
Data Structure

This illustrates a data structure, a means of storing data within a program.

You may see other such structures in the Data Structures category.
A   set  is a collection of elements, without duplicates and without order.



Task

Show each of these set operations:

 Set creation
 Test m ∈ S -- "m is an element in set S"
 A ∪ B -- union; a set of all elements either in set A or in set B.
 A ∩ B -- intersection; a set of all elements in both set A and set B.
 A ∖ B -- difference; a set of all elements in set A, except those in set B.
 A ⊆ B -- subset; true if every element in set A is also in set B.
 A = B -- equality; true if every element of set A is in set B and vice versa.


As an option, show some other set operations.

(If A ⊆ B, but A ≠ B, then A is called a true or proper subset of B, written A ⊂ B or A ⊊ B.)

As another option, show how to modify a mutable set.



One might implement a set using an associative array (with set elements as array keys and some dummy value as the values).

One might also implement a set with a binary search tree, or with a hash table, or with an ordered array of binary bits (operated on with bit-wise binary operators).

The basic test, m ∈ S, is O(n) with a sequential list of elements, O(log n) with a balanced binary search tree, or (O(1) average-case, O(n) worst case) with a hash table.



See also

 Array
 Associative array: Creation, Iteration
 Collections
 Compound data type
 Doubly-linked list: Definition, Element definition, Element insertion, List Traversal, Element Removal
 Linked list
 Queue: Definition, Usage
 Set
 Singly-linked list: Element definition, Element insertion, List Traversal, Element Removal
 Stack


 
[System.Collections.Generic.HashSet[object]]$set1 = 1..4
[System.Collections.Generic.HashSet[object]]$set2 = 3..6
 
#            Operation           +     Definition      +          Result
#--------------------------------+---------------------+-------------------------
$set1.UnionWith($set2)           # Union                 $set1 = 1, 2, 3, 4, 5, 6
$set1.IntersectWith($set2)       # Intersection          $set1 = 3, 4
$set1.ExceptWith($set2)          # Difference            $set1 = 1, 2
$set1.SymmetricExceptWith($set2) # Symmetric difference  $set1 = 1, 2, 6, 5
$set1.IsSupersetOf($set2)        # Test superset         False
$set1.IsSubsetOf($set2)          # Test subset           False
$set1.Equals($set2)              # Test equality         False
$set1.IsProperSupersetOf($set2)  # Test proper superset  False
$set1.IsProperSubsetOf($set2)    # Test proper subset    False
 
5 -in $set1                      # Test membership       False
7 -notin $set1                   # Test non-membership   True
 