The most common linear data structure is the list. By now you are already pretty familiar with the idea of a list and at least one way of representing a list in the computer. Now we are going to look at a particular kind of list: an ordered list. Ordered lists are very similar to the alphabetical list of employee names for the XYZ company. These lists keep items in a specific order such as alphabetical or numerical order. Whenever an item is added to the list, it is placed in the correct sorted position so that the entire list is always sorted.

Before we consider how to implement such a list, we need to consider the abstract view of an ordered list. Since the idea of an abstract view of a list may be a little confusing, let's think about a more familiar example. Consider the abstract view of a television. Regardless of who makes a television, we all expect certain basic things like the ability to change channels and adjust the volume. As long as these operations are available and the TV displays the shows we want to view, we really don't care about who made the TV or how they chose to construct it. The circuitry inside the TV set may be very different from one brand to the next, but the functionality remains the same. Similarly, when we consider the abstract view of an ordered list, we don't worry about the details of implementation. We are only concerned with what the list does, not how it does it.

Suppose we want a list that can hold the following group of sorted numbers: [2 4 6 7]. What are some things that we might want to do with our list? Well, since our list is in order, we will need some way of adding numbers to the list in the proper place, and we will need some way of deleting numbers we don't want from the list. To represent these operations, we will use the following notation: