Sets - Sets(C++)

Sets - Sets(C++)

Sets are the most fundamental structures in all mathematics. Naturally, there are many computer applications for sets. Recognizing this, language designers have provided sets as built-in types in languages like Pascal and SETL. Lacking language support, the C programmer who needs sets is forced to represent them using any of a variety of available data structures, including lists, arrays, search trees, and (for integer sets only) bit vectors. Unfortunately, the effort needed to implement sets detracts from the effort devoted to the application per se. Furthermore, the resulting code is often hard to read and maintain. For example, unless the original programmer has left very clear comments (or assertions) in the code, it may not be obvious to a maintainer that a particular array is being used to represent a set; an innocent change may destroy the invariant property that no two elements of the array may have the same value, causing catastrophic program failure.

This memo describes a new library component that allows C++ programmers to declare and manipulate sets just as if they were types built into the language. The component consists of three unordered collection classes:

class Set<> -- Sets of objects of type
class Bag<> -- Bags of objects of type
class Set_of_p<> -- Sets of pointers to objects of type

As you can see, all three classes are parameterized by the element type, which we denote here (as in Set(C++) by the Greek letter tau ( GREEK SMALL LETTER TAU

). Sets and Bags contain objects of type GREEK SMALL LETTER TAU

. The difference between Sets and Bags is that, while a Set cannot contain more than one object with the same value, a Bag can contain multiple instances. Set_of_p's (which we usually call ``pointer sets''), contain pointers to objects of type GREEK SMALL LETTER TAU

. Pointer sets are typically used to keep track of objects that belong to the client; in fact, such objects may be pointed to by several pointer sets simultaneously. The three classes have nearly identical interfaces.

The three classes have all the expected algebraic (for example, intersection, union) and relational (for example, subset, superset) operations. We will focus on issues that are much more likely than these to trip up new users, including:

the instantiation procedure, including how to satisfy the requirements for type parameters
how to structure your source
how to provide a hash function (needed for Sets and Bags)
information about the implementation that will help you make informed time-space tradeoffs and optimizations such as modifying elements in place.

We do this by presenting three short but complete examples.