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 -------------------------------------------------*/