Sets

Another linear data structure is known as a set. A set is very similar to a list, but with two major differences:

1. A set cannot contain duplicate elements. Each element must be unique in the set.
2. A set does not necessarily keep track of the ordering of the elements within the set.

In fact, the term set comes from mathematics. We’ve probably seen sets already in a math class.

Beyond the typical operations to add and remove elements from a set, there are several operations unique to sets:

• union - find the elements that are contained in one or both of the sets given;
• intersection - find the elements only contained in both sets given;
• set difference - remove all elements from a set that are also contained in another set; and
• subset - test if all elements in one set are also contained in another set.

Again, many of these operations may be familiar from their use in various math classes.

Set Operations and Boolean Logic

In addition, we can easily think of set operations as boolean logic operators. For example, the set operation union is very similar to the boolean operator or, as seen in the diagram below.

¹

As long as an item is contained in one set or the other, it is included in the union of the sets.

Similarly, the same comparison works for the set operation intersection and the boolean and operator.

²

Once again, if an item is contained in the first set and the second set, it is contained in the intersection of those sets.

When to Use a Set

A set is a great choice when we know that our program should prevent duplicate items from being added to a data structure. Likewise, if we know we’ll be using some of the specific operations that are unique to sets, then a set is an excellent choice.

Of course, if we aren’t sure that our data structure will only store unique items, we won’t be able to use a set.