
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


      DIM list$(6)
      list$() = "apple", "banana", "cherry", "date", "elderberry", "fig", "grape"
 
      setA% = %1010101
      PRINT "Set A: " FNlistset(list$(), setA%)
      setB% = %0111110
      PRINT "Set B: " FNlistset(list$(), setB%)
      elementM% = %0000010
      PRINT "Element M: " FNlistset(list$(), elementM%) '
 
      IF elementM% AND setA% THEN
        PRINT "M is an element of set A"
      ELSE
        PRINT "M is not an element of set A"
      ENDIF
      IF elementM% AND setB% THEN
        PRINT "M is an element of set B"
      ELSE
        PRINT "M is not an element of set B"
      ENDIF
 
      PRINT '"The union of A and B is " FNlistset(list$(), setA% OR setB%)
      PRINT "The intersection of A and B is " FNlistset(list$(), setA% AND setB%)
      PRINT "The difference of A and B is " FNlistset(list$(), setA% AND NOT setB%)
 
      IF (setA% AND setB%) = setA% THEN
        PRINT '"Set A is a subset of set B"
      ELSE
        PRINT '"Set A is not a subset of set B"
      ENDIF
      IF setA% = setB% THEN
        PRINT "Set A is equal to set B"
      ELSE
        PRINT "Set A is not equal to set B"
      ENDIF
      END
 
      DEF FNlistset(list$(), set%)
      LOCAL i%, o$
      FOR i% = 0 TO 31
        IF set% AND 1 << i% o$ += list$(i%) + ", "
      NEXT
      = LEFT$(LEFT$(o$))