Program overloads the three operators,
`operator+`, `operator*` and `operator-`,
to provide the union, intersection, and difference operations
for `SetAsArray` instances.
Operators `+`, `*` and `-`
correspond to , and -, respectively.

**Program:** `SetAsArray` Class Union, Intersection and Difference Operator Definitions

The set union operator takes two references to `SetAsArray` instances,
`s` and `t`,
and computes a result of type `SetAsArray`.
The implementation given requires
that the `s` and `t` sets be compatible.
Two sets are deemed to be compatible if they have the same universe.
The result also has the same universe.
Consequently, the Boolean array in all three sets has the same length, *N*.
The set union routine creates a result array of the required size
and then computes the elements of the array as required.
The element of the result is `true`
if either the element of `s`
or the element of `t` is `true`.
Thus, set union is implemented using
the Boolean *or* operator,
`||`.

The set intersection operator is almost identical to set union,
except that the elements of the result are computed using
the Boolean *and* operator.
The set difference operator is also very similar.
In this case, an item is an element of the result
only if it is a member of `s` and not a member of `t`.

Because all three routines are almost identical,
their running times are essentially the same.
I.e., the running time of
the set union, intersection, and difference operations is *O*(*N*),
where .

Copyright © 1997 by Bruno R. Preiss, P.Eng. All rights reserved.