}. This is because
52 a breakpoint of the form a_{x,n,x-1} will also be called a_{x-1,m,x-1} for
53 some m < n. Each cell in the array stores the value of its m (ie. the
54 ending breakpoint of the previous line) as "prev_".
56 For finding A_{sys, brk}, let "me" be the (sys_count,brk) cell in our
57 solution array (state_[start][sys * rank + brk]).
59 Then A_{sys, brk} = A_{sys - 1, me.prev_} :: me
63 start and sys here are indexed from 0.
64 brk is indexed from starting_breakpoints_[start]
65 (for brk, starting_breakpoints_[start] is the beginning
66 of the piece; the smallest value we should ever see here is
67 starting_breakpoints_[start] + 1) */
69 Constrained_breaking::calc_subproblem (vsize start, vsize sys, vsize brk)
71 assert (sys < systems_);
72 assert (start < start_.size ());
73 assert (brk < breaks_.size ());
75 bool found_something = false;
76 vsize start_col = starting_breakpoints_[start];
77 vector<Constrained_break_node> &st = state_[start];
78 vsize rank = breaks_.size () - start_col;
79 vsize max_index = brk - start_col;
80 for (vsize j=sys; j < max_index; j++)
82 if (0 == sys && j > 0)
83 break; /* the first line cannot have its first break after the beginning */
85 Column_x_positions const *cur = &cols_[(j + start_col)*cols_rank_ + brk];
86 Column_x_positions const *prev = NULL;
91 prev = st[(sys-1) * rank + j].line_config_;
92 prev_dem = st[(sys-1) * rank + j].demerits_;
100 combine_demerits (prev, cur, &force, &pen, &dem);
105 int k = sys*rank + max_index;
106 if (isinf (st[k].demerits_) || dem < st[k].demerits_)
108 found_something = true;
109 st[k].demerits_ = dem;
110 st[k].force_ = force;
111 st[k].penalty_ = pen;
113 st[k].line_config_ = cur;
116 return found_something;
119 vector<Column_x_positions>
120 Constrained_breaking::solve ()
124 programming_error (_f ("no system number set in constrained-breaking"));
125 systems_ = breaks_.size () / 4;
129 return get_solution(0, VPOS, systems_);
133 Constrained_breaking::space_line (vsize i, vsize j)
135 bool ragged_right = to_boolean (pscore_->layout ()->c_variable ("ragged-right"));
136 bool ragged_last = to_boolean (pscore_->layout ()->c_variable ("ragged-last"));
137 Column_x_positions col;
139 vector<Grob*> line (all_.begin () + breaks_[i],
140 all_.begin() + breaks_[j] + 1);
142 line[0] = dynamic_cast<Item *> (line[0])->find_prebroken_piece (RIGHT);
143 line.back () = dynamic_cast<Item *> (line.back ())->find_prebroken_piece (LEFT);
147 /* we have no idea what line this will be -- only whether it is the first */
148 Interval line_dims = line_dimensions_int (pscore_->layout (), i);
149 Simple_spacer_wrapper *sp = generate_spacing_problem (line, line_dims);
151 bool last = j == breaks_.size () - 1;
152 bool ragged = ragged_right || (last && ragged_last);
153 sp->solve (&col, ragged);
160 Constrained_breaking::resize (vsize systems)
164 if (!breaks_.size () && pscore_)
166 /* do all the rod/spring problems */
167 breaks_ = pscore_->find_break_indices ();
168 cols_rank_ = breaks_.size ();
169 all_ = pscore_->root_system ()->columns ();
170 cols_.resize (breaks_.size () * breaks_.size ());
171 for (vsize i = 0; i < breaks_.size () - 1; i++)
172 for (vsize j = i + 1; j < breaks_.size (); j++)
174 cols_[i*cols_rank_ + j] = space_line (i, j);
175 if (!cols_[i*cols_rank_ + j].satisfies_constraints_)
179 /* work out all the starting indices */
180 for (vsize i = 0; i < start_.size (); i++)
183 for (j = 0; j < breaks_.size () - 1 && breaks_[j] < start_[i]; j++)
185 starting_breakpoints_.push_back (j);
186 start_[i] = breaks_[j];
188 state_.resize (start_.size ());
191 if (pscore_ && systems_ > valid_systems_)
193 for (vsize i = 0; i < state_.size (); i++)
194 state_[i].resize((breaks_.size () - starting_breakpoints_[i]) * systems_);
196 /* fill out the matrices */
197 for (vsize i = 0; i < state_.size (); i++)
198 for (vsize j = valid_systems_; j < systems_; j++)
199 for (vsize k = starting_breakpoints_[i] + j + 1; k < breaks_.size (); k++)
200 if (!calc_subproblem (i, j, k))
201 break; /* if we couldn't break this, it is too cramped already */
202 valid_systems_ = systems_;
206 vector<Column_x_positions>
207 Constrained_breaking::get_solution (vsize start, vsize end, vsize sys_count)
211 prepare_solution (start, end, sys_count, &rank, &end_brk);
213 vector<Constrained_break_node> const &st = state_[start];
214 vector<Column_x_positions> ret;
216 /* find the first solution that satisfies constraints */
217 for (vsize sys = sys_count-1; sys != VPOS; sys--)
219 for (vsize brk = end_brk; brk != VPOS; brk--)
221 if (!isinf (st[sys*rank + brk].force_))
225 warning ( _("couldn't find line breaking that satisfies constraints" ));
226 ret.push_back (space_line (brk, end_brk));
228 /* build up the good solution */
229 for (vsize cur_sys = sys; cur_sys != VPOS; cur_sys--)
231 assert (brk != VPOS);
232 ret.push_back( *st[cur_sys*rank + brk].line_config_ );
233 brk = st[cur_sys*rank + brk].prev_;
240 /* if we get to here, just put everything on one line */
241 warning ( _("couldn't find line breaking that satisfies constraints" ));
242 ret.push_back (space_line (0, end_brk));
247 Constrained_breaking::get_demerits (vsize start, vsize end, vsize sys_count)
251 prepare_solution (start, end, sys_count, &rank, &brk);
253 return state_[start][(sys_count-1)*rank + brk].demerits_;
257 Constrained_breaking::get_force (vsize start, vsize end, vsize sys_count)
261 prepare_solution (start, end, sys_count, &rank, &brk);
262 vector<Constrained_break_node> const &st = state_[start];
265 for (int sys = sys_count-1; sys >= 0 && brk != VPOS; sys--)
267 f += fabs (st[sys*rank + brk].force_);
268 brk = st[sys*rank + brk].prev_;
277 Constrained_breaking::get_penalty (vsize start, vsize end, vsize sys_count)
281 prepare_solution (start, end, sys_count, &rank, &brk);
283 return state_[start][(sys_count-1)*rank + brk].penalty_;
287 Constrained_breaking::get_page_penalty (vsize start, vsize end, vsize sys_count, vsize sys_num, bool turn)
291 prepare_solution (start, end, sys_count, &rank, &brk);
294 for (sys = sys_count-1; sys > sys_num; sys--)
295 brk = state_[start][sys*rank + brk].prev_;
297 if (brk == VPOS) /* we didn't satisfy constraints */
299 vector<Grob*> const &cols = state_[start][sys*rank + brk].line_config_->cols_;
303 Grob const *pc = cols.back ();
306 SCM pen = pc->get_property ("page-penalty");
307 SCM turn_pen = pc->get_property ("page-turn-penalty");
309 if (!turn && scm_is_number (pen) && fabs (scm_to_double (pen)) < 10000)
310 ret = scm_to_double (pen);
311 if (turn && scm_is_number (turn_pen) && fabs (scm_to_double (turn_pen)) < 10000)
312 ret = scm_to_double (turn_pen);
319 Constrained_breaking::get_min_systems (vsize start, vsize end)
325 prepare_solution (start, end, 1, &rank, &brk);
326 vector<Constrained_break_node> const &st = state_[start];
328 /* sys_count < rank : rank is the # of breakpoints, we can't have more systems */
329 for (sys_count = 0; sys_count < rank; sys_count++)
331 if (sys_count >= valid_systems_)
333 resize (sys_count + 3);
335 if (!isinf (st[sys_count*rank + brk].force_))
336 return sys_count + 1;
338 /* no possible breaks satisfy constraints */
343 Constrained_breaking::get_max_systems (vsize start, vsize end)
345 vsize brk = (end >= start_.size ()) ? breaks_.size () - 1 : starting_breakpoints_[end];
346 return brk - starting_breakpoints_[start];
350 Constrained_breaking::prepare_solution (vsize start, vsize end, vsize sys_count, vsize *rank, vsize *brk)
352 assert (start < start_.size () && (end == VPOS || end <= start_.size ()));
353 assert (start < end);
356 if (end == start_.size ())
359 *rank = breaks_.size () - starting_breakpoints_[start];
360 *brk = end == VPOS ? breaks_.size () - 1 : starting_breakpoints_[end];
361 *brk -= starting_breakpoints_[start];
364 Constrained_breaking::Constrained_breaking ()
366 valid_systems_ = systems_ = 0;
367 start_.push_back (0);
370 Constrained_breaking::Constrained_breaking (vector<int> const &start)
373 valid_systems_ = systems_ = 0;
377 Constrained_breaking::combine_demerits (Column_x_positions const *prev,
378 Column_x_positions const *col,
381 Real *demerits) const
383 Real prev_f = prev ? prev->force_ : 0;
386 if (col->cols_.empty () || !col->satisfies_constraints_)
390 *force = col->force_;
392 Grob *pc = col->cols_.back ();
395 SCM pen = pc->get_property ("penalty");
396 if (scm_is_number (pen) && fabs (scm_to_double (pen)) < 10000)
397 *penalty += scm_to_double (pen);
401 *demerits = (*force) * (*force) + abs (prev_f - *force) + *penalty;