
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


class set
        declare internal_list
 
        def set()
                internal_list = list()
        end
        def set(list)
                internal_list = list
        end
 
        def append(value)
                if not value in internal_list
                        internal_list.append(value)
                end
                return this
        end
        def contains(value)
                return value in internal_list
        end
        def difference(other)
                diff = list()
                for value in this.internal_list
                        diff.append(value)
                end
 
                for i in range(len(diff) - 1, 0)
                        if diff[i] in other.internal_list
                                diff.remove(i)
                        end
                end
 
                return new(set, diff)
        end
        def operator=(other)
                for value in other.internal_list
                        if not value in this.internal_list
                                return false
                        end
                end
                return true
        end
        def intersection(other)
                intersect = list()
                for value in this.internal_list
                        if other.contains(value)
                                intersect.append(value)
                        end
                end
                return new(set, intersect)
        end
        def subset(other)
                for value in this.internal_list
                        if not value in other.internal_list
                                return false
                        end
                end
                return true
        end
        def union(other)
                u = list()
 
                for value in this.internal_list
                        u.append(value)
                end
 
                for value in other.internal_list
                        if not value in u
                                u.append(value)
                        end
                end
 
                return new(set, u)
        end
 
        def toString()
                return str(this.internal_list)
        end
end