
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


// Extend set type
define set->issubsetof(p::set) => .intersection(#p)->size == .size
define set->oncompare(p::set) => .intersection(#p)->size - .size
 
//	Set creation
local(set1) = set('j','k','l','m','n')
local(set2) = set('m','n','o','p','q')
 
//Test m ∈ S -- "m is an element in set S"
#set1 >> 'm' 
 
// A ∪ B -- union; a set of all elements either in set A or in set B.
#set1->union(#set2)
 
//A ∩ B -- intersection; a set of all elements in both set A and set B.
#set1->intersection(#set2)
 
//A ∖ B -- difference; a set of all elements in set A, except those in set B.
#set1->difference(#set2)
 
//A ⊆ B -- subset; true if every element in set A is also in set B.
#set1->issubsetof(#set2)
 
//A = B -- equality; true if every element of set A is in set B and vice-versa.
#set1 == #set2