
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


var s1 : Set<Int> = [1, 2, 3, 4]
let s2 : Set<Int> = [3, 4, 5, 6]
println(s1.union(s2)) // union; prints "[5, 6, 2, 3, 1, 4]"
println(s1.intersect(s2)) // intersection; prints "[3, 4]"
println(s1.subtract(s2)) // difference; prints "[2, 1]"
println(s1.isSubsetOf(s1)) // subset; prints "true"
println(Set<Int>([3, 1]).isSubsetOf(s1)) // subset; prints "true"
println(s1.isStrictSubsetOf(s1)) // proper subset; prints "false"
println(Set<Int>([3, 1]).isStrictSubsetOf(s1)) // proper subset; prints "true"
println(Set<Int>([3, 2, 4, 1]) == s1) // equality; prints "true"
println(s1 == s2) // equality; prints "false"
println(s1.contains(2)) // membership; prints "true"
println(Set<Int>([1, 2, 3, 4]).isSupersetOf(s1)) // superset; prints "true"
println(Set<Int>([1, 2, 3, 4]).isStrictSupersetOf(s1)) // proper superset; prints "false"
println(Set<Int>([1, 2, 3, 4, 5]).isStrictSupersetOf(s1)) // proper superset; prints "true"
println(s1.exclusiveOr(s2)) // symmetric difference; prints "[5, 6, 2, 1]"
println(s1.count) // cardinality; prints "4"
s1.insert(99) // mutability
println(s1) // prints "[99, 2, 3, 1, 4]"
s1.remove(99) // mutability
println(s1) // prints "[2, 3, 1, 4]"
s1.unionInPlace(s2) // mutability
println(s1) // prints "[5, 6, 2, 3, 1, 4]"
s1.subtractInPlace(s2) // mutability
println(s1) // prints "[2, 1]"
s1.exclusiveOrInPlace(s2) // mutability
println(s1) // prints "[5, 6, 2, 3, 1, 4]"