3 * $Id: graph.c,v 1.3 2003/03/10 23:37:21 mdw Exp $
7 * (c) 2003 Mark Wooding
10 /*----- Licensing notice --------------------------------------------------*
12 * This program is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License as published by
14 * the Free Software Foundation; either version 2 of the License, or
15 * (at your option) any later version.
17 * This program is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU General Public License for more details.
22 * You should have received a copy of the GNU General Public License
23 * along with this program; if not, write to the Free Software Foundation,
24 * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
27 /*----- Revision history --------------------------------------------------*
30 * Revision 1.3 2003/03/10 23:37:21 mdw
31 * Fix single point TSP.
33 * Revision 1.2 2003/03/08 00:40:32 mdw
34 * Fix unsigned crapness in travelling-salesman solver.
36 * Revision 1.1 2003/03/07 00:45:13 mdw
37 * Graph theory functions.
41 /*----- Header files ------------------------------------------------------*/
53 /*----- Static variables --------------------------------------------------*/
55 #define INF ((unsigned long)-1)
57 /*----- Utility functions -------------------------------------------------*/
59 static int err(Tcl_Interp *ti, /*const*/ char *p)
61 Tcl_SetResult(ti, p, TCL_STATIC);
67 * Arguments: @Tcl_Interp *ti@ = interpreter to leave errors in
68 * @vec *v@ = pointer to input adjacency matrix
69 * @unsigned long *tt@ = pointer to output adjacency matrix
70 * @size_t *nn@ = where to put the table size
72 * Returns: Tcl return code.
74 * Use: Imports an adjacency matrix.
77 static int import(Tcl_Interp *ti, vec *v, unsigned long **tt, size_t *nn)
83 /* --- Check the table is well-formed --- */
86 return (err(ti, "adjacency matrix must be two-dimensional"));
87 if (v->dim[0].lo != 0 || v->dim[1].lo || v->dim[0].hi != v->dim[1].hi)
88 return (err(ti, "adjacency matrix must be square and zero-origin"));
89 n = *nn = v->dim[0].hi;
91 /* --- Copy the data over --- */
95 t = (void *)Tcl_Alloc(n * sizeof(*t));
96 for (i = 0; i < n; i++) {
98 if (Tcl_GetLongFromObj(ti, v->v[i], &l) != TCL_OK) {
102 t[i] = l >= 0 ? l : INF;
108 /* --- @export@ --- *
110 * Arguments: @Tcl_Interp *ti@ = interpreter to create output vector
111 * @unsigned long *t@ = pointer to table
112 * @size_t n@ = size of the table
114 * Returns: A pointer to the vector, or null.
116 * Use: Exports an adjacency matrix.
119 static vec *export(Tcl_Interp *ti, unsigned long *t, size_t n)
126 b[0].lo = b[1].lo = 0;
127 b[0].hi = b[1].hi = n;
128 if ((v = vec_create(ti, 2, b, 0)) == 0)
130 o = Tcl_NewLongObj(-1);
132 for (i = 0; i < v->n; i++) {
133 v->v[i] = t[i] == INF ? o : Tcl_NewLongObj(t[i]);
134 Tcl_IncrRefCount(v->v[i]);
140 /*----- Floyd-Warshall all-points shortest path ---------------------------*/
142 /* --- @graph-shortest-path VEC@ --- *
144 * Returns a pair of vectors containing, respectively, the shortest path
145 * length and the successor element in the shortest path. If you say
147 * destructure {len path} [graph-shortest-path $v]
149 * then [$len get I J] is the shortest path length from node I to node J, and
150 * [$path get I J] is the first hop on that shortest path. (To compute the
151 * entire path, set K to be that first hop; the next hop is then [$path get K
154 * The adjacency matrix is given in VEC: negative entries indicate no path;
155 * nonnegative entries are weights. All entries must be integers.
158 static int cmd_shortestpath(ClientData cd, Tcl_Interp *ti,
159 int objc, Tcl_Obj *const *objv)
161 vec *v, *lv = 0, *pv = 0;
163 unsigned long *a = 0, *p = 0;
166 /* --- Read in the arguments --- */
169 err(ti, "usage: graph-shortest-path VEC");
172 if ((v = vec_find(ti, objv[1])) == 0 || import(ti, v, &a, &n) != TCL_OK)
175 /* --- Set up the path table --- */
177 p = (void *)Tcl_Alloc(n * n * sizeof(*p));
178 for (i = 0; i < n; i++) {
179 for (j = 0; j < n; j++)
184 /* --- Do the main algorithm --- *
186 * Not so hard. Just brute force and ignorance.
189 for (k = 0; k < n; k++) {
190 for (i = 0; i < n; i++) {
191 for (j = 0; j < n; j++) {
192 if (a[i * n + k] != INF && a[k * n + j] != INF &&
193 a[i * n + k] + a[k * n + j] < a[i * n + j]) {
194 a[i * n + j] = a[i * n + k] + a[k * n + j];
195 p[i * n + j] = p[i * n + k];
201 /* --- Wrap up --- */
203 if ((lv = export(ti, a, n)) == 0 || (pv = export(ti, p, n)) == 0)
205 o = Tcl_NewListObj(0, 0);
206 Tcl_ListObjAppendElement
207 (ti, o, Tcl_NewStringObj(Tcl_GetCommandName(ti, lv->c), -1));
208 Tcl_ListObjAppendElement
209 (ti, o, Tcl_NewStringObj(Tcl_GetCommandName(ti, pv->c), -1));
210 Tcl_SetObjResult(ti, o);
216 if (a) Tcl_Free((void *)a);
217 if (p) Tcl_Free((void *)p);
218 if (lv) vec_destroy(ti, lv);
219 if (pv) vec_destroy(ti, pv);
223 /*----- Travelling Salesman Problem ---------------------------------------*/
225 /* --- @rrange@ --- *
227 * Arguments: @size_t max@ = maximum number wanted
229 * Returns: An integer uniformly distributed on %$[0, max)$%.
232 static size_t rrange(size_t max)
245 /* --- @graph-travelling-salesman [-OPTIONS] ADJ LIST@ --- *
247 * Solves the Travelling Salesman Problem approximately. Returns a list
248 * containing (firstly) the cost of the computed route, and secondly the
249 * route itself. Only the nodes in LIST are considered. The OPTIONS affect
250 * the algorithm in various ways.
252 * -cool FACTOR Cooling factor. Default is 1.001. Must be greater
253 * than 1 for the simulated annealing to work.
255 * -dead COUNT Give up after COUNT cycles with no improvement.
258 * -inner COUNT Perform COUNT loops each cooling cycle. Default is
261 * -temp TEMP Set the initial temperature to TEMP. Default is not
262 * very helpful. Initial setting should be well above
263 * the maximum cost increase from a cycle.
265 * -cycle / -nocycle If -cycle is set, solve the classical problem of
266 * finding a minimal cyclic path. If -nocycle is set,
267 * then start at the first node in LIST, and minimize a
268 * tour without caring where the end goes. The default
272 static int cmd_tsp(ClientData cd, Tcl_Interp *ti,
273 int objc, Tcl_Obj *const *objv)
275 /* --- Initial algorithm parameters --- */
283 /* --- Other variables --- */
286 unsigned long *a = 0;
289 size_t *r = 0, *r_best = 0;
290 unsigned long c_best = 0, c_curr, c;
295 Tcl_Obj *o, *o2, **oo;
297 /* --- Parse the command line --- */
299 for (i = 1; i < objc; i++) {
301 char *p = Tcl_GetStringFromObj(objv[i], &len);
302 if (strcmp(p, "-cool") == 0) {
303 i++; if (i >= objc) goto args;
304 if (Tcl_GetDoubleFromObj(ti, objv[i], &cool) != TCL_OK)
307 err(ti, "cooling factor must be > 1");
310 } else if (strcmp(p, "-temp") == 0) {
311 i++; if (i >= objc) goto args;
312 if (Tcl_GetDoubleFromObj(ti, objv[i], &temp) != TCL_OK)
315 err(ti, "initial temperature must be > 0");
318 } else if (strcmp(p, "-inner") == 0) {
319 i++; if (i >= objc) goto args;
320 if (Tcl_GetLongFromObj(ti, objv[i], &inner) != TCL_OK)
323 err(ti, "inner loop count must be > 0");
326 } else if (strcmp(p, "-dead") == 0) {
327 i++; if (i >= objc) goto args;
328 if (Tcl_GetLongFromObj(ti, objv[i], &dead) != TCL_OK)
331 err(ti, "dead cycles count must be > 0");
334 } else if (strcmp(p, "-cycle") == 0)
336 else if (strcmp(p, "-nocycle") == 0)
338 else if (strcmp(p, "--") == 0) {
340 } else if (*p != '-')
343 err(ti, "bad option for graph-travelling-salesman");
348 /* --- Check the rest --- */
351 err(ti, "usage: graph-travelling-salesman [-OPTIONS] ADJ LIST");
354 if ((v = vec_find(ti, objv[i])) == 0 || import(ti, v, &a, &n) != TCL_OK)
356 if (Tcl_ListObjGetElements(ti, objv[i + 1], &nn, &oo) != TCL_OK)
361 r = (void *)Tcl_Alloc(nn * sizeof(*r));
362 r_best = (void *)Tcl_Alloc(nn * sizeof(*r_best));
363 for (i = 0; i < nn; i++) {
365 if (Tcl_GetLongFromObj(ti, oo[i], &l) != TCL_OK)
367 if (l < 0 || l >= n) {
368 err(ti, "node index out of range");
374 /* --- The one and two node problems are trivial --- *
376 * Avoiding these prevents us from having to mess with special cases later.
380 memcpy(r_best, r, nn * sizeof(*r));
382 c_best = a[r[0] * n + r[0]];
384 c_best = a[r[0] * n + r[1]];
388 /* --- Randomize the initial vector --- *
390 * If we're not cycling, then nail the first item in place.
393 for (i = cycle ? 0 : 1; i < nn; i++) {
395 t = r[i]; r[i] = r[i + j]; r[i + j] = t;
398 /* --- Compute the initial cost --- *
400 * If we're not cycling, don't close off at the end. The easiest way to do
401 * that is to start at the end. There are at least three elements.
404 if (cycle) { j = 0; i = nn - 1; }
405 else { j = nn - 1; i = j - 1; }
408 c += a[r[i] * n + r[j]];
415 /* printf("*** initial cost = %lu; n = %u; nn = %u\n", c, n, nn); */
417 memcpy(r_best, r, nn * sizeof(*r));
419 /* --- Embark on the main loop --- */
424 for (ii = inner; ii; ii--) {
425 size_t i, j, ilo, ihi, jlo, jhi;
427 /* --- Decide on a change to make --- *
429 * We just swap two nodes around on the path. This is simple and seems
430 * to be effective. Don't allow the first node to be moved if we're
438 i = rrange(nn - 1) + 1;
439 j = rrange(nn - 1) + 1;
442 /* --- Compute the change in cost --- *
444 * Since we're only swapping two nodes, we can work out the change
445 * without rescanning the entire path, by just looking at the local
450 continue; /* No change */
451 if (j < i) { t = i; i = j; j = t; }
452 ilo = (i + nn - 1) % nn; ihi = (i + 1) % nn;
453 jlo = (j + nn - 1) % nn; jhi = (j + 1) % nn;
458 /* --- This is where the algorithms differ --- *
460 * If we're producing a cycle, then we need the cost function to wrap
461 * around here. Otherwise, it hits a barrier, and the last node only
462 * has a partial effect.
467 c -= (a[r[jlo] * n + r[j]] +
469 a[r[i] * n + r[ihi]]);
470 c += (a[r[jlo] * n + r[i]] +
472 a[r[j] * n + r[ihi]]);
476 c -= a[r[ilo] * n + r[i]] + a[r[i] * n + r[j]];
477 c += a[r[ilo] * n + r[j]] + a[r[j] * n + r[i]];
479 c -= (a[r[ilo] * n + r[i]] +
480 a[r[i] * n + r[ihi]] +
481 a[r[jlo] * n + r[j]]);
482 c += (a[r[ilo] * n + r[j]] +
483 a[r[j] * n + r[ihi]] +
484 a[r[jlo] * n + r[i]]);
489 /* --- Usual case --- *
491 * This splits into two subcases, depending on whether the areas
497 c -= (a[r[ilo] * n + r[i]] +
499 a[r[j] * n + r[jhi]]);
500 c += (a[r[ilo] * n + r[j]] +
502 a[r[i] * n + r[jhi]]);
504 c -= (a[r[ilo] * n + r[i]] +
505 a[r[i] * n + r[ihi]] +
506 a[r[jlo] * n + r[j]] +
507 a[r[j] * n + r[jhi]]);
508 c += (a[r[ilo] * n + r[j]] +
509 a[r[j] * n + r[ihi]] +
510 a[r[jlo] * n + r[i]] +
511 a[r[i] * n + r[jhi]]);
515 #ifdef PARANOID_CHECKING /* Turn this on to check the shortcut */
519 if (cycle) { jj = 0; ii = nn - 1; }
520 else { jj = nn - 1; ii = jj - 1; }
522 t = r[i]; r[i] = r[j]; r[j] = t;
524 cc += a[r[ii] * n + r[jj]];
530 t = r[i]; r[i] = r[j]; r[j] = t;
532 printf("i = %u; j = %u; c = %lu; cc = %lu\n", i, j, c, cc);
538 /* --- Decide what to do --- */
541 rrange(65536) >= (size_t)(exp(((double)c_curr -
542 (double)c)/temp) * 65536))
545 /* --- Accept the change --- */
550 t = r[i]; r[i] = r[j]; r[j] = t;
551 if (c_curr < c_best) {
553 /* printf("*** new best = %lu\n", c_best); */
554 memcpy(r_best, r, nn * sizeof(*r));
567 o = Tcl_NewListObj(0, 0);
568 o2 = Tcl_NewListObj(0, 0);
569 Tcl_ListObjAppendElement(ti, o, Tcl_NewLongObj(c_best));
570 for (i = 0; i < nn; i++)
571 Tcl_ListObjAppendElement(ti, o2, Tcl_NewLongObj(r_best[i]));
572 Tcl_ListObjAppendElement(ti, o, o2);
573 Tcl_SetObjResult(ti, o);
576 /* --- Tidy up --- */
579 if (a) Tcl_Free((void *)a);
580 if (r) Tcl_Free((void *)r);
581 if (r_best) Tcl_Free((void *)r_best);
585 err(ti, "missing argument for option");
589 /*----- Initialization ----------------------------------------------------*/
591 int Graph_SafeInit(Tcl_Interp *ti)
593 static const struct cmd {
594 /*const*/ char *name;
595 Tcl_ObjCmdProc *proc;
597 { "graph-shortest-path", cmd_shortestpath },
598 { "graph-travelling-salesman", cmd_tsp },
603 if (Tcl_PkgRequire(ti, "vector", "1.0.0", 0) == 0)
605 for (c = cmds; c->name; c++)
606 Tcl_CreateObjCommand(ti, c->name, c->proc, 0, 0);
607 if (Tcl_PkgProvide(ti, "graph", "1.0.0"))
612 int Graph_Init(Tcl_Interp *ti)
614 return (Graph_SafeInit(ti));
617 /*----- That's all, folks -------------------------------------------------*/