Basic Structures:Stacks and Queues

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Stacks and Queues

The stack and the queue are data types that support insertion and deletion operations with well-defined semantics. Stack deletion deletes the element in the stack that was inserted the last, while a queue deletion deletes the element in the queue that was inserted the earliest. For this reason, the stack is often referred to as a LIFO (Last In First Out) data type and the queue as an FIFO (First In First out) data type. A deque (double ended queue) combines the stack and the queue by supporting both types of deletions.

Stacks and queues find a lot of applications in Computer Science. For example, a system stack is used to manage function calls in a program. When a function f is called, the system creates an activation record and places it on top of the system stack. If function f calls function g, the local variables of f are added to its activation record and an activation record is created for g. When g terminates, its activation record is removed and f continues executing with the local variables that were stored in its activation record. A queue is used to schedule jobs at a resource when a first-in first-out policy is to be implemented. Examples could include a queue of print-jobs that are waiting to be printed or a queue of packets waiting to be transmitted over a wire. Stacks and queues are also used routinely to implement higher-level algorithms. For example, a queue is used to implement a breadth- first traversal of a graph. A stack may be used by a compiler to process an expression such as (a + b) × (c + d).

Stack Implementation

Stacks and queues can be implemented using either arrays or linked lists. Although the burden of a correct stack or queue implementation appears to rest on deletion rather than insertion, it is convenient in actual implementations of these data types to place restrictions on the insertion operation as well. For example, in an array implementation of a stack, elements are inserted in a left-to-right order. A stack deletion simply deletes the rightmost element.

A simple array implementation of a stack class is shown below:

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It is easy to see that both stack operations take O(1) time. The stack data type can also be implemented using linked lists by requiring all insertions and deletions to be made at the front of the linked list.

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Queue Implementation

An array implementation of a queue is a bit trickier than that of a stack. Insertions can be made in a left-to-right fashion as with a stack. However, deletions must now be made from the left. Consider a simple example of an array of size 5 into which the integers 10, 20, 30, 40, and 50 are inserted as shown in Figure 2.12(a). Suppose three elements are subsequently deleted (Figure 2.12(b)).

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What if we are now required to insert the integer 60. On one hand, it appears that we are out of room as there is no more place to the right of 50. On the other hand, there are three locations available to the left of 40. This suggests that we use a circular array implementation of a queue, which is described below.

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Figure 2.13 illustrates the operation of this code on an example. The first figure shows an empty queue with first = rear = 0. The second figure shows the queue after the integer 10 is inserted. The third figure shows the queue when 20, 30, 40, 50, and 60 have been inserted. The fourth figure shows the queue after 70 is inserted. Notice that, although one slot remains empty, the queue is now full because Queue::Insert will not permit another element to be inserted. If it did permit an insertion at this stage, rear and front would be the same. This is the condition that Queue:Delete checks to determine whether the queue is empty! This would make it impossible to distinguish between the queue being full and being empty. The fifth figure shows the queue after two integers (10 and 20) are deleted. The last figure shows a full queue after the insertion of integers 80 and 90.

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It is easy to see that both queue operations take O(1) time. The queue data type can also be implemented using linked lists by requiring all insertions and deletions to be made at the front of the linked list.

Acknowledgments

The author would like to thank Kun Gao, Dean Simmons and Mr. U. B. Rao for proofreading this chapter. This work was supported, in part, by the National Science Foundation under grant CCR-9988338.

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