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tsort.c revision 1.14
      1  1.14      cgd /*	$NetBSD: tsort.c,v 1.14 2001/02/21 00:11:36 cgd Exp $	*/
      2   1.9      jtc 
      3   1.1      cgd /*
      4   1.9      jtc  * Copyright (c) 1989, 1993, 1994
      5   1.7      cgd  *	The Regents of the University of California.  All rights reserved.
      6   1.1      cgd  *
      7   1.1      cgd  * This code is derived from software contributed to Berkeley by
      8   1.1      cgd  * Michael Rendell of Memorial University of Newfoundland.
      9   1.1      cgd  *
     10   1.1      cgd  * Redistribution and use in source and binary forms, with or without
     11   1.1      cgd  * modification, are permitted provided that the following conditions
     12   1.1      cgd  * are met:
     13   1.1      cgd  * 1. Redistributions of source code must retain the above copyright
     14   1.1      cgd  *    notice, this list of conditions and the following disclaimer.
     15   1.1      cgd  * 2. Redistributions in binary form must reproduce the above copyright
     16   1.1      cgd  *    notice, this list of conditions and the following disclaimer in the
     17   1.1      cgd  *    documentation and/or other materials provided with the distribution.
     18   1.1      cgd  * 3. All advertising materials mentioning features or use of this software
     19   1.1      cgd  *    must display the following acknowledgement:
     20   1.1      cgd  *	This product includes software developed by the University of
     21   1.1      cgd  *	California, Berkeley and its contributors.
     22   1.1      cgd  * 4. Neither the name of the University nor the names of its contributors
     23   1.1      cgd  *    may be used to endorse or promote products derived from this software
     24   1.1      cgd  *    without specific prior written permission.
     25   1.1      cgd  *
     26   1.1      cgd  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     27   1.1      cgd  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     28   1.1      cgd  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     29   1.1      cgd  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     30   1.1      cgd  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     31   1.1      cgd  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     32   1.1      cgd  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     33   1.1      cgd  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     34   1.1      cgd  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     35   1.1      cgd  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     36   1.1      cgd  * SUCH DAMAGE.
     37   1.1      cgd  */
     38   1.1      cgd 
     39  1.12    lukem #include <sys/cdefs.h>
     40   1.1      cgd #ifndef lint
     41  1.12    lukem __COPYRIGHT("@(#) Copyright (c) 1989, 1993, 1994\n\
     42  1.12    lukem 	The Regents of the University of California.  All rights reserved.\n");
     43   1.1      cgd #endif /* not lint */
     44   1.1      cgd 
     45   1.1      cgd #ifndef lint
     46   1.9      jtc #if 0
     47  1.10      jtc static char sccsid[] = "@(#)tsort.c	8.3 (Berkeley) 5/4/95";
     48   1.9      jtc #endif
     49  1.14      cgd __RCSID("$NetBSD: tsort.c,v 1.14 2001/02/21 00:11:36 cgd Exp $");
     50   1.1      cgd #endif /* not lint */
     51   1.1      cgd 
     52   1.1      cgd #include <sys/types.h>
     53   1.9      jtc 
     54   1.9      jtc #include <ctype.h>
     55   1.9      jtc #include <db.h>
     56   1.9      jtc #include <err.h>
     57   1.1      cgd #include <errno.h>
     58   1.7      cgd #include <fcntl.h>
     59   1.1      cgd #include <stdio.h>
     60   1.7      cgd #include <stdlib.h>
     61   1.1      cgd #include <string.h>
     62  1.10      jtc #include <unistd.h>
     63   1.1      cgd 
     64   1.1      cgd /*
     65   1.7      cgd  *  Topological sort.  Input is a list of pairs of strings separated by
     66   1.1      cgd  *  white space (spaces, tabs, and/or newlines); strings are written to
     67   1.1      cgd  *  standard output in sorted order, one per line.
     68   1.1      cgd  *
     69   1.1      cgd  *  usage:
     70   1.7      cgd  *     tsort [-l] [inputfile]
     71   1.1      cgd  *  If no input file is specified, standard input is read.
     72   1.1      cgd  *
     73   1.1      cgd  *  Should be compatable with AT&T tsort HOWEVER the output is not identical
     74   1.1      cgd  *  (i.e. for most graphs there is more than one sorted order, and this tsort
     75   1.1      cgd  *  usually generates a different one then the AT&T tsort).  Also, cycle
     76   1.1      cgd  *  reporting seems to be more accurate in this version (the AT&T tsort
     77   1.1      cgd  *  sometimes says a node is in a cycle when it isn't).
     78   1.1      cgd  *
     79   1.1      cgd  *  Michael Rendell, michael (at) stretch.cs.mun.ca - Feb 26, '90
     80   1.1      cgd  */
     81   1.1      cgd #define	HASHSIZE	53		/* doesn't need to be big */
     82   1.1      cgd #define	NF_MARK		0x1		/* marker for cycle detection */
     83   1.1      cgd #define	NF_ACYCLIC	0x2		/* this node is cycle free */
     84   1.7      cgd #define	NF_NODEST	0x4		/* Unreachable */
     85   1.7      cgd 
     86   1.1      cgd typedef struct node_str NODE;
     87   1.1      cgd 
     88   1.1      cgd struct node_str {
     89   1.1      cgd 	NODE **n_prevp;			/* pointer to previous node's n_next */
     90   1.1      cgd 	NODE *n_next;			/* next node in graph */
     91   1.7      cgd 	NODE **n_arcs;			/* array of arcs to other nodes */
     92   1.1      cgd 	int n_narcs;			/* number of arcs in n_arcs[] */
     93   1.1      cgd 	int n_arcsize;			/* size of n_arcs[] array */
     94   1.1      cgd 	int n_refcnt;			/* # of arcs pointing to this node */
     95   1.1      cgd 	int n_flags;			/* NF_* */
     96   1.7      cgd 	char n_name[1];			/* name of this node */
     97   1.1      cgd };
     98   1.1      cgd 
     99   1.1      cgd typedef struct _buf {
    100   1.1      cgd 	char *b_buf;
    101   1.1      cgd 	int b_bsize;
    102   1.1      cgd } BUF;
    103   1.1      cgd 
    104   1.7      cgd DB *db;
    105   1.9      jtc NODE *graph, **cycle_buf, **longest_cycle;
    106  1.11  mycroft int debug, longest, quiet;
    107   1.7      cgd 
    108   1.7      cgd void	 add_arc __P((char *, char *));
    109  1.12    lukem void	 clear_cycle __P((void));
    110   1.7      cgd int	 find_cycle __P((NODE *, NODE *, int, int));
    111   1.7      cgd NODE	*get_node __P((char *));
    112   1.7      cgd void	*grow_buf __P((void *, int));
    113  1.12    lukem int	 main __P((int, char **));
    114   1.7      cgd void	 remove_node __P((NODE *));
    115   1.7      cgd void	 tsort __P((void));
    116   1.7      cgd void	 usage __P((void));
    117   1.1      cgd 
    118   1.7      cgd int
    119   1.1      cgd main(argc, argv)
    120   1.1      cgd 	int argc;
    121   1.7      cgd 	char *argv[];
    122   1.1      cgd {
    123  1.12    lukem 	BUF *b;
    124  1.12    lukem 	int c, n;
    125   1.1      cgd 	FILE *fp;
    126   1.7      cgd 	int bsize, ch, nused;
    127   1.1      cgd 	BUF bufs[2];
    128  1.14      cgd 
    129  1.14      cgd 	setprogname(argv[0]);
    130   1.1      cgd 
    131  1.12    lukem 	fp = NULL;
    132  1.12    lukem 	while ((ch = getopt(argc, argv, "dlq")) != -1)
    133   1.9      jtc 		switch (ch) {
    134   1.7      cgd 		case 'd':
    135   1.9      jtc 			debug = 1;
    136   1.9      jtc 			break;
    137   1.7      cgd 		case 'l':
    138   1.9      jtc 			longest = 1;
    139   1.9      jtc 			break;
    140  1.11  mycroft 		case 'q':
    141  1.11  mycroft 			quiet = 1;
    142  1.11  mycroft 			break;
    143   1.7      cgd 		case '?':
    144   1.7      cgd 		default:
    145   1.7      cgd 			usage();
    146   1.7      cgd 		}
    147   1.7      cgd 	argc -= optind;
    148   1.7      cgd 	argv += optind;
    149   1.7      cgd 
    150   1.9      jtc 	switch (argc) {
    151   1.7      cgd 	case 0:
    152   1.1      cgd 		fp = stdin;
    153   1.7      cgd 		break;
    154   1.7      cgd 	case 1:
    155   1.7      cgd 		if ((fp = fopen(*argv, "r")) == NULL)
    156   1.9      jtc 			err(1, "%s", *argv);
    157   1.7      cgd 		break;
    158   1.7      cgd 	default:
    159   1.7      cgd 		usage();
    160   1.1      cgd 	}
    161   1.1      cgd 
    162   1.1      cgd 	for (b = bufs, n = 2; --n >= 0; b++)
    163   1.7      cgd 		b->b_buf = grow_buf(NULL, b->b_bsize = 1024);
    164   1.1      cgd 
    165   1.1      cgd 	/* parse input and build the graph */
    166   1.1      cgd 	for (n = 0, c = getc(fp);;) {
    167   1.1      cgd 		while (c != EOF && isspace(c))
    168   1.1      cgd 			c = getc(fp);
    169   1.1      cgd 		if (c == EOF)
    170   1.1      cgd 			break;
    171   1.1      cgd 
    172   1.1      cgd 		nused = 0;
    173   1.1      cgd 		b = &bufs[n];
    174   1.1      cgd 		bsize = b->b_bsize;
    175   1.1      cgd 		do {
    176   1.1      cgd 			b->b_buf[nused++] = c;
    177   1.7      cgd 			if (nused == bsize)
    178   1.7      cgd 				b->b_buf = grow_buf(b->b_buf, bsize *= 2);
    179   1.1      cgd 			c = getc(fp);
    180   1.1      cgd 		} while (c != EOF && !isspace(c));
    181   1.1      cgd 
    182   1.1      cgd 		b->b_buf[nused] = '\0';
    183   1.1      cgd 		b->b_bsize = bsize;
    184   1.1      cgd 		if (n)
    185   1.1      cgd 			add_arc(bufs[0].b_buf, bufs[1].b_buf);
    186   1.1      cgd 		n = !n;
    187   1.1      cgd 	}
    188   1.1      cgd 	(void)fclose(fp);
    189   1.7      cgd 	if (n)
    190   1.8      cgd 		errx(1, "odd data count");
    191   1.1      cgd 
    192   1.1      cgd 	/* do the sort */
    193   1.1      cgd 	tsort();
    194   1.1      cgd 	exit(0);
    195   1.1      cgd }
    196   1.1      cgd 
    197   1.1      cgd /* double the size of oldbuf and return a pointer to the new buffer. */
    198   1.7      cgd void *
    199   1.1      cgd grow_buf(bp, size)
    200   1.7      cgd 	void *bp;
    201   1.1      cgd 	int size;
    202   1.1      cgd {
    203   1.7      cgd 	if ((bp = realloc(bp, (u_int)size)) == NULL)
    204  1.12    lukem 		err(1, "realloc");
    205   1.7      cgd 	return (bp);
    206   1.1      cgd }
    207   1.1      cgd 
    208   1.1      cgd /*
    209   1.1      cgd  * add an arc from node s1 to node s2 in the graph.  If s1 or s2 are not in
    210   1.1      cgd  * the graph, then add them.
    211   1.1      cgd  */
    212   1.1      cgd void
    213   1.1      cgd add_arc(s1, s2)
    214   1.1      cgd 	char *s1, *s2;
    215   1.1      cgd {
    216  1.12    lukem 	NODE *n1;
    217   1.1      cgd 	NODE *n2;
    218   1.4      cgd 	int bsize, i;
    219   1.1      cgd 
    220   1.7      cgd 	n1 = get_node(s1);
    221   1.1      cgd 
    222   1.1      cgd 	if (!strcmp(s1, s2))
    223   1.1      cgd 		return;
    224   1.1      cgd 
    225   1.7      cgd 	n2 = get_node(s2);
    226   1.1      cgd 
    227   1.1      cgd 	/*
    228   1.3      cgd 	 * Check if this arc is already here.
    229   1.3      cgd 	 */
    230   1.3      cgd 	for (i = 0; i < n1->n_narcs; i++)
    231   1.3      cgd 		if (n1->n_arcs[i] == n2)
    232   1.3      cgd 			return;
    233   1.3      cgd 	/*
    234   1.3      cgd 	 * Add it.
    235   1.1      cgd 	 */
    236   1.1      cgd 	if (n1->n_narcs == n1->n_arcsize) {
    237   1.1      cgd 		if (!n1->n_arcsize)
    238   1.1      cgd 			n1->n_arcsize = 10;
    239   1.1      cgd 		bsize = n1->n_arcsize * sizeof(*n1->n_arcs) * 2;
    240   1.7      cgd 		n1->n_arcs = grow_buf(n1->n_arcs, bsize);
    241   1.1      cgd 		n1->n_arcsize = bsize / sizeof(*n1->n_arcs);
    242   1.1      cgd 	}
    243   1.1      cgd 	n1->n_arcs[n1->n_narcs++] = n2;
    244   1.1      cgd 	++n2->n_refcnt;
    245   1.1      cgd }
    246   1.1      cgd 
    247   1.7      cgd /* Find a node in the graph (insert if not found) and return a pointer to it. */
    248   1.1      cgd NODE *
    249   1.7      cgd get_node(name)
    250   1.1      cgd 	char *name;
    251   1.1      cgd {
    252   1.7      cgd 	DBT data, key;
    253   1.7      cgd 	NODE *n;
    254   1.1      cgd 
    255   1.7      cgd 	if (db == NULL &&
    256   1.7      cgd 	    (db = dbopen(NULL, O_RDWR, 0, DB_HASH, NULL)) == NULL)
    257   1.9      jtc 		err(1, "db: %s", name);
    258   1.7      cgd 
    259   1.7      cgd 	key.data = name;
    260   1.7      cgd 	key.size = strlen(name) + 1;
    261   1.7      cgd 
    262   1.9      jtc 	switch ((*db->get)(db, &key, &data, 0)) {
    263   1.7      cgd 	case 0:
    264  1.12    lukem 		memmove(&n, data.data, sizeof(n));
    265   1.7      cgd 		return (n);
    266   1.7      cgd 	case 1:
    267   1.7      cgd 		break;
    268   1.7      cgd 	default:
    269   1.7      cgd 	case -1:
    270   1.9      jtc 		err(1, "db: %s", name);
    271   1.7      cgd 	}
    272   1.1      cgd 
    273   1.7      cgd 	if ((n = malloc(sizeof(NODE) + key.size)) == NULL)
    274  1.12    lukem 		err(1, "malloc");
    275   1.1      cgd 
    276   1.1      cgd 	n->n_narcs = 0;
    277   1.1      cgd 	n->n_arcsize = 0;
    278   1.7      cgd 	n->n_arcs = NULL;
    279   1.1      cgd 	n->n_refcnt = 0;
    280   1.1      cgd 	n->n_flags = 0;
    281  1.12    lukem 	memmove(n->n_name, name, key.size);
    282   1.1      cgd 
    283   1.7      cgd 	/* Add to linked list. */
    284   1.9      jtc 	if ((n->n_next = graph) != NULL)
    285   1.1      cgd 		graph->n_prevp = &n->n_next;
    286   1.1      cgd 	n->n_prevp = &graph;
    287   1.1      cgd 	graph = n;
    288   1.1      cgd 
    289   1.7      cgd 	/* Add to hash table. */
    290   1.7      cgd 	data.data = &n;
    291   1.7      cgd 	data.size = sizeof(n);
    292   1.7      cgd 	if ((*db->put)(db, &key, &data, 0))
    293   1.9      jtc 		err(1, "db: %s", name);
    294   1.7      cgd 	return (n);
    295   1.7      cgd }
    296   1.7      cgd 
    297   1.7      cgd 
    298   1.7      cgd /*
    299   1.7      cgd  * Clear the NODEST flag from all nodes.
    300   1.7      cgd  */
    301   1.7      cgd void
    302   1.7      cgd clear_cycle()
    303   1.7      cgd {
    304   1.7      cgd 	NODE *n;
    305   1.7      cgd 
    306   1.9      jtc 	for (n = graph; n != NULL; n = n->n_next)
    307   1.7      cgd 		n->n_flags &= ~NF_NODEST;
    308   1.1      cgd }
    309   1.1      cgd 
    310   1.1      cgd /* do topological sort on graph */
    311   1.1      cgd void
    312   1.1      cgd tsort()
    313   1.1      cgd {
    314  1.12    lukem 	NODE *n, *next;
    315  1.12    lukem 	int cnt, i;
    316   1.1      cgd 
    317   1.9      jtc 	while (graph != NULL) {
    318   1.1      cgd 		/*
    319   1.7      cgd 		 * Keep getting rid of simple cases until there are none left,
    320   1.1      cgd 		 * if there are any nodes still in the graph, then there is
    321   1.1      cgd 		 * a cycle in it.
    322   1.1      cgd 		 */
    323   1.1      cgd 		do {
    324   1.9      jtc 			for (cnt = 0, n = graph; n != NULL; n = next) {
    325   1.1      cgd 				next = n->n_next;
    326   1.1      cgd 				if (n->n_refcnt == 0) {
    327   1.1      cgd 					remove_node(n);
    328   1.1      cgd 					++cnt;
    329   1.1      cgd 				}
    330   1.1      cgd 			}
    331   1.9      jtc 		} while (graph != NULL && cnt);
    332   1.1      cgd 
    333   1.9      jtc 		if (graph == NULL)
    334   1.1      cgd 			break;
    335   1.1      cgd 
    336   1.1      cgd 		if (!cycle_buf) {
    337   1.1      cgd 			/*
    338   1.7      cgd 			 * Allocate space for two cycle logs - one to be used
    339   1.1      cgd 			 * as scratch space, the other to save the longest
    340   1.1      cgd 			 * cycle.
    341   1.1      cgd 			 */
    342   1.9      jtc 			for (cnt = 0, n = graph; n != NULL; n = n->n_next)
    343   1.1      cgd 				++cnt;
    344   1.7      cgd 			cycle_buf = malloc((u_int)sizeof(NODE *) * cnt);
    345   1.7      cgd 			longest_cycle = malloc((u_int)sizeof(NODE *) * cnt);
    346   1.7      cgd 			if (cycle_buf == NULL || longest_cycle == NULL)
    347  1.12    lukem 				err(1, "malloc");
    348   1.1      cgd 		}
    349  1.13     ross 		for (n = graph; n != NULL; n = n->n_next) {
    350  1.13     ross 			if (!(n->n_flags & NF_ACYCLIC)) {
    351  1.12    lukem 				if ((cnt = find_cycle(n, n, 0, 0)) != 0) {
    352  1.11  mycroft 					if (!quiet) {
    353  1.11  mycroft 						warnx("cycle in data");
    354  1.11  mycroft 						for (i = 0; i < cnt; i++)
    355  1.11  mycroft 							warnx("%s",
    356  1.11  mycroft 							    longest_cycle[i]->n_name);
    357  1.11  mycroft 					}
    358   1.1      cgd 					remove_node(n);
    359   1.7      cgd 					clear_cycle();
    360   1.1      cgd 					break;
    361   1.7      cgd 				} else {
    362   1.1      cgd 					/* to avoid further checks */
    363   1.7      cgd 					n->n_flags  |= NF_ACYCLIC;
    364   1.7      cgd 					clear_cycle();
    365   1.7      cgd 				}
    366  1.13     ross 			}
    367  1.13     ross 		}
    368   1.9      jtc 		if (n == NULL)
    369   1.9      jtc 			errx(1, "internal error -- could not find cycle");
    370   1.1      cgd 	}
    371   1.1      cgd }
    372   1.1      cgd 
    373   1.1      cgd /* print node and remove from graph (does not actually free node) */
    374   1.1      cgd void
    375   1.1      cgd remove_node(n)
    376  1.12    lukem 	NODE *n;
    377   1.1      cgd {
    378  1.12    lukem 	NODE **np;
    379  1.12    lukem 	int i;
    380   1.1      cgd 
    381   1.1      cgd 	(void)printf("%s\n", n->n_name);
    382   1.1      cgd 	for (np = n->n_arcs, i = n->n_narcs; --i >= 0; np++)
    383   1.1      cgd 		--(*np)->n_refcnt;
    384   1.1      cgd 	n->n_narcs = 0;
    385   1.1      cgd 	*n->n_prevp = n->n_next;
    386   1.1      cgd 	if (n->n_next)
    387   1.1      cgd 		n->n_next->n_prevp = n->n_prevp;
    388   1.1      cgd }
    389   1.1      cgd 
    390   1.7      cgd 
    391   1.7      cgd /* look for the longest? cycle from node from to node to. */
    392   1.7      cgd int
    393   1.1      cgd find_cycle(from, to, longest_len, depth)
    394   1.1      cgd 	NODE *from, *to;
    395   1.1      cgd 	int depth, longest_len;
    396   1.1      cgd {
    397  1.12    lukem 	NODE **np;
    398  1.12    lukem 	int i, len;
    399   1.1      cgd 
    400   1.1      cgd 	/*
    401   1.1      cgd 	 * avoid infinite loops and ignore portions of the graph known
    402   1.1      cgd 	 * to be acyclic
    403   1.1      cgd 	 */
    404   1.7      cgd 	if (from->n_flags & (NF_NODEST|NF_MARK|NF_ACYCLIC))
    405   1.7      cgd 		return (0);
    406   1.7      cgd 	from->n_flags |= NF_MARK;
    407   1.1      cgd 
    408   1.1      cgd 	for (np = from->n_arcs, i = from->n_narcs; --i >= 0; np++) {
    409   1.1      cgd 		cycle_buf[depth] = *np;
    410   1.1      cgd 		if (*np == to) {
    411   1.1      cgd 			if (depth + 1 > longest_len) {
    412   1.1      cgd 				longest_len = depth + 1;
    413   1.1      cgd 				(void)memcpy((char *)longest_cycle,
    414   1.1      cgd 				    (char *)cycle_buf,
    415   1.1      cgd 				    longest_len * sizeof(NODE *));
    416   1.1      cgd 			}
    417   1.1      cgd 		} else {
    418   1.7      cgd 			if ((*np)->n_flags & (NF_MARK|NF_ACYCLIC|NF_NODEST))
    419   1.7      cgd 				continue;
    420   1.1      cgd 			len = find_cycle(*np, to, longest_len, depth + 1);
    421   1.7      cgd 
    422   1.7      cgd 			if (debug)
    423   1.9      jtc 				(void)printf("%*s %s->%s %d\n", depth, "",
    424   1.9      jtc 				    from->n_name, to->n_name, len);
    425   1.7      cgd 
    426   1.7      cgd 			if (len == 0)
    427   1.9      jtc 				(*np)->n_flags |= NF_NODEST;
    428   1.7      cgd 
    429   1.7      cgd 			if (len > longest_len)
    430   1.1      cgd 				longest_len = len;
    431   1.7      cgd 
    432   1.7      cgd 			if (len > 0 && !longest)
    433   1.5      cgd 				break;
    434   1.1      cgd 		}
    435   1.1      cgd 	}
    436   1.7      cgd 	from->n_flags &= ~NF_MARK;
    437   1.7      cgd 	return (longest_len);
    438   1.1      cgd }
    439   1.1      cgd 
    440   1.1      cgd void
    441   1.7      cgd usage()
    442   1.7      cgd {
    443  1.11  mycroft 	(void)fprintf(stderr, "usage: tsort [-lq] [file]\n");
    444   1.7      cgd 	exit(1);
    445   1.1      cgd }
    446