A set of integers, all in the range MIN through MAX, can be represented by a boolean array b of size MAX-MIN+1. Element b[i-MIN] is true if i belongs to the set and false if not.
Define a class set that represents sets of integers in this way. MAX and MIN will be defined as constants and apply to all objects of class set.
Provide class set with constructors set() (no arguments), which creates an empty set, and set ( int n ) which creates a one-element set containing only the integer n.
Equip the class with operators +, - (unary and binary), *, +=, -=, *=, ==, !=, <, >, <=, >=, and <<. Operators +, binary -, *, ==, !=, <, >, <=, >=, have the same meaning they have in Pascal, unary - represents the complement of a set (contains those elements im the specified range that do not belong to the given set), operator << prints a set: the set containing 3, 5 and 7 is printed as {3, 5, 7}.
Also provide the member functions insert(n), remove(n), and member(n) for inserting an integer, removing an integer, and testing whether an integer belongs to the set.
Prepare a header file, a source file, and a test file with a main() function using the set class.
Example:
const MIN = 10; const MAX = 30; The universal set is { 10 .. 30 } . union: { 10, 15, 17 } + { 12, 15 } = { 10, 12, 15, 17 } difference: { 10, 15, 17 } - { 12, 15 } = { 10, 17 } intersection: { 10, 15, 17 } * { 12, 15 } = { 15 } complement: - { 10 .. 20 } = { 21 .. 30 }
All the following relations will return true: { 10, 15 } == { 15, 10 } { 10, 15 } < { 10, 15, 20 } { 10, 15 } <= { 10, 15, 20} { 10, 15 } <= { 10, 15 } { 10, 15, 20 } > { 10, 15 } { 10, 15 , 20 } >= { 10, 15 } { 10, 15 } >= { 10, 15 }
All the following relations will return false: { 10, 15 } < { 10, 15 } { 11, 12 } < { 13, 14, 15 } { 10, 15 } > { 10, 15 } { 13, 14, 15 } > { 11, 12 }