
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(){
  //Set Creation
  Set A = new Set.from([1,2,3]);
  Set B = new Set.from([1,2,3,4,5]);
  Set C = new Set.from([1,2,4,5]);
 
  print('Set A = $A');
  print('Set B = $B');
  print('Set C = $C');
  print('');
  //Test if element is in set
  int m = 3;
  print('m = 5');
  print('m in A = ${A.contains(m)}');
  print('m in B = ${B.contains(m)}');
  print('m in C = ${C.contains(m)}');
  print('');
  //Union of two sets
  Set AC = A.union(C);
  print('Set AC = Union of A and C = $AC');
  print('');
  //Intersection of two sets
  Set A_C = A.intersection(C);
  print('Set A_C = Intersection of A and C = $A_C');
  print('');
  //Difference of two sets
  Set A_diff_C = A.difference(C);
  print('Set A_diff_C = Difference between A and C = $A_diff_C');
  print('');
  //Test if set is subset of another set
  print('A is a subset of B = ${B.containsAll(A)}');
  print('C is a subset of B = ${B.containsAll(C)}');
  print('A is a subset of C = ${C.containsAll(A)}');
  print('');
  //Test if two sets are equal
  print('A is equal to B  = ${B.containsAll(A) && A.containsAll(B)}');
  print('B is equal to AC = ${B.containsAll(AC) && AC.containsAll(B)}');
}