


struct::disjointset(n) Tcl Data Structures struct::disjointset(n)


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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 ele-
       ments. Hence the alternative term merge-find for this.

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

       o      a finite set S, containing

       o      a number of elements E, split into

       o      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.



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struct::disjointset(n) Tcl Data Structures struct::disjointset(n)


       o      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/Dis-
       joint_set_data_structure.

API
       The package exports a single command, ::struct::disjointset. All  func-
       tionality  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 fol-
              lowing general form:

              disjointsetName option ?arg arg ...?
                     The  option  and the args determine the exact behavior of
                     the command. The following commands are possible for dis-
                     jointset 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  main-
              tains  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.




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struct::disjointset(n) Tcl Data Structures struct::disjointset(n)


       disjointsetName num-partitions
              Returns the number of partitions the  named  disjoint  set  cur-
              rently 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://source-
       forge.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, parti-
       tioned set, union

CATEGORY
       Data structures















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