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 /*----- Header files ------------------------------------------------------*/
39 /*----- Static variables --------------------------------------------------*/
41 #define INF ((unsigned long)-1)
43 /*----- Utility functions -------------------------------------------------*/
45 static int err(Tcl_Interp
*ti
, /*const*/ char *p
)
47 Tcl_SetResult(ti
, p
, TCL_STATIC
);
53 * Arguments: @Tcl_Interp *ti@ = interpreter to leave errors in
54 * @vec *v@ = pointer to input adjacency matrix
55 * @unsigned long *tt@ = pointer to output adjacency matrix
56 * @size_t *nn@ = where to put the table size
58 * Returns: Tcl return code.
60 * Use: Imports an adjacency matrix.
63 static int import(Tcl_Interp
*ti
, vec
*v
, unsigned long **tt
, size_t *nn
)
69 /* --- Check the table is well-formed --- */
72 return (err(ti
, "adjacency matrix must be two-dimensional"));
73 if (v
->dim
[0].lo
!= 0 || v
->dim
[1].lo
|| v
->dim
[0].hi
!= v
->dim
[1].hi
)
74 return (err(ti
, "adjacency matrix must be square and zero-origin"));
75 n
= *nn
= v
->dim
[0].hi
;
77 /* --- Copy the data over --- */
81 t
= (void *)Tcl_Alloc(n
* sizeof(*t
));
82 for (i
= 0; i
< n
; i
++) {
84 if (Tcl_GetLongFromObj(ti
, v
->v
[i
], &l
) != TCL_OK
) {
88 t
[i
] = l
>= 0 ? l
: INF
;
96 * Arguments: @Tcl_Interp *ti@ = interpreter to create output vector
97 * @unsigned long *t@ = pointer to table
98 * @size_t n@ = size of the table
100 * Returns: A pointer to the vector, or null.
102 * Use: Exports an adjacency matrix.
105 static vec
*export(Tcl_Interp
*ti
, unsigned long *t
, size_t n
)
112 b
[0].lo
= b
[1].lo
= 0;
113 b
[0].hi
= b
[1].hi
= n
;
114 if ((v
= vec_create(ti
, 2, b
, 0)) == 0)
116 o
= Tcl_NewLongObj(-1);
118 for (i
= 0; i
< v
->n
; i
++) {
119 v
->v
[i
] = t
[i
] == INF ? o
: Tcl_NewLongObj(t
[i
]);
120 Tcl_IncrRefCount(v
->v
[i
]);
126 /*----- Floyd-Warshall all-points shortest path ---------------------------*/
128 /* --- @graph-shortest-path VEC@ --- *
130 * Returns a pair of vectors containing, respectively, the shortest path
131 * length and the successor element in the shortest path. If you say
133 * destructure {len path} [graph-shortest-path $v]
135 * then [$len get I J] is the shortest path length from node I to node J, and
136 * [$path get I J] is the first hop on that shortest path. (To compute the
137 * entire path, set K to be that first hop; the next hop is then [$path get K
140 * The adjacency matrix is given in VEC: negative entries indicate no path;
141 * nonnegative entries are weights. All entries must be integers.
144 static int cmd_shortestpath(ClientData cd
, Tcl_Interp
*ti
,
145 int objc
, Tcl_Obj
*const *objv
)
147 vec
*v
, *lv
= 0, *pv
= 0;
149 unsigned long *a
= 0, *p
= 0;
152 /* --- Read in the arguments --- */
155 err(ti
, "usage: graph-shortest-path VEC");
158 if ((v
= vec_find(ti
, objv
[1])) == 0 || import(ti
, v
, &a
, &n
) != TCL_OK
)
161 /* --- Set up the path table --- */
163 p
= (void *)Tcl_Alloc(n
* n
* sizeof(*p
));
164 for (i
= 0; i
< n
; i
++) {
165 for (j
= 0; j
< n
; j
++)
170 /* --- Do the main algorithm --- *
172 * Not so hard. Just brute force and ignorance.
175 for (k
= 0; k
< n
; k
++) {
176 for (i
= 0; i
< n
; i
++) {
177 for (j
= 0; j
< n
; j
++) {
178 if (a
[i
* n
+ k
] != INF
&& a
[k
* n
+ j
] != INF
&&
179 a
[i
* n
+ k
] + a
[k
* n
+ j
] < a
[i
* n
+ j
]) {
180 a
[i
* n
+ j
] = a
[i
* n
+ k
] + a
[k
* n
+ j
];
181 p
[i
* n
+ j
] = p
[i
* n
+ k
];
187 /* --- Wrap up --- */
189 if ((lv
= export(ti
, a
, n
)) == 0 || (pv
= export(ti
, p
, n
)) == 0)
191 o
= Tcl_NewListObj(0, 0);
192 Tcl_ListObjAppendElement
193 (ti
, o
, Tcl_NewStringObj(Tcl_GetCommandName(ti
, lv
->c
), -1));
194 Tcl_ListObjAppendElement
195 (ti
, o
, Tcl_NewStringObj(Tcl_GetCommandName(ti
, pv
->c
), -1));
196 Tcl_SetObjResult(ti
, o
);
202 if (a
) Tcl_Free((void *)a
);
203 if (p
) Tcl_Free((void *)p
);
204 if (lv
) vec_destroy(ti
, lv
);
205 if (pv
) vec_destroy(ti
, pv
);
209 /*----- Travelling Salesman Problem ---------------------------------------*/
211 /* --- @rrange@ --- *
213 * Arguments: @size_t max@ = maximum number wanted
215 * Returns: An integer uniformly distributed on %$[0, max)$%.
218 static size_t rrange(size_t max
)
231 /* --- @graph-travelling-salesman [-OPTIONS] ADJ LIST@ --- *
233 * Solves the Travelling Salesman Problem approximately. Returns a list
234 * containing (firstly) the cost of the computed route, and secondly the
235 * route itself. Only the nodes in LIST are considered. The OPTIONS affect
236 * the algorithm in various ways.
238 * -cool FACTOR Cooling factor. Default is 1.001. Must be greater
239 * than 1 for the simulated annealing to work.
241 * -dead COUNT Give up after COUNT cycles with no improvement.
244 * -inner COUNT Perform COUNT loops each cooling cycle. Default is
247 * -temp TEMP Set the initial temperature to TEMP. Default is not
248 * very helpful. Initial setting should be well above
249 * the maximum cost increase from a cycle.
251 * -cycle / -nocycle If -cycle is set, solve the classical problem of
252 * finding a minimal cyclic path. If -nocycle is set,
253 * then start at the first node in LIST, and minimize a
254 * tour without caring where the end goes. The default
258 static int cmd_tsp(ClientData cd
, Tcl_Interp
*ti
,
259 int objc
, Tcl_Obj
*const *objv
)
261 /* --- Initial algorithm parameters --- */
269 /* --- Other variables --- */
272 unsigned long *a
= 0;
275 size_t *r
= 0, *r_best
= 0;
276 unsigned long c_best
= 0, c_curr
, c
;
281 Tcl_Obj
*o
, *o2
, **oo
;
283 /* --- Parse the command line --- */
285 for (i
= 1; i
< objc
; i
++) {
287 char *p
= Tcl_GetStringFromObj(objv
[i
], &len
);
288 if (strcmp(p
, "-cool") == 0) {
289 i
++; if (i
>= objc
) goto args
;
290 if (Tcl_GetDoubleFromObj(ti
, objv
[i
], &cool
) != TCL_OK
)
293 err(ti
, "cooling factor must be > 1");
296 } else if (strcmp(p
, "-temp") == 0) {
297 i
++; if (i
>= objc
) goto args
;
298 if (Tcl_GetDoubleFromObj(ti
, objv
[i
], &temp
) != TCL_OK
)
301 err(ti
, "initial temperature must be > 0");
304 } else if (strcmp(p
, "-inner") == 0) {
305 i
++; if (i
>= objc
) goto args
;
306 if (Tcl_GetLongFromObj(ti
, objv
[i
], &inner
) != TCL_OK
)
309 err(ti
, "inner loop count must be > 0");
312 } else if (strcmp(p
, "-dead") == 0) {
313 i
++; if (i
>= objc
) goto args
;
314 if (Tcl_GetLongFromObj(ti
, objv
[i
], &dead
) != TCL_OK
)
317 err(ti
, "dead cycles count must be > 0");
320 } else if (strcmp(p
, "-cycle") == 0)
322 else if (strcmp(p
, "-nocycle") == 0)
324 else if (strcmp(p
, "--") == 0) {
326 } else if (*p
!= '-')
329 err(ti
, "bad option for graph-travelling-salesman");
334 /* --- Check the rest --- */
337 err(ti
, "usage: graph-travelling-salesman [-OPTIONS] ADJ LIST");
340 if ((v
= vec_find(ti
, objv
[i
])) == 0 || import(ti
, v
, &a
, &n
) != TCL_OK
)
342 if (Tcl_ListObjGetElements(ti
, objv
[i
+ 1], &nn
, &oo
) != TCL_OK
)
347 r
= (void *)Tcl_Alloc(nn
* sizeof(*r
));
348 r_best
= (void *)Tcl_Alloc(nn
* sizeof(*r_best
));
349 for (i
= 0; i
< nn
; i
++) {
351 if (Tcl_GetLongFromObj(ti
, oo
[i
], &l
) != TCL_OK
)
353 if (l
< 0 || l
>= n
) {
354 err(ti
, "node index out of range");
360 /* --- The one and two node problems are trivial --- *
362 * Avoiding these prevents us from having to mess with special cases later.
366 memcpy(r_best
, r
, nn
* sizeof(*r
));
368 c_best
= a
[r
[0] * n
+ r
[0]];
370 c_best
= a
[r
[0] * n
+ r
[1]];
374 /* --- Randomize the initial vector --- *
376 * If we're not cycling, then nail the first item in place.
379 for (i
= cycle ?
0 : 1; i
< nn
; i
++) {
381 t
= r
[i
]; r
[i
] = r
[i
+ j
]; r
[i
+ j
] = t
;
384 /* --- Compute the initial cost --- *
386 * If we're not cycling, don't close off at the end. The easiest way to do
387 * that is to start at the end. There are at least three elements.
390 if (cycle
) { j
= 0; i
= nn
- 1; }
391 else { j
= nn
- 1; i
= j
- 1; }
394 c
+= a
[r
[i
] * n
+ r
[j
]];
401 /* printf("*** initial cost = %lu; n = %u; nn = %u\n", c, n, nn); */
403 memcpy(r_best
, r
, nn
* sizeof(*r
));
405 /* --- Embark on the main loop --- */
410 for (ii
= inner
; ii
; ii
--) {
411 size_t i
, j
, ilo
, ihi
, jlo
, jhi
;
413 /* --- Decide on a change to make --- *
415 * We just swap two nodes around on the path. This is simple and seems
416 * to be effective. Don't allow the first node to be moved if we're
424 i
= rrange(nn
- 1) + 1;
425 j
= rrange(nn
- 1) + 1;
428 /* --- Compute the change in cost --- *
430 * Since we're only swapping two nodes, we can work out the change
431 * without rescanning the entire path, by just looking at the local
436 continue; /* No change */
437 if (j
< i
) { t
= i
; i
= j
; j
= t
; }
438 ilo
= (i
+ nn
- 1) % nn
; ihi
= (i
+ 1) % nn
;
439 jlo
= (j
+ nn
- 1) % nn
; jhi
= (j
+ 1) % nn
;
444 /* --- This is where the algorithms differ --- *
446 * If we're producing a cycle, then we need the cost function to wrap
447 * around here. Otherwise, it hits a barrier, and the last node only
448 * has a partial effect.
453 c
-= (a
[r
[jlo
] * n
+ r
[j
]] +
455 a
[r
[i
] * n
+ r
[ihi
]]);
456 c
+= (a
[r
[jlo
] * n
+ r
[i
]] +
458 a
[r
[j
] * n
+ r
[ihi
]]);
462 c
-= a
[r
[ilo
] * n
+ r
[i
]] + a
[r
[i
] * n
+ r
[j
]];
463 c
+= a
[r
[ilo
] * n
+ r
[j
]] + a
[r
[j
] * n
+ r
[i
]];
465 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
466 a
[r
[i
] * n
+ r
[ihi
]] +
467 a
[r
[jlo
] * n
+ r
[j
]]);
468 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
469 a
[r
[j
] * n
+ r
[ihi
]] +
470 a
[r
[jlo
] * n
+ r
[i
]]);
475 /* --- Usual case --- *
477 * This splits into two subcases, depending on whether the areas
483 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
485 a
[r
[j
] * n
+ r
[jhi
]]);
486 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
488 a
[r
[i
] * n
+ r
[jhi
]]);
490 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
491 a
[r
[i
] * n
+ r
[ihi
]] +
492 a
[r
[jlo
] * n
+ r
[j
]] +
493 a
[r
[j
] * n
+ r
[jhi
]]);
494 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
495 a
[r
[j
] * n
+ r
[ihi
]] +
496 a
[r
[jlo
] * n
+ r
[i
]] +
497 a
[r
[i
] * n
+ r
[jhi
]]);
501 #ifdef PARANOID_CHECKING /* Turn this on to check the shortcut */
505 if (cycle
) { jj
= 0; ii
= nn
- 1; }
506 else { jj
= nn
- 1; ii
= jj
- 1; }
508 t
= r
[i
]; r
[i
] = r
[j
]; r
[j
] = t
;
510 cc
+= a
[r
[ii
] * n
+ r
[jj
]];
516 t
= r
[i
]; r
[i
] = r
[j
]; r
[j
] = t
;
518 printf("i = %u; j = %u; c = %lu; cc = %lu\n", i
, j
, c
, cc
);
524 /* --- Decide what to do --- */
527 rrange(65536) >= (size_t)(exp(((double)c_curr
-
528 (double)c
)/temp
) * 65536))
531 /* --- Accept the change --- */
536 t
= r
[i
]; r
[i
] = r
[j
]; r
[j
] = t
;
537 if (c_curr
< c_best
) {
539 /* printf("*** new best = %lu\n", c_best); */
540 memcpy(r_best
, r
, nn
* sizeof(*r
));
553 o
= Tcl_NewListObj(0, 0);
554 o2
= Tcl_NewListObj(0, 0);
555 Tcl_ListObjAppendElement(ti
, o
, Tcl_NewLongObj(c_best
));
556 for (i
= 0; i
< nn
; i
++)
557 Tcl_ListObjAppendElement(ti
, o2
, Tcl_NewLongObj(r_best
[i
]));
558 Tcl_ListObjAppendElement(ti
, o
, o2
);
559 Tcl_SetObjResult(ti
, o
);
562 /* --- Tidy up --- */
565 if (a
) Tcl_Free((void *)a
);
566 if (r
) Tcl_Free((void *)r
);
567 if (r_best
) Tcl_Free((void *)r_best
);
571 err(ti
, "missing argument for option");
575 /*----- Initialization ----------------------------------------------------*/
577 int Graph_SafeInit(Tcl_Interp
*ti
)
579 static const struct cmd
{
580 /*const*/ char *name
;
581 Tcl_ObjCmdProc
*proc
;
583 { "graph-shortest-path", cmd_shortestpath
},
584 { "graph-travelling-salesman", cmd_tsp
},
589 if (Tcl_PkgRequire(ti
, "vector", "1.0.0", 0) == 0)
591 for (c
= cmds
; c
->name
; c
++)
592 Tcl_CreateObjCommand(ti
, c
->name
, c
->proc
, 0, 0);
593 if (Tcl_PkgProvide(ti
, "graph", "1.0.0"))
598 int Graph_Init(Tcl_Interp
*ti
)
600 return (Graph_SafeInit(ti
));
603 /*----- That's all, folks -------------------------------------------------*/