5 * (c) 2003 Mark Wooding
8 /*----- Licensing notice --------------------------------------------------*
10 * This program is free software; you can redistribute it and/or modify
11 * it under the terms of the GNU General Public License as published by
12 * the Free Software Foundation; either version 2 of the License, or
13 * (at your option) any later version.
15 * This program is distributed in the hope that it will be useful,
16 * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18 * GNU General Public License for more details.
20 * You should have received a copy of the GNU General Public License
21 * along with this program; if not, write to the Free Software Foundation,
22 * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
25 /*----- Header files ------------------------------------------------------*/
37 /*----- Static variables --------------------------------------------------*/
39 #define INF ((unsigned long)-1)
41 /*----- Utility functions -------------------------------------------------*/
43 static int err(Tcl_Interp *ti, /*const*/ char *p)
45 Tcl_SetResult(ti, p, TCL_STATIC);
51 * Arguments: @Tcl_Interp *ti@ = interpreter to leave errors in
52 * @vec *v@ = pointer to input adjacency matrix
53 * @unsigned long *tt@ = pointer to output adjacency matrix
54 * @size_t *nn@ = where to put the table size
56 * Returns: Tcl return code.
58 * Use: Imports an adjacency matrix.
61 static int import(Tcl_Interp *ti, vec *v, unsigned long **tt, size_t *nn)
67 /* --- Check the table is well-formed --- */
70 return (err(ti, "adjacency matrix must be two-dimensional"));
71 if (v->dim[0].lo != 0 || v->dim[1].lo || v->dim[0].hi != v->dim[1].hi)
72 return (err(ti, "adjacency matrix must be square and zero-origin"));
73 n = *nn = v->dim[0].hi;
75 /* --- Copy the data over --- */
79 t = (void *)Tcl_Alloc(n * sizeof(*t));
80 for (i = 0; i < n; i++) {
82 if (Tcl_GetLongFromObj(ti, v->v[i], &l) != TCL_OK) {
86 t[i] = l >= 0 ? l : INF;
94 * Arguments: @Tcl_Interp *ti@ = interpreter to create output vector
95 * @unsigned long *t@ = pointer to table
96 * @size_t n@ = size of the table
98 * Returns: A pointer to the vector, or null.
100 * Use: Exports an adjacency matrix.
103 static vec *export(Tcl_Interp *ti, unsigned long *t, size_t n)
110 b[0].lo = b[1].lo = 0;
111 b[0].hi = b[1].hi = n;
112 if ((v = vec_create(ti, 2, b, 0)) == 0)
114 o = Tcl_NewLongObj(-1);
116 for (i = 0; i < v->n; i++) {
117 v->v[i] = t[i] == INF ? o : Tcl_NewLongObj(t[i]);
118 Tcl_IncrRefCount(v->v[i]);
124 /*----- Floyd-Warshall all-points shortest path ---------------------------*/
126 /* --- @graph-shortest-path VEC@ --- *
128 * Returns a pair of vectors containing, respectively, the shortest path
129 * length and the successor element in the shortest path. If you say
131 * destructure {len path} [graph-shortest-path $v]
133 * then [$len get I J] is the shortest path length from node I to node J, and
134 * [$path get I J] is the first hop on that shortest path. (To compute the
135 * entire path, set K to be that first hop; the next hop is then [$path get K
138 * The adjacency matrix is given in VEC: negative entries indicate no path;
139 * nonnegative entries are weights. All entries must be integers.
142 static int cmd_shortestpath(ClientData cd, Tcl_Interp *ti,
143 int objc, Tcl_Obj *const *objv)
145 vec *v, *lv = 0, *pv = 0;
147 unsigned long *a = 0, *p = 0;
150 /* --- Read in the arguments --- */
153 err(ti, "usage: graph-shortest-path VEC");
156 if ((v = vec_find(ti, objv[1])) == 0 || import(ti, v, &a, &n) != TCL_OK)
159 /* --- Set up the path table --- */
161 p = (void *)Tcl_Alloc(n * n * sizeof(*p));
162 for (i = 0; i < n; i++) {
163 for (j = 0; j < n; j++)
168 /* --- Do the main algorithm --- *
170 * Not so hard. Just brute force and ignorance.
173 for (k = 0; k < n; k++) {
174 for (i = 0; i < n; i++) {
175 for (j = 0; j < n; j++) {
176 if (a[i * n + k] != INF && a[k * n + j] != INF &&
177 a[i * n + k] + a[k * n + j] < a[i * n + j]) {
178 a[i * n + j] = a[i * n + k] + a[k * n + j];
179 p[i * n + j] = p[i * n + k];
185 /* --- Wrap up --- */
187 if ((lv = export(ti, a, n)) == 0 || (pv = export(ti, p, n)) == 0)
189 o = Tcl_NewListObj(0, 0);
190 Tcl_ListObjAppendElement
191 (ti, o, Tcl_NewStringObj(Tcl_GetCommandName(ti, lv->c), -1));
192 Tcl_ListObjAppendElement
193 (ti, o, Tcl_NewStringObj(Tcl_GetCommandName(ti, pv->c), -1));
194 Tcl_SetObjResult(ti, o);
200 if (a) Tcl_Free((void *)a);
201 if (p) Tcl_Free((void *)p);
202 if (lv) vec_destroy(ti, lv);
203 if (pv) vec_destroy(ti, pv);
207 /*----- Travelling Salesman Problem ---------------------------------------*/
209 /* --- @rrange@ --- *
211 * Arguments: @size_t max@ = maximum number wanted
213 * Returns: An integer uniformly distributed on %$[0, max)$%.
216 static size_t rrange(size_t max)
229 /* --- @graph-travelling-salesman [-OPTIONS] ADJ LIST@ --- *
231 * Solves the Travelling Salesman Problem approximately. Returns a list
232 * containing (firstly) the cost of the computed route, and secondly the
233 * route itself. Only the nodes in LIST are considered. The OPTIONS affect
234 * the algorithm in various ways.
236 * -cool FACTOR Cooling factor. Default is 1.001. Must be greater
237 * than 1 for the simulated annealing to work.
239 * -dead COUNT Give up after COUNT cycles with no improvement.
242 * -inner COUNT Perform COUNT loops each cooling cycle. Default is
245 * -temp TEMP Set the initial temperature to TEMP. Default is not
246 * very helpful. Initial setting should be well above
247 * the maximum cost increase from a cycle.
249 * -cycle / -nocycle If -cycle is set, solve the classical problem of
250 * finding a minimal cyclic path. If -nocycle is set,
251 * then start at the first node in LIST, and minimize a
252 * tour without caring where the end goes. The default
256 static int cmd_tsp(ClientData cd, Tcl_Interp *ti,
257 int objc, Tcl_Obj *const *objv)
259 /* --- Initial algorithm parameters --- */
267 /* --- Other variables --- */
270 unsigned long *a = 0;
273 size_t *r = 0, *r_best = 0;
274 unsigned long c_best = 0, c_curr, c;
279 Tcl_Obj *o, *o2, **oo;
281 /* --- Parse the command line --- */
283 for (i = 1; i < objc; i++) {
285 char *p = Tcl_GetStringFromObj(objv[i], &len);
286 if (strcmp(p, "-cool") == 0) {
287 i++; if (i >= objc) goto args;
288 if (Tcl_GetDoubleFromObj(ti, objv[i], &cool) != TCL_OK)
291 err(ti, "cooling factor must be > 1");
294 } else if (strcmp(p, "-temp") == 0) {
295 i++; if (i >= objc) goto args;
296 if (Tcl_GetDoubleFromObj(ti, objv[i], &temp) != TCL_OK)
299 err(ti, "initial temperature must be > 0");
302 } else if (strcmp(p, "-inner") == 0) {
303 i++; if (i >= objc) goto args;
304 if (Tcl_GetLongFromObj(ti, objv[i], &inner) != TCL_OK)
307 err(ti, "inner loop count must be > 0");
310 } else if (strcmp(p, "-dead") == 0) {
311 i++; if (i >= objc) goto args;
312 if (Tcl_GetLongFromObj(ti, objv[i], &dead) != TCL_OK)
315 err(ti, "dead cycles count must be > 0");
318 } else if (strcmp(p, "-cycle") == 0)
320 else if (strcmp(p, "-nocycle") == 0)
322 else if (strcmp(p, "--") == 0) {
324 } else if (*p != '-')
327 err(ti, "bad option for graph-travelling-salesman");
332 /* --- Check the rest --- */
335 err(ti, "usage: graph-travelling-salesman [-OPTIONS] ADJ LIST");
338 if ((v = vec_find(ti, objv[i])) == 0 || import(ti, v, &a, &n) != TCL_OK)
340 if (Tcl_ListObjGetElements(ti, objv[i + 1], &nn, &oo) != TCL_OK)
345 r = (void *)Tcl_Alloc(nn * sizeof(*r));
346 r_best = (void *)Tcl_Alloc(nn * sizeof(*r_best));
347 for (i = 0; i < nn; i++) {
349 if (Tcl_GetLongFromObj(ti, oo[i], &l) != TCL_OK)
351 if (l < 0 || l >= n) {
352 err(ti, "node index out of range");
358 /* --- The one and two node problems are trivial --- *
360 * Avoiding these prevents us from having to mess with special cases later.
364 memcpy(r_best, r, nn * sizeof(*r));
366 c_best = a[r[0] * n + r[0]];
368 c_best = a[r[0] * n + r[1]];
372 /* --- Randomize the initial vector --- *
374 * If we're not cycling, then nail the first item in place.
377 for (i = cycle ? 0 : 1; i < nn; i++) {
379 t = r[i]; r[i] = r[i + j]; r[i + j] = t;
382 /* --- Compute the initial cost --- *
384 * If we're not cycling, don't close off at the end. The easiest way to do
385 * that is to start at the end. There are at least three elements.
388 if (cycle) { j = 0; i = nn - 1; }
389 else { j = nn - 1; i = j - 1; }
392 c += a[r[i] * n + r[j]];
399 /* printf("*** initial cost = %lu; n = %u; nn = %u\n", c, n, nn); */
401 memcpy(r_best, r, nn * sizeof(*r));
403 /* --- Embark on the main loop --- */
408 for (ii = inner; ii; ii--) {
409 size_t i, j, ilo, ihi, jlo, jhi;
411 /* --- Decide on a change to make --- *
413 * We just swap two nodes around on the path. This is simple and seems
414 * to be effective. Don't allow the first node to be moved if we're
422 i = rrange(nn - 1) + 1;
423 j = rrange(nn - 1) + 1;
426 /* --- Compute the change in cost --- *
428 * Since we're only swapping two nodes, we can work out the change
429 * without rescanning the entire path, by just looking at the local
434 continue; /* No change */
435 if (j < i) { t = i; i = j; j = t; }
436 ilo = (i + nn - 1) % nn; ihi = (i + 1) % nn;
437 jlo = (j + nn - 1) % nn; jhi = (j + 1) % nn;
442 /* --- This is where the algorithms differ --- *
444 * If we're producing a cycle, then we need the cost function to wrap
445 * around here. Otherwise, it hits a barrier, and the last node only
446 * has a partial effect.
451 c -= (a[r[jlo] * n + r[j]] +
453 a[r[i] * n + r[ihi]]);
454 c += (a[r[jlo] * n + r[i]] +
456 a[r[j] * n + r[ihi]]);
460 c -= a[r[ilo] * n + r[i]] + a[r[i] * n + r[j]];
461 c += a[r[ilo] * n + r[j]] + a[r[j] * n + r[i]];
463 c -= (a[r[ilo] * n + r[i]] +
464 a[r[i] * n + r[ihi]] +
465 a[r[jlo] * n + r[j]]);
466 c += (a[r[ilo] * n + r[j]] +
467 a[r[j] * n + r[ihi]] +
468 a[r[jlo] * n + r[i]]);
473 /* --- Usual case --- *
475 * This splits into two subcases, depending on whether the areas
481 c -= (a[r[ilo] * n + r[i]] +
483 a[r[j] * n + r[jhi]]);
484 c += (a[r[ilo] * n + r[j]] +
486 a[r[i] * n + r[jhi]]);
488 c -= (a[r[ilo] * n + r[i]] +
489 a[r[i] * n + r[ihi]] +
490 a[r[jlo] * n + r[j]] +
491 a[r[j] * n + r[jhi]]);
492 c += (a[r[ilo] * n + r[j]] +
493 a[r[j] * n + r[ihi]] +
494 a[r[jlo] * n + r[i]] +
495 a[r[i] * n + r[jhi]]);
499 #ifdef PARANOID_CHECKING /* Turn this on to check the shortcut */
503 if (cycle) { jj = 0; ii = nn - 1; }
504 else { jj = nn - 1; ii = jj - 1; }
506 t = r[i]; r[i] = r[j]; r[j] = t;
508 cc += a[r[ii] * n + r[jj]];
514 t = r[i]; r[i] = r[j]; r[j] = t;
516 printf("i = %u; j = %u; c = %lu; cc = %lu\n", i, j, c, cc);
522 /* --- Decide what to do --- */
525 rrange(65536) >= (size_t)(exp(((double)c_curr -
526 (double)c)/temp) * 65536))
529 /* --- Accept the change --- */
534 t = r[i]; r[i] = r[j]; r[j] = t;
535 if (c_curr < c_best) {
537 /* printf("*** new best = %lu\n", c_best); */
538 memcpy(r_best, r, nn * sizeof(*r));
551 o = Tcl_NewListObj(0, 0);
552 o2 = Tcl_NewListObj(0, 0);
553 Tcl_ListObjAppendElement(ti, o, Tcl_NewLongObj(c_best));
554 for (i = 0; i < nn; i++)
555 Tcl_ListObjAppendElement(ti, o2, Tcl_NewLongObj(r_best[i]));
556 Tcl_ListObjAppendElement(ti, o, o2);
557 Tcl_SetObjResult(ti, o);
560 /* --- Tidy up --- */
563 if (a) Tcl_Free((void *)a);
564 if (r) Tcl_Free((void *)r);
565 if (r_best) Tcl_Free((void *)r_best);
569 err(ti, "missing argument for option");
573 /*----- Initialization ----------------------------------------------------*/
575 int Graph_SafeInit(Tcl_Interp *ti)
577 static const struct cmd {
578 /*const*/ char *name;
579 Tcl_ObjCmdProc *proc;
581 { "graph-shortest-path", cmd_shortestpath },
582 { "graph-travelling-salesman", cmd_tsp },
587 if (Tcl_PkgRequire(ti, "vector", "1.0.0", 0) == 0)
589 for (c = cmds; c->name; c++)
590 Tcl_CreateObjCommand(ti, c->name, c->proc, 0, 0);
591 if (Tcl_PkgProvide(ti, "graph", "1.0.0"))
596 int Graph_Init(Tcl_Interp *ti)
598 return (Graph_SafeInit(ti));
601 /*----- That's all, folks -------------------------------------------------*/