3 * $Id: graph.c,v 1.1 2003/03/07 00:45:13 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 1.1 2003/03/07 00:45:13 mdw
31 * Graph theory functions.
35 /*----- Header files ------------------------------------------------------*/
47 /*----- Static variables --------------------------------------------------*/
49 #define INF ((unsigned long)-1)
51 /*----- Utility functions -------------------------------------------------*/
53 static int err(Tcl_Interp
*ti
, /*const*/ char *p
)
55 Tcl_SetResult(ti
, p
, TCL_STATIC
);
61 * Arguments: @Tcl_Interp *ti@ = interpreter to leave errors in
62 * @vec *v@ = pointer to input adjacency matrix
63 * @unsigned long *tt@ = pointer to output adjacency matrix
64 * @size_t *nn@ = where to put the table size
66 * Returns: Tcl return code.
68 * Use: Imports an adjacency matrix.
71 static int import(Tcl_Interp
*ti
, vec
*v
, unsigned long **tt
, size_t *nn
)
77 /* --- Check the table is well-formed --- */
80 return (err(ti
, "adjacency matrix must be two-dimensional"));
81 if (v
->dim
[0].lo
!= 0 || v
->dim
[1].lo
|| v
->dim
[0].hi
!= v
->dim
[1].hi
)
82 return (err(ti
, "adjacency matrix must be square and zero-origin"));
83 n
= *nn
= v
->dim
[0].hi
;
85 /* --- Copy the data over --- */
89 t
= (void *)Tcl_Alloc(n
* sizeof(*t
));
90 for (i
= 0; i
< n
; i
++) {
92 if (Tcl_GetLongFromObj(ti
, v
->v
[i
], &l
) != TCL_OK
) {
96 t
[i
] = l
>= 0 ? l
: INF
;
102 /* --- @export@ --- *
104 * Arguments: @Tcl_Interp *ti@ = interpreter to create output vector
105 * @unsigned long *t@ = pointer to table
106 * @size_t n@ = size of the table
108 * Returns: A pointer to the vector, or null.
110 * Use: Exports an adjacency matrix.
113 static vec
*export(Tcl_Interp
*ti
, unsigned long *t
, size_t n
)
120 b
[0].lo
= b
[1].lo
= 0;
121 b
[0].hi
= b
[1].hi
= n
;
122 if ((v
= vec_create(ti
, 2, b
, 0)) == 0)
124 o
= Tcl_NewLongObj(-1);
126 for (i
= 0; i
< v
->n
; i
++) {
127 v
->v
[i
] = t
[i
] == INF ? o
: Tcl_NewLongObj(t
[i
]);
128 Tcl_IncrRefCount(v
->v
[i
]);
134 /*----- Floyd-Warshall all-points shortest path ---------------------------*/
136 /* --- @graph-shortest-path VEC@ --- *
138 * Returns a pair of vectors containing, respectively, the shortest path
139 * length and the successor element in the shortest path. If you say
141 * destructure {len path} [graph-shortest-path $v]
143 * then [$len get I J] is the shortest path length from node I to node J, and
144 * [$path get I J] is the first hop on that shortest path. (To compute the
145 * entire path, set K to be that first hop; the next hop is then [$path get K
148 * The adjacency matrix is given in VEC: negative entries indicate no path;
149 * nonnegative entries are weights. All entries must be integers.
152 static int cmd_shortestpath(ClientData cd
, Tcl_Interp
*ti
,
153 int objc
, Tcl_Obj
*const *objv
)
155 vec
*v
, *lv
= 0, *pv
= 0;
157 unsigned long *a
= 0, *p
= 0;
160 /* --- Read in the arguments --- */
163 err(ti
, "usage: graph-shortest-path VEC");
166 if ((v
= vec_find(ti
, objv
[1])) == 0 || import(ti
, v
, &a
, &n
) != TCL_OK
)
169 /* --- Set up the path table --- */
171 p
= (void *)Tcl_Alloc(n
* n
* sizeof(*p
));
172 for (i
= 0; i
< n
; i
++) {
173 for (j
= 0; j
< n
; j
++)
178 /* --- Do the main algorithm --- *
180 * Not so hard. Just brute force and ignorance.
183 for (k
= 0; k
< n
; k
++) {
184 for (i
= 0; i
< n
; i
++) {
185 for (j
= 0; j
< n
; j
++) {
186 if (a
[i
* n
+ k
] != INF
&& a
[k
* n
+ j
] != INF
&&
187 a
[i
* n
+ k
] + a
[k
* n
+ j
] < a
[i
* n
+ j
]) {
188 a
[i
* n
+ j
] = a
[i
* n
+ k
] + a
[k
* n
+ j
];
189 p
[i
* n
+ j
] = p
[i
* n
+ k
];
195 /* --- Wrap up --- */
197 if ((lv
= export(ti
, a
, n
)) == 0 || (pv
= export(ti
, p
, n
)) == 0)
199 o
= Tcl_NewListObj(0, 0);
200 Tcl_ListObjAppendElement
201 (ti
, o
, Tcl_NewStringObj(Tcl_GetCommandName(ti
, lv
->c
), -1));
202 Tcl_ListObjAppendElement
203 (ti
, o
, Tcl_NewStringObj(Tcl_GetCommandName(ti
, pv
->c
), -1));
204 Tcl_SetObjResult(ti
, o
);
210 if (a
) Tcl_Free((void *)a
);
211 if (p
) Tcl_Free((void *)p
);
212 if (lv
) vec_destroy(ti
, lv
);
213 if (pv
) vec_destroy(ti
, pv
);
217 /*----- Travelling Salesman Problem ---------------------------------------*/
219 /* --- @rrange@ --- *
221 * Arguments: @size_t max@ = maximum number wanted
223 * Returns: An integer uniformly distributed on %$[0, max)$%.
226 static size_t rrange(size_t max
)
239 /* --- @graph-travelling-salesman [-OPTIONS] ADJ LIST@ --- *
241 * Solves the Travelling Salesman Problem approximately. Returns a list
242 * containing (firstly) the cost of the computed route, and secondly the
243 * route itself. Only the nodes in LIST are considered. The OPTIONS affect
244 * the algorithm in various ways.
246 * -cool FACTOR Cooling factor. Default is 1.001. Must be greater
247 * than 1 for the simulated annealing to work.
249 * -dead COUNT Give up after COUNT cycles with no improvement.
252 * -inner COUNT Perform COUNT loops each cooling cycle. Default is
255 * -init TEMP Set the initial temperature to TEMP. Default is not
256 * very helpful. Initial setting should be well above
257 * the maximum cost increase from a cycle.
259 * -cycle / -nocycle If -cycle is set, solve the classical problem of
260 * finding a minimal cyclic path. If -nocycle is set,
261 * then start at the first node in LIST, and minimize a
262 * tour without caring where the end goes. The default
266 static int cmd_tsp(ClientData cd
, Tcl_Interp
*ti
,
267 int objc
, Tcl_Obj
*const *objv
)
269 /* --- Initial algorithm parameters --- */
277 /* --- Other variables --- */
280 unsigned long *a
= 0;
283 size_t *r
= 0, *r_best
= 0;
284 unsigned long c_best
= 0, c_curr
, c
;
289 Tcl_Obj
*o
, *o2
, **oo
;
291 /* --- Parse the command line --- */
293 for (i
= 1; i
< objc
; i
++) {
295 char *p
= Tcl_GetStringFromObj(objv
[i
], &len
);
296 if (strcmp(p
, "-cool") == 0) {
297 i
++; if (i
>= objc
) goto args
;
298 if (Tcl_GetDoubleFromObj(ti
, objv
[i
], &cool
) != TCL_OK
)
301 err(ti
, "cooling factor must be > 1");
304 } else if (strcmp(p
, "-init") == 0) {
305 i
++; if (i
>= objc
) goto args
;
306 if (Tcl_GetDoubleFromObj(ti
, objv
[i
], &temp
) != TCL_OK
)
309 err(ti
, "initial temperature must be > 0");
312 } else if (strcmp(p
, "-inner") == 0) {
313 i
++; if (i
>= objc
) goto args
;
314 if (Tcl_GetLongFromObj(ti
, objv
[i
], &inner
) != TCL_OK
)
317 err(ti
, "inner loop count must be > 0");
320 } else if (strcmp(p
, "-dead") == 0) {
321 i
++; if (i
>= objc
) goto args
;
322 if (Tcl_GetLongFromObj(ti
, objv
[i
], &dead
) != TCL_OK
)
325 err(ti
, "dead cycles count must be > 0");
328 } else if (strcmp(p
, "-cycle") == 0)
330 else if (strcmp(p
, "-nocycle") == 0)
332 else if (strcmp(p
, "--") == 0) {
334 } else if (*p
!= '-')
337 err(ti
, "bad option for graph-travelling-salesman");
342 /* --- Check the rest --- */
345 err(ti
, "usage: graph-travelling-salesman [-OPTIONS] ADJ LIST");
348 if ((v
= vec_find(ti
, objv
[i
])) == 0 || import(ti
, v
, &a
, &n
) != TCL_OK
)
350 if (Tcl_ListObjGetElements(ti
, objv
[i
+ 1], &nn
, &oo
) != TCL_OK
)
355 r
= (void *)Tcl_Alloc(nn
* sizeof(*r
));
356 r_best
= (void *)Tcl_Alloc(nn
* sizeof(*r_best
));
357 for (i
= 0; i
< nn
; i
++) {
359 if (Tcl_GetLongFromObj(ti
, oo
[i
], &l
) != TCL_OK
)
361 if (l
< 0 || l
>= n
) {
362 err(ti
, "node index out of range");
368 /* --- The one and two node problems are trivial --- *
370 * Avoiding these prevents us from having to mess with special cases later.
374 memcpy(r_best
, r
, nn
* sizeof(*r
));
376 c_best
= a
[r
[0] * n
+ r
[0]];
378 c_best
= a
[r
[0] * n
+ r
[1]];
382 /* --- Randomize the initial vector --- *
384 * If we're not cycling, then nail the first item in place.
387 for (i
= cycle ?
0 : 1; i
< nn
; i
++) {
389 t
= r
[i
]; r
[i
] = r
[i
+ j
]; r
[i
+ j
] = t
;
392 /* --- Compute the initial cost --- *
394 * If we're not cycling, don't close off at the end. The easiest way to do
395 * that is to start at the end. There are at least three elements.
398 if (cycle
) { j
= 0; i
= nn
- 1; }
399 else { j
= nn
- 1; i
= j
- 1; }
402 c
+= a
[r
[i
] * n
+ r
[j
]];
409 /* printf("*** initial cost = %lu\n", c_best); */
411 memcpy(r_best
, r
, nn
* sizeof(*r
));
413 /* --- Embark on the main loop --- */
418 for (ii
= inner
; ii
; ii
--) {
419 size_t i
, j
, ilo
, ihi
, jlo
, jhi
;
421 /* --- Decide on a change to make --- *
423 * We just swap two nodes around on the path. This is simple and seems
424 * to be effective. Don't allow the first node to be moved if we're
432 i
= rrange(nn
- 1) + 1;
433 j
= rrange(nn
- 1) + 1;
436 /* --- Compute the change in cost --- *
438 * Since we're only swapping two nodes, we can work out the change
439 * without rescanning the entire path, by just looking at the local
444 continue; /* No change */
445 if (j
< i
) { t
= i
; i
= j
; j
= t
; }
446 ilo
= (i
- 1) % nn
; ihi
= (i
+ 1) % nn
;
447 jlo
= (j
- 1) % nn
; jhi
= (j
+ 1) % nn
;
452 /* --- This is where the algorithms differ --- *
454 * If we're producing a cycle, then we need the cost function to wrap
455 * around here. Otherwise, it hits a barrier, and the last node only
456 * has a partial effect.
461 c
-= (a
[r
[jlo
] * n
+ r
[j
]] +
463 a
[r
[i
] * n
+ r
[ihi
]]);
464 c
+= (a
[r
[jlo
] * n
+ r
[i
]] +
466 a
[r
[j
] * n
+ r
[ihi
]]);
470 c
-= a
[r
[ilo
] * n
+ r
[i
]] + a
[r
[i
] * n
+ r
[j
]];
471 c
+= a
[r
[ilo
] * n
+ r
[j
]] + a
[r
[j
] * n
+ r
[i
]];
473 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
474 a
[r
[i
] * n
+ r
[ihi
]] +
475 a
[r
[jlo
] * n
+ r
[j
]]);
476 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
477 a
[r
[j
] * n
+ r
[ihi
]] +
478 a
[r
[jlo
] * n
+ r
[i
]]);
483 /* --- Usual case --- *
485 * This splits into two subcases, depending on whether the areas
491 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
493 a
[r
[j
] * n
+ r
[jhi
]]);
494 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
496 a
[r
[i
] * n
+ r
[jhi
]]);
498 c
-= (a
[r
[ilo
] * n
+ r
[i
]] +
499 a
[r
[i
] * n
+ r
[ihi
]] +
500 a
[r
[jlo
] * n
+ r
[j
]] +
501 a
[r
[j
] * n
+ r
[jhi
]]);
502 c
+= (a
[r
[ilo
] * n
+ r
[j
]] +
503 a
[r
[j
] * n
+ r
[ihi
]] +
504 a
[r
[jlo
] * n
+ r
[i
]] +
505 a
[r
[i
] * n
+ r
[jhi
]]);
509 /* --- Decide what to do --- */
512 rrange(65536) >= (size_t)(exp(((double)c_curr
-
513 (double)c
)/temp
) * 65536))
516 /* --- Accept the change --- */
521 t
= r
[i
]; r
[i
] = r
[j
]; r
[j
] = t
;
522 if (c_curr
< c_best
) {
524 /* printf("*** new best = %lu\n", c_best); */
525 memcpy(r_best
, r
, nn
* sizeof(*r
));
538 o
= Tcl_NewListObj(0, 0);
539 o2
= Tcl_NewListObj(0, 0);
540 Tcl_ListObjAppendElement(ti
, o
, Tcl_NewLongObj(c_best
));
541 for (i
= 0; i
< nn
; i
++)
542 Tcl_ListObjAppendElement(ti
, o2
, Tcl_NewLongObj(r_best
[i
]));
543 Tcl_ListObjAppendElement(ti
, o
, o2
);
544 Tcl_SetObjResult(ti
, o
);
547 /* --- Tidy up --- */
550 if (a
) Tcl_Free((void *)a
);
551 if (r
) Tcl_Free((void *)r
);
552 if (r_best
) Tcl_Free((void *)r_best
);
556 err(ti
, "missing argument for option");
560 /*----- Initialization ----------------------------------------------------*/
562 int Graph_SafeInit(Tcl_Interp
*ti
)
564 static const struct cmd
{
565 /*const*/ char *name
;
566 Tcl_ObjCmdProc
*proc
;
568 { "graph-shortest-path", cmd_shortestpath
},
569 { "graph-travelling-salesman", cmd_tsp
},
574 if (Tcl_PkgRequire(ti
, "vector", "1.0.0", 0) == 0)
576 for (c
= cmds
; c
->name
; c
++)
577 Tcl_CreateObjCommand(ti
, c
->name
, c
->proc
, 0, 0);
578 if (Tcl_PkgProvide(ti
, "graph", "1.0.0"))
583 int Graph_Init(Tcl_Interp
*ti
)
585 return (Graph_SafeInit(ti
));
588 /*----- That's all, folks -------------------------------------------------*/