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 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.
KEYWORDS¶
disjoint set, equivalence class, find, merge find, partition, partitioned set,
union
CATEGORY¶
Data structures