
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


import "/set" for Set
 
var fruits = Set.new(["apple", "pear", "orange", "banana"])
System.print("fruits  : %(fruits)")
var fruits2 = Set.new(["melon", "orange", "lemon", "gooseberry"])
System.print("fruits2 : %(fruits2)\n")
 
System.print("fruits  contains 'banana'     : %(fruits.contains("banana"))")
System.print("fruits2 contains 'elderberry' : %(fruits2.contains("elderberry"))\n")
 
System.print("Union        : %(fruits.union(fruits2))")
System.print("Intersection : %(fruits.intersect(fruits2))")
System.print("Difference   : %(fruits.except(fruits2))\n")
 
System.print("fruits2 is a subset of fruits : %(fruits2.subsetOf(fruits))\n")
var fruits3 = fruits.copy()
System.print("fruits3 : %(fruits3)\n")
System.print("fruits2 and fruits are equal  : %(fruits2 == fruits)")
System.print("fruits3 and fruits are equal  : %(fruits3 == fruits)\n")
 
var fruits4 = Set.new(["apple", "orange"])
System.print("fruits4 : %(fruits4)\n")
System.print("fruits3 is a proper subset of fruits : %(fruits3.properSubsetOf(fruits))")
System.print("fruits4 is a proper subset of fruits : %(fruits4.properSubsetOf(fruits))\n")
 
var fruits5 = Set.new(["cherry", "blueberry", "raspberry"])
System.print("fruits5 : %(fruits5)\n")
fruits5.add("guava")
System.print("fruits5 + 'guava'  : %(fruits5)")
fruits5.remove("cherry")
System.print("fruits5 - 'cherry' : %(fruits5)")