struct::disjointset(n) Tcl Data Structures struct::disjointset(n) ______________________________________________________________________________
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
_________________________________________________________________
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.
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.
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
struct 1.0 struct::disjointset(n)
Mac OS X 10.8 - Generated Thu Sep 6 06:05:12 CDT 2012