author | wenzelm |
Sun, 15 Sep 2019 13:42:01 +0200 | |
changeset 70699 | 3eb30d80cee6 |
parent 70692 | 41b5e515c238 |
child 70764 | 6d36b30fdd67 |
permissions | -rw-r--r-- |
46611 | 1 |
/* Title: Pure/General/graph.scala |
2 |
Author: Makarius |
|
3 |
||
4 |
Directed graphs. |
|
5 |
*/ |
|
6 |
||
7 |
package isabelle |
|
8 |
||
9 |
||
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
10 |
import scala.collection.immutable.{SortedMap, SortedSet} |
46611 | 11 |
import scala.annotation.tailrec |
12 |
||
13 |
||
14 |
object Graph |
|
15 |
{ |
|
48348 | 16 |
class Duplicate[Key](val key: Key) extends Exception |
70651 | 17 |
{ |
18 |
override def toString: String = "Graph.Duplicate(" + key.toString + ")" |
|
19 |
} |
|
48348 | 20 |
class Undefined[Key](val key: Key) extends Exception |
70651 | 21 |
{ |
22 |
override def toString: String = "Graph.Undefined(" + key.toString + ")" |
|
23 |
} |
|
48348 | 24 |
class Cycles[Key](val cycles: List[List[Key]]) extends Exception |
70651 | 25 |
{ |
26 |
override def toString: String = cycles.mkString("Graph.Cycles(", ",\n", ")") |
|
27 |
} |
|
46611 | 28 |
|
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
29 |
def empty[Key, A](implicit ord: Ordering[Key]): Graph[Key, A] = |
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
30 |
new Graph[Key, A](SortedMap.empty(ord)) |
46667 | 31 |
|
70636 | 32 |
def make[Key, A](entries: List[((Key, A), List[Key])], |
70692 | 33 |
symmetric: Boolean = false)(implicit ord: Ordering[Key]): Graph[Key, A] = |
49560 | 34 |
{ |
35 |
val graph1 = |
|
70692 | 36 |
(empty[Key, A](ord) /: entries) { case (graph, ((x, info), _)) => graph.new_node(x, info) } |
49560 | 37 |
val graph2 = |
67935 | 38 |
(graph1 /: entries) { case (graph, ((x, _), ys)) => |
39 |
(graph /: ys)({ case (g, y) => if (symmetric) g.add_edge(y, x) else g.add_edge(x, y) }) } |
|
49560 | 40 |
graph2 |
41 |
} |
|
42 |
||
46667 | 43 |
def string[A]: Graph[String, A] = empty(Ordering.String) |
44 |
def int[A]: Graph[Int, A] = empty(Ordering.Int) |
|
45 |
def long[A]: Graph[Long, A] = empty(Ordering.Long) |
|
49560 | 46 |
|
47 |
||
48 |
/* XML data representation */ |
|
49 |
||
50 |
def encode[Key, A](key: XML.Encode.T[Key], info: XML.Encode.T[A]): XML.Encode.T[Graph[Key, A]] = |
|
60215 | 51 |
(graph: Graph[Key, A]) => { |
49560 | 52 |
import XML.Encode._ |
53 |
list(pair(pair(key, info), list(key)))(graph.dest) |
|
60215 | 54 |
} |
49560 | 55 |
|
59245
be4180f3c236
more formal Graph_Display.Node (with ordering) and Graph_Display.Edge;
wenzelm
parents:
59212
diff
changeset
|
56 |
def decode[Key, A](key: XML.Decode.T[Key], info: XML.Decode.T[A])( |
59212 | 57 |
implicit ord: Ordering[Key]): XML.Decode.T[Graph[Key, A]] = |
60215 | 58 |
(body: XML.Body) => { |
49560 | 59 |
import XML.Decode._ |
59245
be4180f3c236
more formal Graph_Display.Node (with ordering) and Graph_Display.Edge;
wenzelm
parents:
59212
diff
changeset
|
60 |
make(list(pair(pair(key, info), list(key)))(body))(ord) |
60215 | 61 |
} |
46611 | 62 |
} |
63 |
||
64 |
||
46712 | 65 |
final class Graph[Key, A] private(rep: SortedMap[Key, (A, (SortedSet[Key], SortedSet[Key]))]) |
46611 | 66 |
{ |
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
67 |
type Keys = SortedSet[Key] |
46611 | 68 |
type Entry = (A, (Keys, Keys)) |
69 |
||
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
70 |
def ordering: Ordering[Key] = rep.ordering |
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
71 |
def empty_keys: Keys = SortedSet.empty[Key](ordering) |
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
72 |
|
46666
b01b6977a5e8
clarified signature -- avoid oddities of Iterable like Iterator.map;
wenzelm
parents:
46661
diff
changeset
|
73 |
|
b01b6977a5e8
clarified signature -- avoid oddities of Iterable like Iterator.map;
wenzelm
parents:
46661
diff
changeset
|
74 |
/* graphs */ |
46611 | 75 |
|
76 |
def is_empty: Boolean = rep.isEmpty |
|
48507 | 77 |
def defined(x: Key): Boolean = rep.isDefinedAt(x) |
68321 | 78 |
def domain: Set[Key] = rep.keySet |
46611 | 79 |
|
68496 | 80 |
def size: Int = rep.size |
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
81 |
def iterator: Iterator[(Key, Entry)] = rep.iterator |
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
82 |
|
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
83 |
def keys_iterator: Iterator[Key] = iterator.map(_._1) |
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
84 |
def keys: List[Key] = keys_iterator.toList |
46611 | 85 |
|
49560 | 86 |
def dest: List[((Key, A), List[Key])] = |
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
87 |
(for ((x, (i, (_, succs))) <- iterator) yield ((x, i), succs.toList)).toList |
46611 | 88 |
|
46666
b01b6977a5e8
clarified signature -- avoid oddities of Iterable like Iterator.map;
wenzelm
parents:
46661
diff
changeset
|
89 |
override def toString: String = |
49560 | 90 |
dest.map({ case ((x, _), ys) => |
91 |
x.toString + " -> " + ys.iterator.map(_.toString).mkString("{", ", ", "}") }) |
|
46666
b01b6977a5e8
clarified signature -- avoid oddities of Iterable like Iterator.map;
wenzelm
parents:
46661
diff
changeset
|
92 |
.mkString("Graph(", ", ", ")") |
46611 | 93 |
|
94 |
private def get_entry(x: Key): Entry = |
|
95 |
rep.get(x) match { |
|
96 |
case Some(entry) => entry |
|
97 |
case None => throw new Graph.Undefined(x) |
|
98 |
} |
|
99 |
||
100 |
private def map_entry(x: Key, f: Entry => Entry): Graph[Key, A] = |
|
101 |
new Graph[Key, A](rep + (x -> f(get_entry(x)))) |
|
102 |
||
103 |
||
104 |
/* nodes */ |
|
105 |
||
106 |
def get_node(x: Key): A = get_entry(x)._1 |
|
107 |
||
108 |
def map_node(x: Key, f: A => A): Graph[Key, A] = |
|
109 |
map_entry(x, { case (i, ps) => (f(i), ps) }) |
|
110 |
||
111 |
||
112 |
/* reachability */ |
|
113 |
||
114 |
/*nodes reachable from xs -- topologically sorted for acyclic graphs*/ |
|
115 |
def reachable(next: Key => Keys, xs: List[Key]): (List[List[Key]], Keys) = |
|
116 |
{ |
|
48350
09bf3b73e446
clarified topological ordering: preserve order of adjacency via reverse fold;
wenzelm
parents:
48348
diff
changeset
|
117 |
def reach(x: Key, reached: (List[Key], Keys)): (List[Key], Keys) = |
46611 | 118 |
{ |
119 |
val (rs, r_set) = reached |
|
120 |
if (r_set(x)) reached |
|
121 |
else { |
|
48350
09bf3b73e446
clarified topological ordering: preserve order of adjacency via reverse fold;
wenzelm
parents:
48348
diff
changeset
|
122 |
val (rs1, r_set1) = (next(x) :\ (rs, r_set + x))(reach) |
46611 | 123 |
(x :: rs1, r_set1) |
124 |
} |
|
125 |
} |
|
126 |
def reachs(reached: (List[List[Key]], Keys), x: Key): (List[List[Key]], Keys) = |
|
127 |
{ |
|
128 |
val (rss, r_set) = reached |
|
48350
09bf3b73e446
clarified topological ordering: preserve order of adjacency via reverse fold;
wenzelm
parents:
48348
diff
changeset
|
129 |
val (rs, r_set1) = reach(x, (Nil, r_set)) |
46611 | 130 |
(rs :: rss, r_set1) |
131 |
} |
|
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
132 |
((List.empty[List[Key]], empty_keys) /: xs)(reachs) |
46611 | 133 |
} |
134 |
||
135 |
/*immediate*/ |
|
136 |
def imm_preds(x: Key): Keys = get_entry(x)._2._1 |
|
137 |
def imm_succs(x: Key): Keys = get_entry(x)._2._2 |
|
138 |
||
139 |
/*transitive*/ |
|
140 |
def all_preds(xs: List[Key]): List[Key] = reachable(imm_preds, xs)._1.flatten |
|
141 |
def all_succs(xs: List[Key]): List[Key] = reachable(imm_succs, xs)._1.flatten |
|
142 |
||
46613 | 143 |
/*strongly connected components; see: David King and John Launchbury, |
144 |
"Structuring Depth First Search Algorithms in Haskell"*/ |
|
145 |
def strong_conn: List[List[Key]] = |
|
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
146 |
reachable(imm_preds, all_succs(keys))._1.filterNot(_.isEmpty).reverse |
46613 | 147 |
|
46611 | 148 |
|
149 |
/* minimal and maximal elements */ |
|
150 |
||
151 |
def minimals: List[Key] = |
|
152 |
(List.empty[Key] /: rep) { |
|
153 |
case (ms, (m, (_, (preds, _)))) => if (preds.isEmpty) m :: ms else ms } |
|
154 |
||
155 |
def maximals: List[Key] = |
|
156 |
(List.empty[Key] /: rep) { |
|
157 |
case (ms, (m, (_, (_, succs)))) => if (succs.isEmpty) m :: ms else ms } |
|
158 |
||
159 |
def is_minimal(x: Key): Boolean = imm_preds(x).isEmpty |
|
160 |
def is_maximal(x: Key): Boolean = imm_succs(x).isEmpty |
|
161 |
||
66830 | 162 |
def is_isolated(x: Key): Boolean = is_minimal(x) && is_maximal(x) |
163 |
||
46611 | 164 |
|
46668 | 165 |
/* node operations */ |
46611 | 166 |
|
167 |
def new_node(x: Key, info: A): Graph[Key, A] = |
|
168 |
{ |
|
48648 | 169 |
if (defined(x)) throw new Graph.Duplicate(x) |
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
170 |
else new Graph[Key, A](rep + (x -> (info, (empty_keys, empty_keys)))) |
46611 | 171 |
} |
172 |
||
46613 | 173 |
def default_node(x: Key, info: A): Graph[Key, A] = |
48648 | 174 |
if (defined(x)) this else new_node(x, info) |
46613 | 175 |
|
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
176 |
private def del_adjacent(fst: Boolean, x: Key)(map: SortedMap[Key, Entry], y: Key) |
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
177 |
: SortedMap[Key, Entry] = |
46611 | 178 |
map.get(y) match { |
179 |
case None => map |
|
180 |
case Some((i, (preds, succs))) => |
|
181 |
map + (y -> (i, if (fst) (preds - x, succs) else (preds, succs - x))) |
|
182 |
} |
|
183 |
||
184 |
def del_node(x: Key): Graph[Key, A] = |
|
185 |
{ |
|
186 |
val (preds, succs) = get_entry(x)._2 |
|
187 |
new Graph[Key, A]( |
|
188 |
(((rep - x) /: preds)(del_adjacent(false, x)) /: succs)(del_adjacent(true, x))) |
|
189 |
} |
|
190 |
||
46614
165886a4fe64
clarified Graph.restrict (formerly Graph.subgraph) based on public graph operations;
wenzelm
parents:
46613
diff
changeset
|
191 |
def restrict(pred: Key => Boolean): Graph[Key, A] = |
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
192 |
(this /: iterator){ case (graph, (x, _)) => if (!pred(x)) graph.del_node(x) else graph } |
46614
165886a4fe64
clarified Graph.restrict (formerly Graph.subgraph) based on public graph operations;
wenzelm
parents:
46613
diff
changeset
|
193 |
|
70699 | 194 |
def exclude(pred: Key => Boolean): Graph[Key, A] = restrict(name => !pred(name)) |
195 |
||
46611 | 196 |
|
46668 | 197 |
/* edge operations */ |
46611 | 198 |
|
59259
399506ee38a5
clarified static full_graph vs. dynamic visible_graph;
wenzelm
parents:
59245
diff
changeset
|
199 |
def edges_iterator: Iterator[(Key, Key)] = |
399506ee38a5
clarified static full_graph vs. dynamic visible_graph;
wenzelm
parents:
59245
diff
changeset
|
200 |
for { x <- keys_iterator; y <- imm_succs(x).iterator } yield (x, y) |
399506ee38a5
clarified static full_graph vs. dynamic visible_graph;
wenzelm
parents:
59245
diff
changeset
|
201 |
|
46611 | 202 |
def is_edge(x: Key, y: Key): Boolean = |
48507 | 203 |
defined(x) && defined(y) && imm_succs(x)(y) |
46611 | 204 |
|
205 |
def add_edge(x: Key, y: Key): Graph[Key, A] = |
|
206 |
if (is_edge(x, y)) this |
|
207 |
else |
|
208 |
map_entry(y, { case (i, (preds, succs)) => (i, (preds + x, succs)) }). |
|
209 |
map_entry(x, { case (i, (preds, succs)) => (i, (preds, succs + y)) }) |
|
210 |
||
211 |
def del_edge(x: Key, y: Key): Graph[Key, A] = |
|
212 |
if (is_edge(x, y)) |
|
213 |
map_entry(y, { case (i, (preds, succs)) => (i, (preds - x, succs)) }). |
|
214 |
map_entry(x, { case (i, (preds, succs)) => (i, (preds, succs - y)) }) |
|
215 |
else this |
|
216 |
||
217 |
||
218 |
/* irreducible paths -- Hasse diagram */ |
|
219 |
||
46661
d2ac78ba805e
prefer sorted Map/Set for canonical order of results -- pass ordering via fresh copy of empty;
wenzelm
parents:
46659
diff
changeset
|
220 |
private def irreducible_preds(x_set: Keys, path: List[Key], z: Key): List[Key] = |
46611 | 221 |
{ |
222 |
def red(x: Key)(x1: Key) = is_edge(x, x1) && x1 != z |
|
223 |
@tailrec def irreds(xs0: List[Key], xs1: List[Key]): List[Key] = |
|
224 |
xs0 match { |
|
225 |
case Nil => xs1 |
|
226 |
case x :: xs => |
|
60215 | 227 |
if (!x_set(x) || x == z || path.contains(x) || |
46611 | 228 |
xs.exists(red(x)) || xs1.exists(red(x))) |
229 |
irreds(xs, xs1) |
|
230 |
else irreds(xs, x :: xs1) |
|
231 |
} |
|
232 |
irreds(imm_preds(z).toList, Nil) |
|
233 |
} |
|
234 |
||
235 |
def irreducible_paths(x: Key, y: Key): List[List[Key]] = |
|
236 |
{ |
|
237 |
val (_, x_set) = reachable(imm_succs, List(x)) |
|
238 |
def paths(path: List[Key])(ps: List[List[Key]], z: Key): List[List[Key]] = |
|
239 |
if (x == z) (z :: path) :: ps |
|
240 |
else (ps /: irreducible_preds(x_set, path, z))(paths(z :: path)) |
|
241 |
if ((x == y) && !is_edge(x, x)) List(Nil) else paths(Nil)(Nil, y) |
|
242 |
} |
|
243 |
||
244 |
||
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
245 |
/* transitive closure and reduction */ |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
246 |
|
50447
2e22cdccdc38
clarified transitive_closure: proper cumulation of transitive steps, which is essential for Warshall-style algorithms;
wenzelm
parents:
50445
diff
changeset
|
247 |
private def transitive_step(z: Key): Graph[Key, A] = |
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
248 |
{ |
50447
2e22cdccdc38
clarified transitive_closure: proper cumulation of transitive steps, which is essential for Warshall-style algorithms;
wenzelm
parents:
50445
diff
changeset
|
249 |
val (preds, succs) = get_entry(z)._2 |
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
250 |
var graph = this |
50447
2e22cdccdc38
clarified transitive_closure: proper cumulation of transitive steps, which is essential for Warshall-style algorithms;
wenzelm
parents:
50445
diff
changeset
|
251 |
for (x <- preds; y <- succs) graph = graph.add_edge(x, y) |
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
252 |
graph |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
253 |
} |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
254 |
|
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
255 |
def transitive_closure: Graph[Key, A] = (this /: keys_iterator)(_.transitive_step(_)) |
50447
2e22cdccdc38
clarified transitive_closure: proper cumulation of transitive steps, which is essential for Warshall-style algorithms;
wenzelm
parents:
50445
diff
changeset
|
256 |
|
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
257 |
def transitive_reduction_acyclic: Graph[Key, A] = |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
258 |
{ |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
259 |
val trans = this.transitive_closure |
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
260 |
if (trans.iterator.exists({ case (x, (_, (_, succs))) => succs.contains(x) })) |
50452
bfb5964e3041
stateless dockable window for graphview, which is triggered by the active area of the corresponding diagnostic command;
wenzelm
parents:
50447
diff
changeset
|
261 |
error("Cyclic graph") |
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
262 |
|
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
263 |
var graph = this |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
264 |
for { |
56372
fadb0fef09d7
more explicit iterator terminology, in accordance to Scala 2.8 library;
wenzelm
parents:
50452
diff
changeset
|
265 |
(x, (_, (_, succs))) <- iterator |
50445
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
266 |
y <- succs |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
267 |
if trans.imm_preds(y).exists(z => trans.is_edge(x, z)) |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
268 |
} graph = graph.del_edge(x, y) |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
269 |
graph |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
270 |
} |
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
271 |
|
68c9a6538c0e
added graph operations for transitive closure and reduction in Scala -- unproven and thus better left out of the kernel-relevant ML module;
wenzelm
parents:
49560
diff
changeset
|
272 |
|
46611 | 273 |
/* maintain acyclic graphs */ |
274 |
||
275 |
def add_edge_acyclic(x: Key, y: Key): Graph[Key, A] = |
|
276 |
if (is_edge(x, y)) this |
|
277 |
else { |
|
278 |
irreducible_paths(y, x) match { |
|
279 |
case Nil => add_edge(x, y) |
|
280 |
case cycles => throw new Graph.Cycles(cycles.map(x :: _)) |
|
281 |
} |
|
282 |
} |
|
283 |
||
48348 | 284 |
def add_deps_acyclic(y: Key, xs: List[Key]): Graph[Key, A] = |
46611 | 285 |
(this /: xs)(_.add_edge_acyclic(_, y)) |
286 |
||
287 |
def topological_order: List[Key] = all_succs(minimals) |
|
288 |
} |