
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


#include <stdio.h>
 
typedef unsigned int set_t; /* probably 32 bits; change according to need */
 
void show_set(set_t x, const char *name)
{
	int i;
	printf("%s is:", name);
	for (i = 0; (1U << i) <= x; i++)
		if (x & (1U << i))
			printf(" %d", i);
	putchar('\n');
}
 
int main(void)
{
	int i;
	set_t a, b, c;
 
	a = 0; /* empty set */
	for (i = 0; i < 10; i += 3) /* add 0 3 6 9 to set a */
		a |= (1U << i);
	show_set(a, "a");
 
	for (i = 0; i < 5; i++)
		printf("\t%d%s in set a\n", i, (a & (1U << i)) ? "":" not");
 
	b = a;
	b |= (1U << 5); b |= (1U << 10); /* b is a plus 5, 10 */
	b &= ~(1U << 0);	/* sans 0 */
	show_set(b, "b");
 
	show_set(a | b, "union(a, b)");
	show_set(c = a & b, "c = common(a, b)");
	show_set(a & ~b, "a - b"); /* diff, not arithmetic minus */
	show_set(b & ~a, "b - a");
	printf("b is%s a subset of a\n", !(b & ~a) ? "" : " not");
	printf("c is%s a subset of a\n", !(c & ~a) ? "" : " not");
 
	printf("union(a, b) - common(a, b) %s union(a - b, b - a)\n",
		((a | b) & ~(a & b)) == ((a & ~b) | (b & ~a))
			? "equals" : "does not equal");
 
	return 0;
}