GAP (datastructures) - Chapter 5: Union-Find

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5 Union-Find
5.1 Introduction
5.2 API
5.2-1 IsPartitionDS
5.2-2 PartitionDS
5.2-3 PartitionDS
5.2-4 Representative
5.2-5 Unite
5.2-6 RootsIteratorOfPartitionDS
5.2-7 NumberParts
5.2-8 SizeUnderlyingSetDS
5.2-9 PartsOfPartitionDS

### 5 Union-Find

#### 5.1 Introduction

datastructures defines the interface for mutable data structures representing partitions of `[1..n]`, commonly known as union-find data structures. Key operations are `Unite` (5.2-5) which fuses two parts of a partition and `Representative` (5.2-4) which returns a canonical representative of the part containing a given point.

#### 5.2 API

##### 5.2-1 IsPartitionDS

`‣ IsPartitionDS`( arg ) | ( filter )

Returns: `true` or `false`

Category of datastructures representing partitions. Equality is identity and family is ignored.

##### 5.2-2 PartitionDS

`‣ PartitionDS`( filter, n ) | ( constructor )

Family containing all partition data structures Returns the trivial partition of the set `[1..n]`.

##### 5.2-3 PartitionDS

`‣ PartitionDS`( filter, partition ) | ( constructor )

Returns the union find structure of partition.

##### 5.2-4 Representative

`‣ Representative`( unionfind, k ) | ( operation )

Returns: a positive integer

Returns a canonical representative of the part of the partition that k is contained in.

##### 5.2-5 Unite

`‣ Unite`( unionfind, k1, k2 ) | ( operation )

Fuses the parts of the partition unionfind containing k1 and k2.

##### 5.2-6 RootsIteratorOfPartitionDS

`‣ RootsIteratorOfPartitionDS`( unionfind ) | ( operation )

Returns: an iterator

Returns an iterator that runs through canonical representatives of parts of the partition unionfind.

##### 5.2-7 NumberParts

`‣ NumberParts`( unionfind ) | ( attribute )

Returns: a positive integer

Returns the number of parts of the partition unionfind.

##### 5.2-8 SizeUnderlyingSetDS

`‣ SizeUnderlyingSetDS`( unionfind ) | ( attribute )

Returns: a positive integer

Returns the size of the underlying set of the partition unionfind.

##### 5.2-9 PartsOfPartitionDS

`‣ PartsOfPartitionDS`( unionfind ) | ( attribute )

Returns: a list of lists

Returns the partition unionfind as a list of lists.

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