roget_components.w

模拟器提供了一个简单易用的平台

% This file is part of the Stanford GraphBase (c) Stanford University 1993
@i boilerplate.w %<< legal stuff: PLEASE READ IT BEFORE MAKING ANY CHANGES!
@i gb_types.w

\def\title{ROGET\_\,COMPONENTS}
\def\<#1>{$\langle${\rm#1}$\rangle$}

\prerequisite{GB\_\,ROGET}
@* Strong components. This demonstration program computes the
strong components of GraphBase graphs derived from Roget's Thesaurus,
using a variant of Tarjan's algorithm [R. E. Tarjan, ``Depth-first
@^Tarjan, Robert Endre@>
search and linear graph algorithms,'' {\sl SIAM Journal on Computing\/
\bf1} (1972), 146--160]. We also determine the relationships
between strong components.

Two vertices belong to the same strong component if and only if they
are reachable from each other via directed paths.

We will print the strong components in ``reverse topological order'';
that is, if |v| is reachable from~|u| but |u| is not reachable
from~|v|, the strong component containing~|v| will be listed before
the strong component containing~|u|.

Vertices from the |roget| graph are identified both by name and by
category number.

@d specs(v) (filename? v-g->vertices+1L: v->cat_no), v->name
  /* category number and category name */

@ We permit command-line options in \UNIX/ style so that a variety of
graphs can be studied:
The user can say `\.{-n}\<number>', `\.{-d}\<number>', `\.{-p}\<number>',
and/or `\.{-s}\<number>' to change the default values of the parameters
in the graph |roget(n,d,p,s)|. Or `\.{-g}\<filename>' to change the
graph itself.
@^UNIX dependencies@>

@p
#include "gb_graph.h" /* the GraphBase data structures */
#include "gb_roget.h" /* the |roget| routine */
#include "gb_save.h" /* |restore_graph| */
@h@#
@<Global variables@>@;
main(argc,argv)
  int argc; /* the number of command-line arguments */
  char *argv[]; /* an array of strings containing those arguments */
{@+Graph *g; /* the graph we will work on */
  register Vertex *v; /* the current vertex of interest */
  unsigned long n=0; /* the desired number of vertices (0 means infinity) */
  unsigned long d=0; /* the minimum distance between categories in arcs */
  unsigned long p=0; /* 65536 times the probability of rejecting an arc */
  long s=0; /* the random number seed */
  char *filename=NULL; /* external graph substituted for |roget| */
  @<Scan the command-line options@>;
  g=(filename? restore_graph(filename): roget(n,d,p,s));
  if (g==NULL) {
    fprintf(stderr,"Sorry, can't create the graph! (error code %ld)\n",
             panic_code);
    return -1;
  }
  printf("Reachability analysis of %s\n\n",g->id);
  @<Perform Tarjan's algorithm on |g|@>;
  return 0; /* normal exit */
}

@ @<Scan the command-line options@>=
while (--argc) {
@^UNIX dependencies@>
  if (sscanf(argv[argc],"-n%lu",&n)==1) ;
  else if (sscanf(argv[argc],"-d%lu",&d)==1) ;
  else if (sscanf(argv[argc],"-p%lu",&p)==1) ;
  else if (sscanf(argv[argc],"-s%ld",&s)==1) ;
  else if (strncmp(argv[argc],"-g",2)==0) filename=argv[argc]+2;
  else {
    fprintf(stderr,"Usage: %s [-nN][-dN][-pN][-sN][-gfoo]\n",argv[0]);
    return -2;
  }
}

@ Tarjan's algorithm is inherently recursive. We will implement
the recursion explicitly via linked lists, instead of using \CEE/'s runtime
stack, because some computer systems
bog down in the presence of deeply nested recursion.

Each vertex goes through three stages during the algorithm: First it is
``unseen''; then it is ``active''; finally it becomes ``settled,'' when it
has been assigned to a strong component.

The data structures that represent the current state of the algorithm
are implemented by using five of the utility fields in each vertex:
|rank|, |parent|, |untagged|, |link|, and |min|. We will consider each of
these in turn.

@ First is the integer |rank| field, which is zero when a vertex is unseen.
As soon as the vertex is first examined, it becomes active and its |rank|
becomes and remains nonzero. Indeed, the $k$th vertex to become active
will receive rank~$k$. When a vertex finally becomes settled, its rank
is reset to infinity.

It's convenient to think of Tarjan's algorithm as a simple adventure
game in which we want to explore all the rooms of a cave. Passageways between
the rooms allow one-way travel only. When we come
into a room for the first time, we assign a new number to that room;
this is its rank. Later on we might happen to enter the same room
again, and we will notice that it has nonzero rank. Then we'll be able
to make a quick exit, saying ``we've already been here.'' (The extra
complexities of computer games, like dragons that might need to be
vanquished, do not arise.)

@d rank z.I /* the |rank| of a vertex is stored in utility field |z| */

@<Glob...@>=
long nn; /* the number of vertices that have been seen */

@ The active vertices will always form an oriented tree, whose arcs are
a subset of the arcs in the original graph. A tree arc from |u| to~|v|
will be represented by |v->parent==u|. Every active vertex has a
parent, which is usually another active vertex; the only exception is
the root of the tree, whose |parent| is |NULL|.

In the cave analogy, the ``parent'' of room |v| is the room we were in
immediately before entering |v| the first time. By following parent
pointers, we will be able to leave the cave whenever we want.

As soon as a vertex becomes settled, its |parent| field changes
significance.  Then |v->parent| is set equal to the unique
representative of the strong component containing vertex~|v|. Thus
two settled vertices will belong to the same strong component if and only
if they have the same |parent|.

@d parent y.V /* the |parent| of a vertex is stored in utility field |y| */

@ All arcs in the original directed graph are explored systematically during
a depth-first search. Whenever we look at an arc, we tag it so that
we won't need to explore it again. In a cave, for example, we might
mark each passageway between rooms once we've tried to go through it.

The algorithm doesn't actually place a tag on its |Arc| records; instead,
each vertex |v| has a pointer |v->untagged| that leads to all
hitherto-unexplored arcs from~|v|. The arcs of the list that appear
between |v->arcs| and |v->untagged| are the ones already examined.

@d untagged x.A
 /* the |untagged| field points to an |Arc| record, or |NULL| */ 

@ The algorithm maintains two special stacks: |active_stack| contains
all the currently active vertices, and |settled_stack| contains all the
currently settled vertices. Each vertex has a |link| field that points
to the vertex that is next lower on its stack, or to |NULL| if the vertex is
at the bottom. The vertices on |active_stack| always appear in increasing
order of rank from bottom to top.

@d link w.V /* the |link| field of a vertex occupies utility field |w| */

@<Glob...@>=
Vertex * active_stack; /* the top of the stack of active vertices */
Vertex * settled_stack; /* the top of the stack of settled vertices */

@ Finally there's a |min| field, which is the tricky part that makes
everything work. If vertex~|v| is unseen or settled, its |min| field is
irrelevant. Otherwise |v->min| points to the active vertex~|u|
of smallest rank having the following property:
Either |u==v| or there is a directed path from |v| to |u| consisting of
zero or more mature tree arcs followed by a single non-tree arc.

What is a tree arc, you ask. And what is a mature arc? Good questions. At the
moment when arcs of the graph are tagged, we classify them either as tree
arcs (if they correspond to a new |parent| link in the tree of active
nodes) or non-tree arcs (otherwise). A tree arc becomes mature when it
is no longer on the path from the root to the current vertex being
explored. We also say that a vertex becomes mature when it is
no longer on that path. All arcs from a mature vertex have been tagged.

We said before that every vertex is initially unseen, then active, and
finally settled. With our new definitions, we see further that every arc starts
out untagged, then it becomes either a non-tree arc or a tree arc. In the
latter case, the arc begins as an immature tree arc and eventually matures.

Just believe these definitions, for now. All will become clear soon.

@d min v.V /* the |min| field of a vertex occupies utility field |v| */

@ Depth-first search explores a graph by systematically visiting all
vertices and seeing what they can lead to. In Tarjan's algorithm, as
we have said, the active vertices form an oriented tree. One of these
vertices is called the current vertex.

If the current vertex still has an arc that hasn't been tagged, we
tag one such arc and there are two cases: Either the arc leads to
an unseen vertex, or it doesn't. If it does, the arc becomes a tree
arc; the previously unseen vertex becomes active, and it becomes the
new current vertex.  On the other hand if the arc leads to a vertex
that has already been seen, the arc becomes a non-tree arc and the
current vertex doesn't change.

Finally there will come a time when the current vertex~|v| has no
untagged arcs. At this point, the
algorithm might decide that |v| and all its descendants form a strong
component. Indeed, this condition turns out to be true if and only if