Provided by: libtree-dagnode-perl_1.17-1_all bug

NAME

       Tree::DAG_Node - An N-ary tree

SYNOPSIS

       Using as a base class:

               package Game::Tree::Node;

               use parent 'Tree::DAG_Node';

               # Now add your own methods overriding/extending the methods in C<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");
               ...

       Using with utf-8 data:

               read_tree($file_name) works with utf-8 data. See t/read.tree.t and t/tree.utf8.attributes.txt.
               Such a file can be created by redirecting the output of tree2string() to a file of type utf-8.

       See the docs for Encode for the difference between utf8 and utf-8. In brief, use utf-8.

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:

       o A tree is a special case of an acyclic directed graph
       o A tree is a network of nodes where there's exactly one root node
           Also, the only primary relationship between nodes is the mother-daughter relationship.

       o No node can be its own mother, or its mother's mother, etc
       o Each node in the tree has exactly one parent
           Except for the root of course, which is parentless.

       o Each node can have any number (0 .. N) 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.

       o 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.

       o There's an idea of up versus down
           Up means towards to the root, and down means away from the root (and towards the leaves).

       o There's an idea of left versus right
           Left  is toward the start (index 0) of a given node's daughter list, and right is 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:

       o mother -- this node's mother.  undef if this is a root
       o daughters -- the (possibly empty) list of daughters of this node
       o 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.

       o 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 acquaintance 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 hashref $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.

           See however the comments under "new($hashref)" for options newly supported in the call to new().

           (This is not to say that options in general for a constructor are bad --  "random_network($options)",
           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 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($hashref)" 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($hashref)" constructor -- never by the end user.

           Currently  there are no documented options for putting in the $options hashref, 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"

METHODS

   add_daughter(LIST)
       An exact synonym for "add_daughters(LIST)".

   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  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.

   add_daughter_left(LIST)
       An exact synonym for "add_daughters_left(LIST)".

   add_daughters_left(LIST)
       This  method  is  just  like  "add_daughters(LIST)",  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.

   add_left_sister(LIST)
       An exact synonym for "add_left_sisters(LIST)".

   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).

   add_right_sister(LIST)
       An exact synonym for "add_right_sisters(LIST)".

   add_right_sisters(LIST)
       Just like add_left_sisters (which see), except that 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).

   address()
   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:

       o ROOT's my_daughter_index is 0
       o A's my_daughter_index is, suppose, 2
           A is index 2 in ROOT's daughter list.

       o B's my_daughter_index is, suppose, 0
           B is index 0 in A's daughter list.

       o $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 meant to figure out
       what nodes are to the right of what other nodes.)

   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.

   attribute()
   attribute(SCALAR)
       Exact synonyms for "attributes()" and "attributes(SCALAR)".

   attributes()
   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.

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

       Not to be confused with "remove_daughters(LIST)".

   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.

   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.

   copy($option)
       Returns a copy the calling node (the invocant). E.g.: my($copy) = $node -> copy;

       $option is a hashref of options, with these (key => value) pairs:

       o no_attribute_copy => $Boolean
           If set to 1, do not copy the node's attributes.

           If not specified, defaults to 0, which copies attributes.

   copy_at_and_under()
   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.

   copy_tree()
   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.

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

       See also "WHEN AND HOW TO DESTROY THE TREE".

   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.)

   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".)

   draw_ascii_tree([$options])
       Here, the [] refer to an optional parameter.

       Returns an arrayref of lines suitable for printing.

       Draws a nice ASCII-art representation of the tree structure.

       The tree looks like:

                            |
                         <Root>
                  /-------+-----+---+---\
                  |       |     |   |   |
                 <I>     <H>   <D> <E> <B>
                /---\   /---\   |   |   |
                |   |   |   |  <F> <F> <C>
               <J> <J> <J> <J>  |   |
                |   |   |   |  <G> <G>
               <K> <L> <K> <L>
                    |       |
                   <M>     <M>
                    |       |
                   <N>     <N>
                    |       |
                   <O>     <O>

       See scripts/cut.and.paste.subtrees.pl.

       Example usage:

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

       draw_ascii_tree() takes parameters you set in the $options hashref:

       o h_compact
           Takes 0 or 1.  Sets the extent to which draw_ascii_tree() tries to save horizontal space.

           If I think of a better scrunching algorithm, there'll be a "2" setting for this.

           Default: 1.

       o h_spacing
           Takes a number 0 or greater.  Sets the number of spaces  inserted  horizontally  between  nodes  (and
           groups of nodes) in a tree.

           Default: 1.

       o no_name
           If true, draw_ascii_tree() doesn't print the name of the node; it simply prints a "*".

           Default: 0 (i.e., print the node name.)

       o v_compact
           Takes  a number 0, 1, or 2.  Sets the degree to which draw_ascii_tree() tries to save vertical space.
           Defaults to 1.

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

       See also "tree2string([$options], [$some_tree])".

   dump_names($options)
       Returns an array.

       Dumps,  as  an indented list, the names of the nodes starting at $node, and continuing under it.  Options
       are:

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

           Default: 0.

       o tick -- a string to preface each entry with
           This  string  goes between the indenting-spacing and the node's name.  You may prefer "*" or "-> " or
           something.

           Default: ''.

       o indent -- the string used to indent with
           Another sane value might be '. ' (period, space).  Setting it to empty-string suppresses indenting.

           Default: ' ' x 2.

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

       Note: Names are converted to a printable form using the undocumented function _dump_quote().

   format_node([$options], [$node])
       Here, [] represent optional parameters.

       Returns a string consisting of the node's name and, optionally, it's attributes.

       Possible keys in the $options hashref:

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string returned.

           Default: 0 (include attributes).

       Calls "hashref2string($hashref)".

       Called by "node2string([$options], [$node])".

       You would not normally call this method.

       If you don't wish to supply options, use format_node({}, $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.

   generation_under($node)
       Like  "generation()", but returns only the nodes in $node's generation that are also descendants of $node
       -- 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($node)" 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().

       head2 hashref2string($hashref)

       Returns the given hashref as a string.

       Called by "format_node([$options], [$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).

   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.

   is_root()
       Returns 1 if the caller is the root, and 0 if it is not.

   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.

   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 "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   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 "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   lol_to_tree($lol)
       This must be called as a class method.

       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.

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

       See also "is_root()" and "root()".

   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.

   name()
   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.

   new($hashref)
       These options are supported in $hashref:

       o attributes => A hashref of attributes
       o daughters => An arrayref of nodes
       o mother => A node
       o name => A string

       See also "MAIN CONSTRUCTOR, AND INITIALIZER" for a long discussion on object creation.

   new_daughter()
   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.

       # Note that if you radically change 'mother'/'daughters' bookkeeping, #  you  may  have  to  change  this
       routine, since it's one of the places # that directly writes to 'daughters' and 'mother'.

   new_daughter_left()
   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.

       # Note that if you radically change 'mother'/'daughters' bookkeeping, #  you  may  have  to  change  this
       routine, since it's one of the places # that directly writes to 'daughters' and 'mother'.

   node2string($options, $t, $vert_dashes)
       Returns a string of the node's name and attributes, with a leading indent, suitable for printing.

       Possible keys in the $options hashref:

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string returned.

           Default: 0 (include attributes).

       Calls "format_node([$options], [$node])".

       Called by "tree2string([$options], [$some_tree])".

   random_network($options)
       This method can be called as a class method or as an object method.

       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($options)",  here's
       the code...")

       It takes four options:

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

       o min_depth -- minimum depth for the tree
           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.

           Default: 2.

       o max_depth -- maximum depth for the tree
           The tree will not be deeper than this.

           Default: 3 plus min_depth.

       o max_children -- maximum number of children any mother in the tree can have.
           Default: 4.

   read_attributes($s)
       Parses the string $s and extracts the name and  attributes,  assuming  the  format  is  as  generated  by
       "tree2string([$options], [$some_tree])".

       This bascially means the string was generated by "hashref2string($hashref)".

       Attributes may be absent, in which case they default to {}.

       Returns a new node with this name and these attributes.

       This method is for use by "read_tree($file_name)".

       See t/tree.without.attributes.txt and t/tree.with.attributes.txt for sample data.

   read_tree($file_name)
       Returns the root of the tree read from $file_name.

       The  file must have been written by re-directing the output of "tree2string([$options], [$some_tree])" to
       a file, since it makes assumptions about the format of the stringified attributes.

       read_tree() works with utf-8 data. See t/read.tree.t and t/tree.utf8.attributes.txt.

       Note: To call this method you need a caller. It'll be a tree of 1 node. The reason is  that  inside  this
       method it calls various other methods, and for these calls it needs $self. That way, those methods can be
       called from anywhere, and not just from within read_tree().

       For reading and writing trees to databases, see Tree::DAG_Node::Persist.

   remove_daughter(LIST)
       An exact synonym for "remove_daughters(LIST)".

   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 "clear_daughters()".

   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, respectively).  But N3's daughter list is unaffected.

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

   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.)

       #  Note  that  if  you  radically  change 'mother'/'daughters' bookkeeping, # you may have to change this
       routine, since it's one of the places # that directly writes to 'daughters' and 'mother'.

   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 "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

   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 "add_left_sisters(LIST)" and "add_right_sisters(LIST)".

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

       Not to be confused with "is_root()".

   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".)

   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.)

   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).

   simple_lol_to_tree($simple_lol)
       This must be called as a class method.

       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'.

   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.

   string2hashref($s)
       Returns a hashref built from the string.

       The string is expected to be something like '{AutoCommit => '1', PrintError => "0", ReportError => 1}'.

       The empty string is returned as {}.

   tree_to_lol()
       Returns that tree (starting at $node) represented as a LoL, like what $lol, above, holds.   (This  is  as
       opposed to "tree_to_lol_notation($options)", 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($options)" doesn't do just what you want?

   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 printability 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.

       Note: Names are converted to a printable form using the undocumented function _dump_quote().

   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.

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

       Note: Names are converted to a printable form using the undocumented function _dump_quote().

   tree2string([$options], [$some_tree])
       Here, the [] represent optional parameters.

       Returns an arrayref of lines, suitable for printing.

       Draws a nice ASCII-art representation of the tree structure.

       The tree looks like:

               Root. Attributes: {# => "0"}
                  |---I. Attributes: {# => "1"}
                  |   |---J. Attributes: {# => "3"}
                  |   |   |---K. Attributes: {# => "3"}
                  |   |---J. Attributes: {# => "4"}
                  |       |---L. Attributes: {# => "5"}
                  |           |---M. Attributes: {# => "5"}
                  |               |---N. Attributes: {# => "5"}
                  |                   |---O. Attributes: {# => "5"}
                  |---H. Attributes: {# => "2"}
                  |   |---J. Attributes: {# => "3"}
                  |   |   |---K. Attributes: {# => "3"}
                  |   |---J. Attributes: {# => "4"}
                  |       |---L. Attributes: {# => "5"}
                  |           |---M. Attributes: {# => "5"}
                  |               |---N. Attributes: {# => "5"}
                  |                   |---O. Attributes: {# => "5"}
                  |---D. Attributes: {# => "6"}
                  |   |---F. Attributes: {# => "8"}
                  |       |---G. Attributes: {# => "8"}
                  |---E. Attributes: {# => "7"}
                  |   |---F. Attributes: {# => "8"}
                  |       |---G. Attributes: {# => "8"}
                  |---B. Attributes: {# => "9"}
                      |---C. Attributes: {# => "9"}

       Or, without attributes:

               Root
                  |---I
                  |   |---J
                  |   |   |---K
                  |   |---J
                  |       |---L
                  |           |---M
                  |               |---N
                  |                   |---O
                  |---H
                  |   |---J
                  |   |   |---K
                  |   |---J
                  |       |---L
                  |           |---M
                  |               |---N
                  |                   |---O
                  |---D
                  |   |---F
                  |       |---G
                  |---E
                  |   |---F
                  |       |---G
                  |---B
                      |---C

       See scripts/cut.and.paste.subtrees.pl.

       Example usage:

         print map("$_\n", @{$tree->tree2string});

       Can be called with $some_tree set to any $node, and will print the tree assuming $node is the root.

       If you don't wish to supply options, use tree2string({}, $node).

       Possible keys in the $options hashref (which defaults to {}):

       o no_attributes => $Boolean
           If 1, the node's attributes are not included in the string returned.

           Default: 0 (include attributes).

       Calls "node2string($options, $t, $vert_dashes)".

       See also "draw_ascii_tree([$options])".

   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).

   walk_down($options)
       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:

       o Starting point
           Start at the $node given.

       o Callback
           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:

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

       Callbackback
           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.)

       o Return

       $node->walk_down($options)  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.

WHEN AND HOW TO DESTROY THE TREE

       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  $obj->name  as  a  write  method,  as  it's  used  in   /lol_to_tree($lol)   and
       "random_network($options)".)

FAQ

   Which is the best tree processing module?
       "Tree::DAG_Node", as it happens. More details: "SEE ALSO".

   How to process every node in tree?
       See  "walk_down($options)". $options normally looks like this, assuming we wish to pass in an arrayref as
       a stack:

               my(@stack);

               $tree -> walk_down
               ({
                       callback =>
                       sub
                       {
                               my(@node, $options) = @_;

                               # Process $node, using $options...

                               push @{$$options{stack} }, $node -> name;

                               return 1; # Keep walking.
                       },
                       _depth => 0,
                       stack  => \@stack,
               });

               # Process @stack...

   How do I switch from Tree to Tree::DAG_Node?
       o The node's name
           In "Tree" you use $node -> value and in "Tree::DAG_Node" it's $node -> name.

       o The node's attributes
           In "Tree" you use $node -> meta and in "Tree::DAG_Node" it's $node -> attributes.

   Are there techniques for processing lists of nodes?
       o Copy the daughter list, and change it
                   @them    = $mother->daughters;
                   @removed = splice(@them, 0, 2, @new_nodes);

                   $mother->set_daughters(@them);

       o Select a sub-set of nodes
                   $mother->set_daughters
                   (
                           grep($_->name =~ /wanted/, $mother->daughters)
                   );

   Why did you break up the sections of methods in the POD?
       Because I want to list the methods in alphabetical order.

   Why did you move the POD to the end?
       Because the apostrophes in the text confused the syntax hightlighter in my editor UltraEdit.

SEE ALSO

       o HTML::Element, HTML::Tree and HTML::TreeBuilder
           Sean is also the author of these modules.

       o Tree
           Lightweight.

       o Tree::Binary
           Lightweight.

       o Tree::DAG_Node::Persist
           Lightweight.

       o Tree::Persist
           Lightweight.

       o Forest
           Uses Moose.

       "Tree::DAG_Node" itself is also lightweight.

REFERENCES

       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.)

MACHINE-READABLE CHANGE LOG

       The file Changes was converted into Changelog.ini by Module::Metadata::Changes.

SUPPORT

       Email the author, or log a bug on RT:

       <https://rt.cpan.org/Public/Dist/Display.html?Name=Tree::DAG_Node>.

ACKNOWLEDGEMENTS

       The code to print the tree, in tree2string(), was adapted from Forest::Tree::Writer::ASCIIWithBranches by
       the dread Stevan Little.

MAINTAINER

       David Hand, "<cogent@cpan.org>" up to V 1.06.

       Ron Savage "<rsavage@cpan.org>" from V 1.07.

       In this POD, usage of 'I' refers to Sean, up until V 1.07.

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.   It   is   released   under   the   Artistic  License  2.0.   See
       <http://opensource.org/licenses/Artistic-2.0>.

       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.

perl v5.18.1                                       2013-10-21                                Tree::DAG_Node(3pm)