# Sets/ADT

### From charlesreid1

Abstract data type for the Sets data type.

## Contents

## Public methods

The Set type must provide the following basic methods for manipulating the Set:

- S.add(e) - add element e to set
- S.discard(e) / S.discard(e) - (quietly) remove element e from set
- e in S or S.contains(e) - returns true if container contains e
- len(s) or S.size() - return the number of elements in the set
- iter(S) or S.iterator() - returns an iterator over the set

These five methods will suffice to implement a large variety of other functions.

## Removal methods

The following removal methods can be defined:

- S.remove(e) - removes an element e from the set, raise exception if empty
- S.pop() - removes an arbitrary element from the set, raise exception if empty
- S.clear() - removes all elements from the set

## Utility methods

Need to define some regular ol utility methods:

- size
- isEmpty

## Set operations

### Set Operations Involving Two Sets

Some set operations involving two sets:

- equals - return true if two sets S and T have identical elements
- less than or equal to - return true if S is subset of T
- less than - return true if S is proper subset of T
- greater than or equal to - return true if S is superset of T
- greater than - return true if S is proper superset of T
- isDisjoint - returns true if S and T have no common elements

### Set Operations Involving Constructing New Sets

Operations involving constructing new sets from existing sets:

- Union of S and T - returns all elements in either S or T or both
- intersection of S and T - returns all elements in both S and T
- Symmetric difference - returns all elements that are in S but not T, or T but not S
- Remove all - remove all items from this set that are in the passed set
- Retain all - retain only items from this set that are in the passed set

## Flags

Maps and DictionariesSeries on Data Structures
Maps Map implementations: Maps/AbstractMap Dictionary implementations: Dictionaries/LinkedDict
Hash Maps/OOP Hash Maps/Dynamic Resizing Hash functions: Hash Functions Hash map implementations: Hash Maps/AbstractHashMap
Skip Lists Java implementations: SkipList
Sets
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