<P/>
<Package>datastructures</Package> defines the interface for mutable data structures
representing partitions of <C>[1..n]</C>, commonly known as union-find data structures.
Key operations are
<Ref Oper="Unite" Label="for IsPartitionDS and IsMutable, IsPosInt, IsPosInt"/>
which fuses two parts of a partition and
<Ref Oper="Representative" Label="for IsPartitionDS, IsPosInt"/> which
returns a canonical representative of the part containing a given point.
<P/>
</Section>
<P/>
<ManSection>
<Filt Arg="arg" Name="IsPartitionDS" Label="for IsObject"/>
<Returns><K>true</K> or <K>false</K>
</Returns>
<Description>
Category of datastructures representing partitions.
Equality is identity and family is ignored.
</Description>
</ManSection>
<ManSection>
<Constr Arg="filter, n" Name="PartitionDSCons" Label="for IsPartitionDS, IsPosInt"/>
<Description>
Family containing all partition data structures
Returns the trivial partition of the set <C>[1..n]</C>.
</Description>
</ManSection>
<ManSection>
<Constr Arg="filter, partition" Name="PartitionDSCons" Label="for IsPartitionDS, IsCyclotomicCollColl"/>
<Description>
Returns the union find structure of <A>partition</A>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="filter, n" Name="PartitionDS" Label="for IsFunction, IsPosInt"/>
<Description>
Returns the trivial partition of the set <C>[1..n]</C>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="n" Name="PartitionDS" Label="for IsPosInt"/>
<Description>
Returns the trivial partition of the set <C>[1..n]</C>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="filter, partition" Name="PartitionDS" Label="for IsFunction, IsCyclotomicCollColl"/>
<Description>
Returns the union find structure of <A>partition</A>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="partition" Name="PartitionDS" Label="for IsCyclotomicCollColl"/>
<Description>
Returns the union find structure of <A>partition</A>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="unionfind, k" Name="Representative" Label="for IsPartitionDS, IsPosInt"/>
<Returns>a positive integer
</Returns>
<Description>
Returns a canonical representative of the part of the partition that
<A>k</A> is contained in.
</Description>
</ManSection>
<ManSection>
<Oper Arg="unionfind, k1, k2" Name="Unite" Label="for IsPartitionDS and IsMutable, IsPosInt, IsPosInt"/>
<Description>
Fuses the parts of the partition <A>unionfind</A> containing <A>k1</A>
and <A>k2</A>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="unionfind" Name="RootsIteratorOfPartitionDS" Label="for IsPartitionDS"/>
<Returns>an iterator
</Returns>
<Description>
Returns an iterator that runs through canonical representatives of parts
of the partition <A>unionfind</A>.
</Description>
</ManSection>
<ManSection>
<Oper Arg="unionfind" Name="RootsOfPartitionDS" Label="for IsPartitionDS"/>
<Returns>A list.
</Returns>
<Description>
Returns a list of the canonical representatives of the parts
of the partition <A>unionfind</A>.
</Description>
</ManSection>
<ManSection>
<Attr Arg="unionfind" Name="NumberParts" Label="for IsPartitionDS"/>
<Returns>a positive integer
</Returns>
<Description>
Returns the number of parts of the partition <A>unionfind</A>.
</Description>
</ManSection>
<ManSection>
<Attr Arg="unionfind" Name="SizeUnderlyingSetDS" Label="for IsPartitionDS"/>
<Returns>a positive integer
</Returns>
<Description>
Returns the size of the underlying set of the partition <A>unionfind</A>.
</Description>
</ManSection>
<ManSection>
<Attr Arg="unionfind" Name="PartsOfPartitionDS" Label="for IsPartitionDS"/>
<Returns>a list of lists
</Returns>
<Description>
Returns the partition <A>unionfind</A> as a list of lists.
</Description>
</ManSection>
</Section>
<P/>
</Chapter>
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