C++ sets class 1.0
You can use the sets class to perform set operations in your programs.
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You can use the sets class to perform set operations in your programs. It represents set elements as bits in a private array of unsigned long integers. The array size is a defined constant which can be changed to suit your application.
The sets class supports the following set operations by means of C++ operator overloading:
union
The union of two sets A, B is the set of all elements which belong to either A or B. In the sets class, the symbol + is the binary union operator:
A + B = {x: x is in A -or- x is in B }
intersection
The intersection of two sets A, B is the set of all elements which belong to both A and B. The symbol * is the binary intersection operator:
A * B = {x: x is in A -and- x is in B }
example
Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Then
A + B = {1, 2, 3, 4, 5, 6}
A * B = {3, 4}
complement
In set theory, sets are subsets of a fixed universal set U. In the sets class, U is the set of elements numbered from 1 to MAX_WORDS * WORD_SIZE. In the class declaration file below, the following definitions are made:
#define MAX_WORDS 2
#define WORD_SIZE ( 8 * sizeof( unsigned long ) )
These parameters make the range of U, 1 to 64 in sets. To increase or decrease the size of U, change the defined value of MAX_WORDS.
The complement of set A is the set of elements belonging to U but not belonging to A. The symbol ~ is the unary complement operator:
~A = {x: x is in U, x is not in A }
example
Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Then
~A = {5, 6, 7, . . .}
~B = {1, 2, 7, 8, 9, . . .}
difference
The difference of two sets A, B is the set of all elements which belong to A less those in B. The symbol - is the binary difference operator:
A - B = {x: x is in A, x is not in B}
example
Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Then
A - B = {1, 2}
It can be shown that A - B = A * ~B.
symmetric difference
The symmetric difference of two sets A, B is the set of all elements which belong to A or to B, but not both.
Requirements
tags
the set all elements the sets which belong the symbol elements which sets class two sets max words example let the binary difference the symmetric difference
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