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 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

       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.

       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/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

struct									1.0						    struct::disjointset(n)