Class 26: Stacks and Their Implementation

Held: Tuesday, March 8, 2005

Summary: Today we investigate the first important linear structure: The Stack. A stack collects objects and returns them in the reverse order that they were added.

Overview:

• Collections.
• Linear structures.
• The Stack ADT.
• Implementing stacks.

Collections

• One of the key topics of ADT design is the of collections: ADTs that group values together.
• Note that are a variety of ways we think about collecting values:
  • We might organize them into a set, with a key operation of membership.
  • We might organize them in the list, with a key operation of iteration (visiting each element).
  • We might organize them in an array, with a key operation of access by position.
  • You can think of other ways to organize values.
• Much of our focus these next few weeks will be on collections and how to implement them.

About Linear Structures

• Linear Structures are one of the simplest forms of collections.
• Linear structures typically provide two basic operations:
  • put, add an element to the collection
  • get, get an element from the collection, removing it from the collection
• Since get requires a non-empty collection, most collections provide an isEmpty predicate.
• You can think of linear structures as a form of "job jar" or "to do list".
• The choice of what get returns is up to the policy of the particular kind of linear structure.
  • The Stack ADT uses a last in, first out (LIFO) policy.
  • The Queue ADT uses a first in, first out (FIFO) policy.
  • Priority queues use a best first policy. (They therefore need a way to determine what is best.)
• There are a few related operations that you may find helpful:
  • peek returns the object to be returned by get, but without deleting it.
  • size returns the number of elements in the structure.
• It might also be useful to have an isFull operation.
  • Why might you argue for or against isFull?
• The individual operations traditionally have different names in the different types of linear structures.
  • Why? The structures were invented first. Then someone realized they had a commonality. By that point, the names were ingrained.

Stacks

• LIFO policy.
• LIFO mimics many common operations,
  • What happens with procedure calls in most programming languages.
  • The plates in a cafeteria.
• ...
• Naming is somewhat different (since stacks were designed before the general linear structures).
  • put is typically called push.
  • get is typically called pop.
  • peek is typically called top.

Implementing Stacks

• How do we implement stacks?
• One technique is to use partially-filled arrays.
• When we put something on the stack, we add it to the end of the filled section.
• When we pop something from the stack, we remove the last thing from the filled section.