
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


void main() {
    import std.stdio, std.algorithm, std.range;
 
    // Not true sets, items can be repeated, but must be sorted.
    auto s1 = [1, 2, 3, 4, 5, 6].assumeSorted;
    auto s2 = [2, 5, 6, 3, 4, 8].sort(); // [2,3,4,5,6,8].
    auto s3 = [1, 2, 5].assumeSorted;
 
    assert(s1.canFind(4)); // Linear search.
    assert(s1.contains(4)); // Binary search.
    assert(s1.setUnion(s2).equal([1,2,2,3,3,4,4,5,5,6,6,8]));
    assert(s1.setIntersection(s2).equal([2, 3, 4, 5, 6]));
    assert(s1.setDifference(s2).equal([1]));
    assert(s1.setSymmetricDifference(s2).equal([1, 8]));
    assert(s3.setDifference(s1).empty); // It's a subset.
    assert(!s1.equal(s2));
 
    auto s4 = [[1, 4, 7, 8], [1, 7], [1, 7, 8], [4], [7]];
    const s5 = [1, 1, 1, 4, 4, 7, 7, 7, 7, 8, 8];
    assert(s4.nWayUnion.equal(s5));
}