
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


 
-- set of numbers is a table
-- create one set with 3 elements
 
CREATE TABLE myset1 (element NUMBER);
 
INSERT INTO myset1 VALUES (1);
INSERT INTO myset1 VALUES (2);
INSERT INTO myset1 VALUES (3);
 
commit;
 
-- check if 1 is an element
 
SELECT 'TRUE' BOOL FROM dual
WHERE 1 IN 
(SELECT element FROM myset1);
 
-- create second set with 3 elements
 
CREATE TABLE myset2 (element NUMBER);
 
INSERT INTO myset2 VALUES (1);
INSERT INTO myset2 VALUES (5);
INSERT INTO myset2 VALUES (6);
 
commit;
 
-- union sets
 
SELECT element FROM myset1
UNION
SELECT element FROM myset2;
 
-- intersection
 
SELECT element FROM myset1
INTERSECT
SELECT element FROM myset2;
 
-- difference
 
SELECT element FROM myset1
minus
SELECT element FROM myset2;
 
-- subset
 
-- change myset2 to only have 1 as element
 
DELETE FROM myset2 WHERE NOT element = 1;
 
commit;
 
-- check if myset2 subset of myset1
 
SELECT 'TRUE' BOOL FROM dual
WHERE 0 =  (SELECT COUNT(*) FROM 
(SELECT element FROM myset2
minus
SELECT element FROM myset1));
 
-- equality
 
-- change myset1 to only have 1 as element
 
DELETE FROM myset1 WHERE NOT element = 1;
 
commit;
 
 -- check if myset2 subset of myset1 and
 -- check if myset1 subset of myset2 and
 
SELECT 'TRUE' BOOL FROM dual
WHERE 
0 =  (SELECT COUNT(*) FROM 
(SELECT element FROM myset2
minus
SELECT element FROM myset1)) AND
0 =
(SELECT COUNT(*) FROM 
(SELECT element FROM myset1
minus
SELECT element FROM myset2));
 