Version 5.0 The LEDA User Manual

6.12 Partitions ( partition )
1. Definition
An instance P of the data type partition consists of a finite set of items (partition item)
and a partition of this set into blocks.
#include < LEDA/core/partition.h >
2. Creation
partition P ;
creates an instance P of type partition and initializes it to the empty
partition.
3. Operations
partition item P.make block( ) returns a new partition item it and adds the block
it to partition P .
partition item P.find(partition item p)
int P.size(partition item p)
returns a canonical item of the block that contains
item p, i.e., iff P.same block(p, q) then P.find(p)
and P.find(q) return the same item.
Precondition: p is an item in P .
returns the size of the block containing p.
int P.number of blocks( ) returns the number of blocks in P .
bool P.same block(partition item p, partition item q)
returns true if p and q belong to the same block of
partition P .
Precondition: p and q are items in P .
void P.union blocks(partition item p, partition item q)
void P.split(const list& L)
4. Implementation
unites the blocks of partition P containing items
p and q.
Precondition: p and q are items in P .
turns all items in L to singleton blocks.
Precondition: L is a union of blocks.
Partitions are implemented by the union find algorithm with weighted union and path
compression (cf. [86]). Any sequence of n make block and m ≥ n other operations (except