
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


using System.Console;
using Nemerle.Collections;
 
module RCSet
{
    HasSubset[T](this super : Set[T], sub : Set[T]) : bool
    {
        super.ForAll(x => sub.Contains(x))
    }
 
    Main() : void
    {
        def names1 = Set(["Bob", "Billy", "Tom", "Dick", "Harry"]);
        def names2 = Set(["Bob", "Mary", "Alice", "Louisa"]);
        //def names3 = Set(["Bob", "Bob"]);        // unfortunately, duplicated elements are not well handled by the stock
                                                   // implementation, this statement would throw an ArgumentException
        def elem = names1.Contains("Bob");         // element test
        def names1u2 = names1.Sum(names2);         // union
        def names1d2 = names1.Subtract(names2);    // difference
        def names1i2 = names1.Intersect(names2);   // intersection
        def same = names1.Equals(names2);          // equality
        def sub12 = names1.HasSubset(names2);      // subset
 
        WriteLine($"$names1u2\n$names1d2\n$names1i2");
        WriteLine($"$same\t$sub12");
    }
}