NAME

       struct::disjointset - Disjoint set data structure

SYNOPSIS

       package require Tcl  8.4

       package require struct::disjointset  ?1.0?

       ::struct::disjointset disjointsetName

       disjointsetName option ?arg arg ...?

       disjointsetName add-partition elements

       disjointsetName partitions

       disjointsetName num-partitions

       disjointsetName equal a b

       disjointsetName merge a b

       disjointsetName find e

       disjointsetName destroy

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DESCRIPTION

       This  package  provides  disjoint  sets. An alternative name for this kind of structure is
       merge-find.

       Normally when dealing with sets and their elements the question  is  "Is  this  element  E
       contained in this set S?", with both E and S known.

       Here  the  question  is  "Which  of  several sets contains the element E?". I.e. while the
       element is known, the set is not, and we wish to find it quickly.  It  is  not  quite  the
       inverse  of  the original question, but close.  Another operation which is often wanted is
       that of quickly merging two sets  into  one,  with  the  result  still  fast  for  finding
       elements. Hence the alternative term merge-find for this.

       Why  now  is  this  named  a  disjoint-set  ?  Because another way of describing the whole
       situation is that we have

       •      a finite set S, containing

       •      a number of elements E, split into

       •      a set of partitions P. The latter term applies, because the  intersection  of  each
              pair  P,  P'  of partitions is empty, with the union of all partitions covering the
              whole set.

       •      An alternative name for  the  partitions  would  be  equvalence  classes,  and  all
              elements in the same class are considered as equal.

       Here is a pictorial representation of the concepts listed above:
              +-----------------+ The outer lines are the boundaries of the set S.
              |           /     | The inner regions delineated by the skewed lines
              |  *       /   *  | are the partitions P. The *'s denote the elements
              |      *  / \     | E in the set, each in a single partition, their
              |*       /   \    | equivalence class.
              |       /  *  \   |
              |      / *   /    |
              | *   /\  * /     |
              |    /  \  /      |
              |   /    \/  *    |
              |  / *    \       |
              | /     *  \      |
              +-----------------+

       For more information see http://en.wikipedia.org/wiki/Disjoint_set_data_structure.

API

       The  package  exports  a single command, ::struct::disjointset. All functionality provided
       here can be reached through a subcommand of this command.

       ::struct::disjointset disjointsetName
              Creates a new disjoint set object with an associated global Tcl command whose  name
              is  disjointsetName.  This  command may be used to invoke various operations on the
              disjointset. It has the following general form:

              disjointsetName option ?arg arg ...?
                     The option and the args determine the exact behavior  of  the  command.  The
                     following commands are possible for disjointset objects:

       disjointsetName add-partition elements
              Creates  a  new  partition  in specified disjoint set, and fills it with the values
              found in the set of elements. The command maintains the integrity of  the  disjoint
              set,  i.e.  it  verifies that none of the elements are already part of the disjoint
              set and throws an error otherwise.

              The result of the command is the empty string.

       disjointsetName partitions
              Returns the set of partitions the named disjoint set currently consists of.

       disjointsetName num-partitions
              Returns the number of partitions the named disjoint set currently consists of.

       disjointsetName equal a b
              Determines if the two elements a and b of the  disjoint  set  belong  to  the  same
              partition.  The  result  of the method is a boolean value, True if the two elements
              are contained in the same partition, and False otherwise.

              An error will be thrown if either a or b are not elements of the disjoint set.

       disjointsetName merge a b
              Determines the partitions the elements a and b are contained  in  and  merges  them
              into  a  single  partition.  If the two elements were already contained in the same
              partition nothing will change.

              The result of the method is the empty string.

       disjointsetName find e
              Returns the partition of the disjoint set which contains the element e.

       disjointsetName destroy
              Destroys the disjoint set object and all associated memory.

BUGS, IDEAS, FEEDBACK

       This document, and the package it describes,  will  undoubtedly  contain  bugs  and  other
       problems.   Please  report  such  in  the  category struct :: disjointset of the Tcllib SF
       Trackers [http://sourceforge.net/tracker/?group_id=12883].  Please also report  any  ideas
       for enhancements you may have for either package and/or documentation.

KEYWORDS

       disjoint set, equivalence class, find, merge find, partition, partitioned set, union

CATEGORY

       Data structures