
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


use Test;
 
my $a = set <a b c>;
my $b = set <b c d>;
my $c = set <a b c d e>;
 
ok 'c' ∈ $a, "c is an element in set A";
nok 'd' ∈ $a, "d is not an element in set A";
 
is-deeply $a ∪ $b, set(<a b c d>), "union; a set of all elements either in set A or in set B";
is-deeply $a ∩ $b, set(<b c>), "intersection; a set of all elements in both set A and set B";
is $a (-) $b, set(<a>), "difference; a set of all elements in set A, except those in set B";
 
ok $a ⊆ $c, "subset; true if every element in set A is also in set B";
nok $c ⊆ $a, "subset; false if every element in set A is not also in set B";
ok $a ⊂ $c, "strict subset; true if every element in set A is also in set B";
nok $a ⊂ $a, "strict subset; false for equal sets";
ok $a === set(<a b c>), "equality; true if every element of set A is in set B and vice-versa";
nok $a === $b, "equality; false for differing sets";