struct::disjointset -
Disjoint set data structure
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
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.
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.
This document, and the package it describes, will undoubtedly contain
bugs and other problems.
Please report such in the category
struct :: disjointset of the
http://sourceforge.net/tracker/?group_id=12883.
Please also report any ideas for enhancements you may have for either
package and/or documentation.
disjoint set, merge find, union, find, partition, partitioned set, equivalence class