scis.regis.edu ● CS-362: Data Structures Week 8 Dr. Jesús Borrego 1

Topics Stacks Queues Final Exam Pointers = Punteros 2

Key Terms Stack – Pilas ▫Push – Insertar ▫Pop - Quitar Queue – Colas ▫Enque – Insertar ▫Dequeue - Eliminar 3

Stacks 4

Stack with Arrays Element 1 can go in first array position, the second in the second position, etc. The top of the stack is the index of the last element added to the stack Stack elements are stored in an array Stack element is accessed only through top To keep track of the top position, use a variable called Top 5

Stack using an Array 6

Stacks If Top = 0, the stack is empty If Top = MAX, stack is full Store the newItem in the array component indicated by Top Increment Top Must avoid an overflow (or underflow) 7

Queue Queue: list of homogeneous elements Elements are: ▫Added at one end (the back or rear) ▫Deleted from the other end (the front) First In First Out (FIFO) data structure ▫Middle elements are inaccessible Example: ▫Waiting line in a bank 8

Queue Operations ▫ initializeQueue ▫ isEmptyQueue ▫ isFullQueue ▫ front ▫ back ▫ addQueue ▫ deleteQueue 9

Queue implementation You need at least four variables: ▫An array to store the queue elements ▫ queueFront and queueRear  To keep track of first and last elements ▫ maxQueueSize  To specify the maximum size of the queue 10

Adding elements 11 To add an element to the queue: ▫Advance queueRear to next array position ▫Add element to position pointed by queueRear Example: array size is 100; originally empty

Deleting Elements 12 To delete an element from the queue: ▫Retrieve element pointed to by queueFront ▫Advance queueFront to next queue element

Implementation of Queues as Arrays (cont'd.) Will this queue design work? ▫Suppose A stands for adding an element to the queue ▫And D stands for deleting an element from the queue ▫Consider the following sequence of operations:  AAADADADADADADADA...

Implementation of Queues as Arrays (cont'd.) The sequence AAADADADADADADADA... would eventually set queueRear to point to the last array position ▫Giving the impression that the queue is full

Implementation of Queues as Arrays (cont'd.) Solution 1: ▫When the queue overflows to the rear (i.e., queueRear points to the last array position):  Check value of queueFront  If value of queueFront indicates that there is room in the front of the array, slide all of the queue elements toward the first array position Problem: too slow for large queues Solution 2: assume that the array is circular

Implementation of Queues as Arrays (cont'd.) To advance the index in a (logically) circular array:

Implementation of Queues as Arrays (cont'd.) 17

Implementation of Queues as Arrays (cont'd.) Case 1:

Implementation of Queues as Arrays (cont'd.) Case 2:

Implementation of Queues as Arrays (cont'd.) Problem: ▫Figures 19-32b and 19-33b have identical values for queueFront and queueRear ▫However, the former represents an empty queue, whereas the latter shows a full queue Solution?

Implementation of Queues as Arrays (cont'd.) Solution 1: keep a count ▫Incremented when a new element is added to the queue ▫Decremented when an element is removed ▫Initially, set to 0 ▫Very useful if user (of queue) frequently needs to know the number of elements in the queue We will implement this solution

Implementation of Queues as Arrays (cont'd.) Solution 2: let queueFront indicate index of the array position preceding the first element ▫ queueRear still indicates index of last one ▫Queue empty if:  queueFront == queueRear ▫Slot indicated by queueFront is reserved  Queue can hold 99 (not 100) elements ▫Queue full if the next available space is the reserved slot indicated by queueFront

Implementation of Queues as Arrays (cont'd.) 23

Summary Stacks and Queues are important data structures Can be implemented as arrays or linked lists We will see in OOP that we can create Abstract Data Types to protect the integrity of the data 24

Final Exam 8 questions from material covered since the mid term Answer all 8 questions; equal weight Submit to WorldClass week 8 Due by Monday midnight (12/16/13) Must have all late submissions by Sunday midnight to get credit 25