
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


package require struct::set
 
# Many ways to build sets
set s1 [list 1 2 3 4]
set s2 {3 4 5 6}
struct::set add s3 {2 3 4 3 2};   # $s3 will be proper set...
set item 5
 
puts "union: [struct::set union $s1 $s2]"
puts "intersection: [struct::set intersect $s1 $s2]"
puts "difference: [struct::set difference $s1 $s2]"
puts "membership predicate: [struct::set contains $s1 $item]"
puts "subset predicate: [struct::set subsetof $s1 $s2]";   # NB: not strict subset test!
puts "equality predicate: [struct::set equal $s1 $s2]"
 
# Adding an element to a set (note that we pass in the name of the variable holding the set):
struct::set include s3 $item
# Removing an element from a set:
struct::set exclude s3 $item
# Getting the cardinality:
puts "cardinality: [struct::set size $s3]