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    Trackers
       [http://core.tcl.tk/tcllib/reportlist].   Please  also report any ideas for enhancements you may have for
       either package and/or documentation.

       When proposing code changes, please provide unified diffs, i.e the output of diff -u.

       Note further that attachments are strongly preferred over inlined patches. Attachments  can  be  made  by
       going  to the Edit form of the ticket immediately after its creation, and then using the left-most button
       in the secondary navigation bar.

KEYWORDS

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

CATEGORY

       Data structures