Provided by: libtree-dagnode-perl_1.06-1_all bug

NAME

       Tree::DAG_Node - (super)class for representing nodes in a tree

SYNOPSIS

       Using as a base class:

         package Game::Tree::Node; # or whatever you're doing
         use Tree::DAG_Node;
         @ISA = qw(Tree::DAG_Node);
         ...your own methods overriding/extending
           the methods in Tree::DAG_Node...

       Using as a class of its own:

         use Tree::DAG_Node;
         my $root = Tree::DAG_Node->new();
         $root->name("I'm the tops");
         my $new_daughter = $root->new_daughter;
         $new_daughter->name("More");
         ...

DESCRIPTION

       This class encapsulates/makes/manipulates objects that represent nodes in a tree
       structure. The tree structure is not an object itself, but is emergent from the linkages
       you create between nodes.  This class provides the methods for making linkages that can be
       used to build up a tree, while preventing you from ever making any kinds of linkages which
       are not allowed in a tree (such as having a node be its own mother or ancestor, or having
       a node have two mothers).

       This is what I mean by a "tree structure", a bit redundantly stated:

       * A tree is a special case of an acyclic directed graph.

       * A tree is a network of nodes where there's exactly one root node (i.e., 'the top'), and
       the only primary relationship between nodes is the mother-daugher relationship.

       * No node can be its own mother, or its mother's mother, etc.

       * Each node in the tree has exactly one "parent" (node in the "up" direction) -- except
       the root, which is parentless.

       * Each node can have any number (0 to any finite number) of daughter nodes.  A given
       node's daughter nodes constitute an ordered list.  (However, you are free to consider this
       ordering irrelevant.  Some applications do need daughters to be ordered, so I chose to
       consider this the general case.)

       * A node can appear in only one tree, and only once in that tree.  Notably (notable
       because it doesn't follow from the two above points), a node cannot appear twice in its
       mother's daughter list.

       * In other words, there's an idea of up (toward the root) versus down (away from the
       root), and left (i.e., toward the start (index 0) of a given node's daughter list) versus
       right (toward the end of a given node's daughter list).

       Trees as described above have various applications, among them: representing syntactic
       constituency, in formal linguistics; representing contingencies in a game tree;
       representing abstract syntax in the parsing of any computer language -- whether in
       expression trees for programming languages, or constituency in the parse of a markup
       language document.  (Some of these might not use the fact that daughters are ordered.)

       (Note: B-Trees are a very special case of the above kinds of trees, and are best treated
       with their own class.  Check CPAN for modules encapsulating B-Trees; or if you actually
       want a database, and for some reason ended up looking here, go look at AnyDBM_File.)

       Many base classes are not usable except as such -- but Tree::DAG_Node can be used as a
       normal class.  You can go ahead and say:

         use Tree::DAG_Node;
         my $root = Tree::DAG_Node->new();
         $root->name("I'm the tops");
         $new_daughter = Tree::DAG_Node->new();
         $new_daughter->name("More");
         $root->add_daughter($new_daughter);

       and so on, constructing and linking objects from Tree::DAG_Node and making useful tree
       structures out of them.

A NOTE TO THE READER

       This class is big and provides lots of methods.  If your problem is simple (say, just
       representing a simple parse tree), this class might seem like using an atomic sledgehammer
       to swat a fly.  But the complexity of this module's bells and whistles shouldn't detract
       from the efficiency of using this class for a simple purpose.  In fact, I'd be very
       surprised if any one user ever had use for more that even a third of the methods in this
       class.  And remember: an atomic sledgehammer will kill that fly.

OBJECT CONTENTS

       Implementationally, each node in a tree is an object, in the sense of being an arbitrarily
       complex data structure that belongs to a class (presumably Tree::DAG_Node, or ones derived
       from it) that provides methods.

       The attributes of a node-object are:

       mother -- this node's mother.  undef if this is a root.
       daughters -- the (possibly empty) list of daughters of this node.
       name -- the name for this node.
           Need not be unique, or even printable.  This is printed in some of the various dumper
           methods, but it's up to you if you don't put anything meaningful or printable here.

       attributes -- whatever the user wants to use it for.
           Presumably a hashref to whatever other attributes the user wants to store without risk
           of colliding with the object's real attributes.  (Example usage: attributes to an SGML
           tag -- you definitely wouldn't want the existence of a "mother=foo" pair in such a tag
           to collide with a node object's 'mother' attribute.)

           Aside from (by default) initializing it to {}, and having the access method called
           "attributes" (described a ways below), I don't do anything with the "attributes" in
           this module.  I basically intended this so that users who don't want/need to bother
           deriving a class from Tree::DAG_Node, could still attach whatever data they wanted in
           a node.

       "mother" and "daughters" are attributes that relate to linkage -- they are never written
       to directly, but are changed as appropriate by the "linkage methods", discussed below.

       The other two (and whatever others you may add in derived classes) are simply accessed
       thru the same-named methods, discussed further below.

       ABOUT THE DOCUMENTED INTERFACE

       Stick to the documented interface (and comments in the source -- especially ones saying
       "undocumented!" and/or "disfavored!" -- do not count as documentation!), and don't rely on
       any behavior that's not in the documented interface.

       Specifically, unless the documentation for a particular method says "this method returns
       thus-and-such a value", then you should not rely on it returning anything meaningful.

       A passing acquintance with at least the broader details of the source code for this class
       is assumed for anyone using this class as a base class -- especially if you're overriding
       existing methods, and definitely if you're overriding linkage methods.

MAIN CONSTRUCTOR, AND INITIALIZER

       the constructor CLASS->new() or CLASS->new({...options...})
           This creates a new node object, calls $object->_init({...options...}) to provide it
           sane defaults (like: undef name, undef mother, no daughters, 'attributes' setting of a
           new empty hashref), and returns the object created.  (If you just said "CLASS->new()"
           or "CLASS->new", then it pretends you called "CLASS->new({})".)

           Currently no options for putting in {...options...} are part of the documented
           interface, but the options is here in case you want to add such behavior in a derived
           class.

           Read on if you plan on using Tree::DAG_New as a base class.  (Otherwise feel free to
           skip to the description of _init.)

           There are, in my mind, two ways to do object construction:

           Way 1: create an object, knowing that it'll have certain uninteresting sane default
           values, and then call methods to change those values to what you want.  Example:

               $node = Tree::DAG_Node->new;
               $node->name('Supahnode!');
               $root->add_daughter($node);
               $node->add_daughters(@some_others)

           Way 2: be able to specify some/most/all the object's attributes in the call to the
           constructor.  Something like:

               $node = Tree::DAG_Node->new({
                 name => 'Supahnode!',
                 mother => $root,
                 daughters => \@some_others
               });

           After some deliberation, I've decided that the second way is a Bad Thing.  First off,
           it is not markedly more concise than the first way.  Second off, it often requires
           subtly different syntax (e.g., \@some_others vs @some_others).  It just complicates
           things for the programmer and the user, without making either appreciably happier.

           (This is not to say that options in general for a constructor are bad --
           "random_network", discussed far below, necessarily takes options.  But note that those
           are not options for the default values of attributes.)

           Anyway, if you use Tree::DAG_Node as a superclass, and you add attributes that need to
           be initialized, what you need to do is provide an _init method that calls
           $this->SUPER::_init($options) to use its superclass's _init method, and then
           initializes the new attributes:

             sub _init {
               my($this, $options) = @_[0,1];
               $this->SUPER::_init($options); # call my superclass's _init to
                 # init all the attributes I'm inheriting

               # Now init /my/ new attributes:
               $this->{'amigos'} = []; # for example
             }

           ...or, as I prefer when I'm being a neat freak:

             sub _init {
               my($this, $options) = @_[0,1];
               $this->SUPER::_init($options);

               $this->_init_amigos($options);
             }

             sub _init_amigos {
               my $this = $_[0];
               # Or my($this,$options) = @_[0,1]; if I'm using $options
               $this->{'amigos'} = [];
             }

           In other words, I like to have each attribute initialized thru a method named
           _init_[attribute], which should expect the object as $_[0] and the the options hashref
           (or {} if none was given) as $_[1].  If you insist on having your _init recognize
           options for setting attributes, you might as well have them dealt with by the
           appropriate _init_[attribute] method, like this:

             sub _init {
               my($this, $options) = @_[0,1];
               $this->SUPER::_init($options);

               $this->_init_amigos($options);
             }

             sub _init_amigos {
               my($this,$options) = @_[0,1]; # I need options this time
               $this->{'amigos'} = [];
               $this->amigos(@{$options->{'amigos'}}) if $options->{'amigos'};
             }

           All this bookkeeping looks silly with just one new attribute in a class derived
           straight from Tree::DAG_Node, but if there's lots of new attributes running around,
           and if you're deriving from a class derived from a class derived from Tree::DAG_Node,
           then tidy stratification/modularization like this can keep you sane.

       the constructor $obj->new() or $obj->new({...options...})
           Just another way to get at the "new" method. This does not copy $obj, but merely
           constructs a new object of the same class as it.  Saves you the bother of going $class
           = ref $obj; $obj2 = $class->new;

       the method $node->_init({...options...})
           Initialize the object's attribute values.  See the discussion above.  Presumably this
           should be called only by the guts of the "new" constructor -- never by the end user.

           Currently there are no documented options for putting in {...options...}, but (in case
           you want to disregard the above rant) the option exists for you to use {...options...}
           for something useful in a derived class.

           Please see the source for more information.

       see also (below) the constructors "new_daughter" and "new_daughter_left"

LINKAGE-RELATED METHODS

       $node->daughters
           This returns the (possibly empty) list of daughters for $node.

       $node->mother
           This returns what node is $node's mother.  This is undef if $node has no mother --
           i.e., if it is a root.

       $mother->add_daughters( LIST )
           This method adds the node objects in LIST to the (right) end of $mother's "daughter"
           list.  Making a node N1 the daughter of another node N2 also means that N1's "mother"
           attribute is "automatically" set to N2; it also means that N1 stops being anything
           else's daughter as it becomes N2's daughter.

           If you try to make a node its own mother, a fatal error results.  If you try to take
           one of a a node N1's ancestors and make it also a daughter of N1, a fatal error
           results.  A fatal error results if anything in LIST isn't a node object.

           If you try to make N1 a daughter of N2, but it's already a daughter of N2, then this
           is a no-operation -- it won't move such nodes to the end of the list or anything; it
           just skips doing anything with them.

       $node->add_daughter( LIST )
           An exact synonym for $node->add_daughters(LIST)

       $mother->add_daughters_left( LIST )
           This method is just like "add_daughters", except that it adds the node objects in LIST
           to the (left) beginning of $mother's daughter list, instead of the (right) end of it.

       $node->add_daughter_left( LIST )
           An exact synonym for $node->add_daughters_left( LIST )

       Note:
           The above link-making methods perform basically an "unshift" or "push" on the mother
           node's daughter list.  To get the full range of list-handling functionality, copy the
           daughter list, and change it, and then call "set_daughters" on the result:

                     @them = $mother->daughters;
                     @removed = splice(@them, 0,2, @new_nodes);
                     $mother->set_daughters(@them);

           Or consider a structure like:

                     $mother->set_daughters(
                                            grep($_->name =~ /NP/ ,
                                                 $mother->daughters
                                                )
                                           );

       the constructor $daughter = $mother->new_daughter, or
       the constructor $daughter = $mother->new_daughter({...options...})
           This constructs a new node (of the same class as $mother), and adds it to the (right)
           end of the daughter list of $mother. This is essentially the same as going

                 $daughter = $mother->new;
                 $mother->add_daughter($daughter);

           but is rather more efficient because (since $daughter is guaranteed new and isn't
           linked to/from anything), it doesn't have to check that $daughter isn't an ancestor of
           $mother, isn't already daughter to a mother it needs to be unlinked from, isn't
           already in $mother's daughter list, etc.

           As you'd expect for a constructor, it returns the node-object created.

       the constructor $mother->new_daughter_left, or
       $mother->new_daughter_left({...options...})
           This is just like $mother->new_daughter, but adds the new daughter to the left (start)
           of $mother's daughter list.

       $mother->remove_daughters( LIST )
           This removes the nodes listed in LIST from $mother's daughter list.  This is a no-
           operation if LIST is empty.  If there are things in LIST that aren't a current
           daughter of $mother, they are ignored.

           Not to be confused with $mother->clear_daughters.

       $node->remove_daughter( LIST )
           An exact synonym for $node->remove_daughters( LIST )

       $node->unlink_from_mother
           This removes node from the daughter list of its mother.  If it has no mother, this is
           a no-operation.

           Returns the mother unlinked from (if any).

       $mother->clear_daughters
           This unlinks all $mother's daughters.  Returns the the list of what used to be
           $mother's daughters.

           Not to be confused with $mother->remove_daughters( LIST ).

       $mother->set_daughters( LIST )
           This unlinks all $mother's daughters, and replaces them with the daughters in LIST.

           Currently implemented as just $mother->clear_daughters followed by
           $mother->add_daughters( LIST ).

       $node->replace_with( LIST )
           This replaces $node in its mother's daughter list, by unlinking $node and replacing it
           with the items in LIST.  This returns a list consisting of $node followed by LIST,
           i.e., the nodes that replaced it.

           LIST can include $node itself (presumably at most once).  LIST can also be empty-list.
           However, if any items in LIST are sisters to $node, they are ignored, and are not in
           the copy of LIST passed as the return value.

           As you might expect for any linking operation, the items in LIST cannot be $node's
           mother, or any ancestor to it; and items in LIST are, of course, unlinked from their
           mothers (if they have any) as they're linked to $node's mother.

           (In the special (and bizarre) case where $node is root, this simply calls
           $this->unlink_from_mother on all the items in LIST, making them roots of their own
           trees.)

           Note that the daughter-list of $node is not necessarily affected; nor are the
           daughter-lists of the items in LIST.  I mention this in case you think replace_with
           switches one node for another, with respect to its mother list and its daughter list,
           leaving the rest of the tree unchanged. If that's what you want, replacing $Old with
           $New, then you want:

             $New->set_daughters($Old->clear_daughters);
             $Old->replace_with($New);

           (I can't say $node's and LIST-items' daughter lists are never affected my replace_with
           -- they can be affected in this case:

             $N1 = ($node->daughters)[0]; # first daughter of $node
             $N2 = ($N1->daughters)[0];   # first daughter of $N1;
             $N3 = Tree::DAG_Node->random_network; # or whatever
             $node->replace_with($N1, $N2, $N3);

           As a side affect of attaching $N1 and $N2 to $node's mother, they're unlinked from
           their parents ($node, and $N1, replectively).  But N3's daughter list is unaffected.

           In other words, this method does what it has to, as you'd expect it to.

       $node->replace_with_daughters
           This replaces $node in its mother's daughter list, by unlinking $node and replacing it
           with its daughters.  In other words, $node becomes motherless and daughterless as its
           daughters move up and take its place.  This returns a list consisting of $node
           followed by the nodes that were its daughters.

           In the special (and bizarre) case where $node is root, this simply unlinks its
           daughters from it, making them roots of their own trees.

           Effectively the same as $node->replace_with($node->daughters), but more efficient,
           since less checking has to be done.  (And I also think $node->replace_with_daughters
           is a more common operation in tree-wrangling than $node->replace_with(LIST), so
           deserves a named method of its own, but that's just me.)

       $node->add_left_sisters( LIST )
           This adds the elements in LIST (in that order) as immediate left sisters of $node.  In
           other words, given that B's mother's daughter-list is (A,B,C,D), calling
           B->add_left_sisters(X,Y) makes B's mother's daughter-list (A,X,Y,B,C,D).

           If LIST is empty, this is a no-op, and returns empty-list.

           This is basically implemented as a call to $node->replace_with(LIST, $node), and so
           all replace_with's limitations and caveats apply.

           The return value of $node->add_left_sisters( LIST ) is the elements of LIST that got
           added, as returned by replace_with -- minus the copies of $node you'd get from a
           straight call to $node->replace_with(LIST, $node).

       $node->add_left_sister( LIST )
           An exact synonym for $node->add_left_sisters(LIST)

       $node->add_right_sisters( LIST )
           Just like add_left_sisters (which see), except that the the elements in LIST (in that
           order) as immediate right sisters of $node;

           In other words, given that B's mother's daughter-list is (A,B,C,D), calling
           B->add_right_sisters(X,Y) makes B's mother's daughter-list (A,B,X,Y,C,D).

       $node->add_right_sister( LIST )
           An exact synonym for $node->add_right_sisters(LIST)

OTHER ATTRIBUTE METHODS

       $node->name or $node->name(SCALAR)
           In the first form, returns the value of the node object's "name" attribute.  In the
           second form, sets it to the value of SCALAR.

       $node->attributes or $node->attributes(SCALAR)
           In the first form, returns the value of the node object's "attributes" attribute.  In
           the second form, sets it to the value of SCALAR.  I intend this to be used to store a
           reference to a (presumably anonymous) hash the user can use to store whatever
           attributes he doesn't want to have to store as object attributes.  In this case, you
           needn't ever set the value of this.  (_init has already initialized it to {}.)
           Instead you can just do...

             $node->attributes->{'foo'} = 'bar';

           ...to write foo => bar.

       $node->attribute or $node->attribute(SCALAR)
           An exact synonym for $node->attributes or $node->attributes(SCALAR)

OTHER METHODS TO DO WITH RELATIONSHIPS

       $node->is_node
           This always returns true.  More pertinently, $object->can('is_node') is true
           (regardless of what "is_node" would do if called) for objects belonging to this class
           or for any class derived from it.

       $node->ancestors
           Returns the list of this node's ancestors, starting with its mother, then grandmother,
           and ending at the root.  It does this by simply following the 'mother' attributes up
           as far as it can.  So if $item IS the root, this returns an empty list.

           Consider that scalar($node->ancestors) returns the ply of this node within the tree --
           2 for a granddaughter of the root, etc., and 0 for root itself.

       $node->root
           Returns the root of whatever tree $node is a member of.  If $node is the root, then
           the result is $node itself.

       $node->is_daughter_of($node2)
           Returns true iff $node is a daughter of $node2.  Currently implemented as just a test
           of ($it->mother eq $node2).

       $node->self_and_descendants
           Returns a list consisting of itself (as element 0) and all the descendants of $node.
           Returns just itself if $node is a terminal_node.

           (Note that it's spelled "descendants", not "descendents".)

       $node->descendants
           Returns a list consisting of all the descendants of $node.  Returns empty-list if
           $node is a terminal_node.

           (Note that it's spelled "descendants", not "descendents".)

       $node->leaves_under
           Returns a list (going left-to-right) of all the leaf nodes under $node.  ("Leaf nodes"
           are also called "terminal nodes" -- i.e., nodes that have no daughters.)  Returns
           $node in the degenerate case of $node being a leaf itself.

       $node->depth_under
           Returns an integer representing the number of branches between this $node and the most
           distant leaf under it.  (In other words, this returns the ply of subtree starting of
           $node.  Consider scalar($it->ancestors) if you want the ply of a node within the whole
           tree.)

       $node->generation
           Returns a list of all nodes (going left-to-right) that are in $node's generation --
           i.e., that are the some number of nodes down from the root.  $root->generation is just
           $root.

           Of course, $node is always in its own generation.

       $node->generation_under(NODE2)
           Like $node->generation, but returns only the nodes in $node's generation that are also
           descendants of NODE2 -- in other words,

               @us = $node->generation_under( $node->mother->mother );

           is all $node's first cousins (to borrow yet more kinship terminology) -- assuming
           $node does indeed have a grandmother.  Actually "cousins" isn't quite an apt word,
           because @us ends up including $node's siblings and $node.

           Actually, "generation_under" is just an alias to "generation", but I figure that this:

              @us = $node->generation_under($way_upline);

           is a bit more readable than this:

              @us = $node->generation($way_upline);

           But it's up to you.

           $node->generation_under($node) returns just $node.

           If you call $node->generation_under($node) but NODE2 is not $node or an ancestor of
           $node, it behaves as if you called just $node->generation().

       $node->self_and_sisters
           Returns a list of all nodes (going left-to-right) that have the same mother as $node
           -- including $node itself. This is just like $node->mother->daughters, except that
           that fails where $node is root, whereas $root->self_and_siblings, as a special case,
           returns $root.

           (Contrary to how you may interpret how this method is named, "self" is not
           (necessarily) the first element of what's returned.)

       $node->sisters
           Returns a list of all nodes (going left-to-right) that have the same mother as $node
           -- not including $node itself.  If $node is root, this returns empty-list.

       $node->left_sister
           Returns the node that's the immediate left sister of $node.  If $node is the leftmost
           (or only) daughter of its mother (or has no mother), then this returns undef.

           (See also $node->add_left_sisters(LIST).)

       $node->left_sisters
           Returns a list of nodes that're sisters to the left of $node.  If $node is the
           leftmost (or only) daughter of its mother (or has no mother), then this returns an
           empty list.

           (See also $node->add_left_sisters(LIST).)

       $node->right_sister
           Returns the node that's the immediate right sister of $node.  If $node is the
           rightmost (or only) daughter of its mother (or has no mother), then this returns
           undef.

           (See also $node->add_right_sisters(LIST).)

       $node->right_sisters
           Returns a list of nodes that're sisters to the right of $node. If $node is the
           rightmost (or only) daughter of its mother (or has no mother), then this returns an
           empty list.

           (See also $node->add_right_sisters(LIST).)

       $node->my_daughter_index
           Returns what index this daughter is, in its mother's "daughter" list.  In other words,
           if $node is ($node->mother->daughters)[3], then $node->my_daughter_index returns 3.

           As a special case, returns 0 if $node has no mother.

       $node->address or $anynode->address(ADDRESS)
           With the first syntax, returns the address of $node within its tree, based on its
           position within the tree.  An address is formed by noting the path between the root
           and $node, and concatenating the daughter-indices of the nodes this passes thru
           (starting with 0 for the root, and ending with $node).

           For example, if to get from node ROOT to node $node, you pass thru ROOT, A, B, and
           $node, then the address is determined as:

           * ROOT's my_daughter_index is 0.

           * A's my_daughter_index is, suppose, 2. (A is index 2 in ROOT's daughter list.)

           * B's my_daughter_index is, suppose, 0. (B is index 0 in A's daughter list.)

           * $node's my_daughter_index is, suppose, 4. ($node is index 4 in B's daughter list.)

           The address of the above-described $node is, therefore, "0:2:0:4".

           (As a somewhat special case, the address of the root is always "0"; and since
           addresses start from the root, all addresses start with a "0".)

           The second syntax, where you provide an address, starts from the root of the tree
           $anynode belongs to, and returns the node corresponding to that address.  Returns
           undef if no node corresponds to that address.  Note that this routine may be somewhat
           liberal in its interpretation of what can constitute an address; i.e., it accepts
           "0.2.0.4", besides "0:2:0:4".

           Also note that the address of a node in a tree is meaningful only in that tree as
           currently structured.

           (Consider how ($address1 cmp $address2) may be magically meaningful to you, if you
           mant to figure out what nodes are to the right of what other nodes.)

       $node->common(LIST)
           Returns the lowest node in the tree that is ancestor-or-self to the nodes $node and
           LIST.

           If the nodes are far enough apart in the tree, the answer is just the root.

           If the nodes aren't all in the same tree, the answer is undef.

           As a degenerate case, if LIST is empty, returns $node.

       $node->common_ancestor(LIST)
           Returns the lowest node that is ancestor to all the nodes given (in nodes $node and
           LIST).  In other words, it answers the question: "What node in the tree, as low as
           possible, is ancestor to the nodes given ($node and LIST)?"

           If the nodes are far enough apart, the answer is just the root -- except if any of the
           nodes are the root itself, in which case the answer is undef (since the root has no
           ancestor).

           If the nodes aren't all in the same tree, the answer is undef.

           As a degenerate case, if LIST is empty, returns $node's mother; that'll be undef if
           $node is root.

YET MORE METHODS

       $node->walk_down({ callback => \&foo, callbackback => \&foo, ... })
           Performs a depth-first traversal of the structure at and under $node.  What it does at
           each node depends on the value of the options hashref, which you must provide.  There
           are three options, "callback" and "callbackback" (at least one of which must be
           defined, as a sub reference), and "_depth".  This is what "walk_down" does, in
           pseudocode form:

           * Start at the $node given.

           * If there's a "callback", call it with $node as the first argument, and the options
           hashref as the second argument (which contains the potentially useful "_depth",
           remember).  This function must return true or false -- if false, it will block the
           next step:

           * If $node has any daughter nodes, increment "_depth", and call
           $daughter->walk_down(options_hashref) for each daughter (in order, of course), where
           options_hashref is the same hashref it was called with.  When this returns, decrements
           "_depth".

           * If there's a "callbackback", call just it as with "callback" (but tossing out the
           return value).  Note that "callback" returning false blocks traversal below $node, but
           doesn't block calling callbackback for $node.  (Incidentally, in the unlikely case
           that $node has stopped being a node object, "callbackback" won't get called.)

           * Return.

           $node->walk_down is the way to recursively do things to a tree (if you start at the
           root) or part of a tree; if what you're doing is best done via pre-pre order
           traversal, use "callback"; if what you're doing is best done with post-order
           traversal, use "callbackback".  "walk_down" is even the basis for plenty of the
           methods in this class.  See the source code for examples both simple and horrific.

           Note that if you don't specify "_depth", it effectively defaults to 0.  You should set
           it to scalar($node->ancestors) if you want "_depth" to reflect the true depth-in-the-
           tree for the nodes called, instead of just the depth below $node.  (If $node is the
           root, there's difference, of course.)

           And by the way, it's a bad idea to modify the tree from the callback.  Unpredictable
           things may happen.  I instead suggest having your callback add to a stack of things
           that need changing, and then, once "walk_down" is all finished, changing those nodes
           from that stack.

           Note that the existence of "walk_down" doesn't mean you can't write you own special-
           use traversers.

       @lines = $node->dump_names({ ...options... });
           Dumps, as an indented list, the names of the nodes starting at $node, and continuing
           under it.  Options are:

           * _depth -- A nonnegative number.  Indicating the depth to consider $node as being at
           (and so the generation under that is that plus one, etc.).  Defaults to 0.  You may
           choose to use set _depth => scalar($node->ancestors).

           * tick -- a string to preface each entry with, between the indenting-spacing and the
           node's name.  Defaults to empty-string.  You may prefer "*" or "-> " or someting.

           * indent -- the string used to indent with.  Defaults to "  " (two spaces).  Another
           sane value might be ". " (period, space).  Setting it to empty-string suppresses
           indenting.

           The dump is not printed, but is returned as a list, where each item is a line, with a
           "\n" at the end.

       the constructor CLASS->random_network({...options...})
       the method $node->random_network({...options...})
           In the first case, constructs a randomly arranged network under a new node, and
           returns the root node of that tree.  In the latter case, constructs the network under
           $node.

           Currently, this is implemented a bit half-heartedly, and half-wittedly.  I basically
           needed to make up random-looking networks to stress-test the various tree-dumper
           methods, and so wrote this.  If you actually want to rely on this for any application
           more serious than that, I suggest examining the source code and seeing if this does
           really what you need (say, in reliability of randomness); and feel totally free to
           suggest changes to me (especially in the form of "I rewrote "random_network", here's
           the code...")

           It takes four options:

           * max_node_count -- maximum number of nodes this tree will be allowed to have
           (counting the root).  Defaults to 25.

           * min_depth -- minimum depth for the tree.  Defaults to 2.  Leaves can be generated
           only after this depth is reached, so the tree will be at least this deep -- unless
           max_node_count is hit first.

           * max_depth -- maximum depth for the tree.  Defaults to 3 plus min_depth.  The tree
           will not be deeper than this.

           * max_children -- maximum number of children any mother in the tree can have.
           Defaults to 4.

       the constructor CLASS->lol_to_tree($lol);
           Converts something like bracket-notation for "Chomsky trees" (or rather, the closest
           you can come with Perl list-of-lists(-of-lists(-of-lists))) into a tree structure.
           Returns the root of the tree converted.

           The conversion rules are that:  1) if the last (possibly the only) item in a given
           list is a scalar, then that is used as the "name" attribute for the node based on this
           list.  2) All other items in the list represent daughter nodes of the current node --
           recursively so, if they are list references; otherwise, (non-terminal) scalars are
           considered to denote nodes with that name.  So ['Foo', 'Bar', 'N'] is an alternate way
           to represent [['Foo'], ['Bar'], 'N'].

           An example will illustrate:

             use Tree::DAG_Node;
             $lol =
               [
                 [
                   [ [ 'Det:The' ],
                     [ [ 'dog' ], 'N'], 'NP'],
                   [ '/with rabies\\', 'PP'],
                   'NP'
                 ],
                 [ 'died', 'VP'],
                 'S'
               ];
              $tree = Tree::DAG_Node->lol_to_tree($lol);
              $diagram = $tree->draw_ascii_tree;
              print map "$_\n", @$diagram;

           ...returns this tree:

                              |
                             <S>
                              |
                           /------------------\
                           |                  |
                         <NP>                <VP>
                           |                  |
                   /---------------\        <died>
                   |               |
                 <NP>            <PP>
                   |               |
                /-------\   </with rabies\>
                |       |
            <Det:The>  <N>
                        |
                      <dog>

           By the way (and this rather follows from the above rules), when denoting a LoL tree
           consisting of just one node, this:

             $tree = Tree::DAG_Node->lol_to_tree( 'Lonely' );

           is okay, although it'd probably occur to you to denote it only as:

             $tree = Tree::DAG_Node->lol_to_tree( ['Lonely'] );

           which is of course fine, too.

       $node->tree_to_lol_notation({...options...})
           Dumps a tree (starting at $node) as the sort of LoL-like bracket notation you see in
           the above example code.  Returns just one big block of text.  The only option is
           "multiline" -- if true, it dumps the text as the sort of indented structure as seen
           above; if false (and it defaults to false), dumps it all on one line (with no
           indenting, of course).

           For example, starting with the tree from the above example, this:

             print $tree->tree_to_lol_notation, "\n";

           prints the following (which I've broken over two lines for sake of printablitity of
           documentation):

             [[[['Det:The'], [['dog'], 'N'], 'NP'], [["/with rabies\x5c"],
             'PP'], 'NP'], [['died'], 'VP'], 'S'],

           Doing this:

             print $tree->tree_to_lol_notation({ multiline => 1 });

           prints the same content, just spread over many lines, and prettily indented.

       $node->tree_to_lol
           Returns that tree (starting at $node) represented as a LoL, like what $lol, above,
           holds.  (This is as opposed to "tree_to_lol_notation", which returns the viewable code
           like what gets evaluated and stored in $lol, above.)

           Lord only knows what you use this for -- maybe for feeding to Data::Dumper, in case
           "tree_to_lol_notation" doesn't do just what you want?

       the constructor CLASS->simple_lol_to_tree($simple_lol);
           This is like lol_to_tree, except that rule 1 doesn't apply -- i.e., all scalars (or
           really, anything not a listref) in the LoL-structure end up as named terminal nodes,
           and only terminal nodes get names (and, of course, that name comes from that scalar
           value).  This method is useful for making things like expression trees, or at least
           starting them off.  Consider that this:

               $tree = Tree::DAG_Node->simple_lol_to_tree(
                 [ 'foo', ['bar', ['baz'], 'quux'], 'zaz', 'pati' ]
               );

           converts from something like a Lispish or Iconish tree, if you pretend the brackets
           are parentheses.

           Note that there is a (possibly surprising) degenerate case of what I'm calling a
           "simple-LoL", and it's like this:

             $tree = Tree::DAG_Node->simple_lol_to_tree('Lonely');

           This is the (only) way you can specify a tree consisting of only a single node, which
           here gets the name 'Lonely'.

       $node->tree_to_simple_lol
           Returns that tree (starting at $node) represented as a simple-LoL -- i.e., one where
           non-terminal nodes are represented as listrefs, and terminal nodes are gotten from the
           contents of those nodes' "name' attributes.

           Note that in the case of $node being terminal, what you get back is the same as
           $node->name.

           Compare to tree_to_simple_lol_notation.

       $node->tree_to_simple_lol_notation({...options...})
           A simple-LoL version of tree_to_lol_notation (which see); takes the same options.

       $list_r = $node->draw_ascii_tree({ ... options ... })
           Draws a nice ASCII-art representation of the tree structure at-and-under $node, with
           $node at the top.  Returns a reference to the list of lines (with no "\n"s or anything
           at the end of them) that make up the picture.

           Example usage:

             print map("$_\n", @{$tree->draw_ascii_tree});

           draw_ascii_tree takes parameters you set in the options hashref:

           * "no_name" -- if true, "draw_ascii_tree" doesn't print the name of the node; simply
           prints a "*".  Defaults to 0 (i.e., print the node name.)

           * "h_spacing" -- number 0 or greater.  Sets the number of spaces inserted horizontally
           between nodes (and groups of nodes) in a tree.  Defaults to 1.

           * "h_compact" -- number 0 or 1.  Sets the extent to which "draw_ascii_tree" tries to
           save horizontal space.  Defaults to 1.  If I think of a better scrunching algorithm,
           there'll be a "2" setting for this.

           * "v_compact" -- number 0, 1, or 2.  Sets the degree to which "draw_ascii_tree" tries
           to save vertical space.  Defaults to 1.

           This occasionally returns trees that are a bit cock-eyed in parts; if anyone can
           suggest a better drawing algorithm, I'd be appreciative.

       $node->copy_tree or $node->copy_tree({...options...})
           This returns the root of a copy of the tree that $node is a member of.  If you pass no
           options, copy_tree pretends you've passed {}.

           This method is currently implemented as just a call to
           $this->root->copy_at_and_under({...options...}), but magic may be added in the future.

           Options you specify are passed down to calls to $node->copy.

       $node->copy_at_and_under or $node->copy_at_and_under({...options...})
           This returns a copy of the subtree consisting of $node and everything under it.

           If you pass no options, copy_at_and_under pretends you've passed {}.

           This works by recursively building up the new tree from the leaves, duplicating nodes
           using $orig_node->copy($options_ref) and then linking them up into a new tree of the
           same shape.

           Options you specify are passed down to calls to $node->copy.

       the constructor $node->copy or $node->copy({...options...})
           Returns a copy of $node, minus its daughter or mother attributes (which are set back
           to default values).

           If you pass no options, "copy" pretends you've passed {}.

           Magic happens with the 'attributes' attribute: if it's a hashref (and it usually is),
           the new node doesn't end up with the same hashref, but with ref to a hash with the
           content duplicated from the original's hashref.  If 'attributes' is not a hashref, but
           instead an object that belongs to a class that provides a method called "copy", then
           that method is called, and the result saved in the clone's 'attribute' attribute.
           Both of these kinds of magic are disabled if the options you pass to "copy" (maybe via
           "copy_tree", or "copy_at_and_under") includes ("no_attribute_copy" => 1).

           The options hashref you pass to "copy" (derictly or indirectly) gets changed slightly
           after you call "copy" -- it gets an entry called "from_to" added to it.  Chances are
           you would never know nor care, but this is reserved for possible future use.  See the
           source if you are wildly curious.

           Note that if you are using $node->copy (whether directly or via $node->copy_tree or
           $node->copy_at_or_under), and it's not properly copying object attributes containing
           references, you probably shouldn't fight it or try to fix it -- simply override
           copy_tree with:

             sub copy_tree {
               use Storable qw(dclone);
               my $this = $_[0];
               return dclone($this->root);
                # d for "deep"
             }

           or

             sub copy_tree {
               use Data::Dumper;
               my $this = $_[0];
               $Data::Dumper::Purity = 1;
               return eval(Dumper($this->root));
             }

           Both of these avoid you having to reinvent the wheel.

           How to override copy_at_or_under with something that uses Storable or Data::Dumper is
           left as an exercise to the reader.

           Consider that if in a derived class, you add attributes with really bizarre contents
           (like a unique-for-all-time-ID), you may need to override "copy".  Consider:

             sub copy {
               my($it, @etc) = @_;
               $it->SUPER::copy(@etc);
               $it->{'UID'} = &get_new_UID;
             }

           ...or the like.  See the source of Tree::DAG_Node::copy for inspiration.

       $node->delete_tree
           Destroys the entire tree that $node is a member of (starting at the root), by nulling
           out each node-object's attributes (including, most importantly, its linkage attributes
           -- hopefully this is more than sufficient to eliminate all circularity in the data
           structure), and then moving it into the class DEADNODE.

           Use this when you're finished with the tree in question, and want to free up its
           memory.  (If you don't do this, it'll get freed up anyway when your program ends.)

           If you try calling any methods on any of the node objects in the tree you've
           destroyed, you'll get an error like:

             Can't locate object method "leaves_under"
               via package "DEADNODE".

           So if you see that, that's what you've done wrong.  (Actually, the class DEADNODE does
           provide one method: a no-op method "delete_tree".  So if you want to delete a tree,
           but think you may have deleted it already, it's safe to call $node->delete_tree on it
           (again).)

           The "delete_tree" method is needed because Perl's garbage collector would never (as
           currently implemented) see that it was time to de-allocate the memory the tree uses --
           until either you call $node->delete_tree, or until the program stops (at "global
           destruction" time, when everything is unallocated).

           Incidentally, there are better ways to do garbage-collecting on a tree, ways which
           don't require the user to explicitly call a method like "delete_tree" -- they involve
           dummy classes, as explained at "http://mox.perl.com/misc/circle-destroy.pod"

           However, introducing a dummy class concept into Tree::DAG_Node would be rather a
           distraction.  If you want to do this with your derived classes, via a DESTROY in a
           dummy class (or in a tree-metainformation class, maybe), then feel free to.

           The only case where I can imagine "delete_tree" failing to totally void the tree, is
           if you use the hashref in the "attributes" attribute to store (presumably among other
           things) references to other nodes' "attributes" hashrefs -- which 1) is maybe a bit
           odd, and 2) is your problem, because it's your hash structure that's circular, not the
           tree's.  Anyway, consider:

                 # null out all my "attributes" hashes
                 $anywhere->root->walk_down({
                   'callback' => sub {
                     $hr = $_[0]->attributes; %$hr = (); return 1;
                   }
                 });
                 # And then:
                 $anywhere->delete_tree;

           (I suppose "delete_tree" is a "destructor", or as close as you can meaningfully come
           for a circularity-rich data structure in Perl.)

       When and How to Destroy

       It should be clear to you that if you've built a big parse tree or something, and then
       you're finished with it, you should call $some_node->delete_tree on it if you want the
       memory back.

       But consider this case:  you've got this tree:

             A
           / | \
          B  C  D
          |     | \
          E     X  Y

       Let's say you decide you don't want D or any of its descendants in the tree, so you call
       D->unlink_from_mother.  This does NOT automagically destroy the tree D-X-Y.  Instead it
       merely splits the tree into two:

            A                        D
           / \                      / \
          B   C                    X   Y
          |
          E

       To destroy D and its little tree, you have to explicitly call delete_tree on it.

       Note, however, that if you call C->unlink_from_mother, and if you don't have a link to C
       anywhere, then it does magically go away.  This is because nothing links to C -- whereas
       with the D-X-Y tree, D links to X and Y, and X and Y each link back to D. Note that
       calling C->delete_tree is harmless -- after all, a tree of only one node is still a tree.

       So, this is a surefire way of getting rid of all $node's children and freeing up the
       memory associated with them and their descendants:

         foreach my $it ($node->clear_daughters) { $it->delete_tree }

       Just be sure not to do this:

         foreach my $it ($node->daughters) { $it->delete_tree }
         $node->clear_daughters;

       That's bad; the first call to $_->delete_tree will climb to the root of $node's tree, and
       nuke the whole tree, not just the bits under $node.  You might as well have just called
       $node->delete_tree.  (Moreavor, once $node is dead, you can't call clear_daughters on it,
       so you'll get an error there.)

BUG REPORTS

       If you find a bug in this library, report it to me as soon as possible, at the address
       listed in the MAINTAINER section, below.  Please try to be as specific as possible about
       how you got the bug to occur.

HELP!

       If you develop a given routine for dealing with trees in some way, and use it a lot, then
       if you think it'd be of use to anyone else, do email me about it; it might be helpful to
       others to include that routine, or something based on it, in a later version of this
       module.

       It's occurred to me that you might like to (and might yourself develop routines to) draw
       trees in something other than ASCII art.  If you do so -- say, for PostScript output, or
       for output interpretable by some external plotting program --  I'd be most interested in
       the results.

RAMBLINGS

       This module uses "strict", but I never wrote it with -w warnings in mind -- so if you use
       -w, do not be surprised if you see complaints from the guts of DAG_Node.  As long as there
       is no way to turn off -w for a given module (instead of having to do it in every single
       subroutine with a "local $^W"), I'm not going to change this. However, I do, at points,
       get bursts of ambition, and I try to fix code in DAG_Node that generates warnings, as I
       come across them -- which is only occasionally.  Feel free to email me any patches for any
       such fixes you come up with, tho.

       Currently I don't assume (or enforce) anything about the class membership of nodes being
       manipulated, other than by testing whether each one provides a method "is_node", a la:

         die "Not a node!!!" unless UNIVERSAL::can($node, "is_node");

       So, as far as I'm concerned, a given tree's nodes are free to belong to different classes,
       just so long as they provide/inherit "is_node", the few methods that this class relies on
       to navigate the tree, and have the same internal object structure, or a superset of it.
       Presumably this would be the case for any object belonging to a class derived from
       "Tree::DAG_Node", or belonging to "Tree::DAG_Node" itself.

       When routines in this class access a node's "mother" attribute, or its "daughters"
       attribute, they (generally) do so directly (via $node->{'mother'}, etc.), for sake of
       efficiency.  But classes derived from this class should probably do this instead thru a
       method (via $node->mother, etc.), for sake of portability, abstraction, and general
       goodness.

       However, no routines in this class (aside from, necessarily, "_init", "_init_name", and
       "name") access the "name" attribute directly; routines (like the various tree draw/dump
       methods) get the "name" value thru a call to $obj->name().  So if you want the object's
       name to not be a real attribute, but instead have it derived dynamically from some feature
       of the object (say, based on some of its other attributes, or based on its address), you
       can to override the "name" method, without causing problems.  (Be sure to consider the
       case of $obj->name as a write method, as it's used in "lol_to_tree" and "random_network".)

SEE ALSO

       HTML::Element

       Wirth, Niklaus.  1976.  Algorithms + Data Structures = Programs Prentice-Hall, Englewood
       Cliffs, NJ.

       Knuth, Donald Ervin.  1997.  Art of Computer Programming, Volume 1, Third Edition:
       Fundamental Algorithms.  Addison-Wesley,  Reading, MA.

       Wirth's classic, currently and lamentably out of print, has a good section on trees.  I
       find it clearer than Knuth's (if not quite as encyclopedic), probably because Wirth's
       example code is in a block-structured high-level language (basically Pascal), instead of
       in assembler (MIX).

       Until some kind publisher brings out a new printing of Wirth's book, try poking around
       used bookstores (or "www.abebooks.com") for a copy.  I think it was also republished in
       the 1980s under the title Algorithms and Data Structures, and in a German edition called
       Algorithmen und Datenstrukturen.  (That is, I'm sure books by Knuth were published under
       those titles, but I'm assuming that they're just later printings/editions of Algorithms +
       Data Structures = Programs.)

MAINTAINER

       David Hand, "<cogent@cpan.org>"

AUTHOR

       Sean M. Burke, "<sburke@cpan.org>"

COPYRIGHT, LICENSE, AND DISCLAIMER

       Copyright 1998-2001, 2004, 2007 by Sean M. Burke and David Hand.

       This program is free software; you can redistribute it and/or modify it under the same
       terms as Perl itself.

       This program is distributed in the hope that it will be useful, but without any warranty;
       without even the implied warranty of merchantability or fitness for a particular purpose.