C++ Programming:
Program Design Including
Data Structures, Fifth Edition
Chapter 18: Stacks and Queues
Objectives
In this chapter, you will:
• Learn about stacks
• Examine various stack operations
• Learn how to implement a stack as an array
• Learn how to implement a stack as a linked list
• Discover stack applications
• Learn how to use a stack to remove recursion
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Objectives (cont'd.)
• Learn about queues
• Examine various queue operations
• Learn how to implement a queue as an
array
• Learn how to implement a queue as a
linked list
• Discover queue applications
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Stacks
• Stack: list of homogenous elements
– Addition and deletion occur only at one end,
called the top of the stack
• Example: in a cafeteria, the second tray can be
removed only if first tray has been removed
– Last in first out (LIFO) data structure
• Operations:
– Push: to add an element onto the stack
– Pop: to remove an element from the stack
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Stacks (cont’d.)
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Stacks (cont’d.)
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Stack Operations
• In the abstract class stackADT:
– initializeStack
– isEmptyStack
– isFullStack
– push
– top
– pop
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Implementation of Stacks as
Arrays
• First element 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 stackTop
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Implementation of Stacks as Arrays
(cont'd.)
• Because stack is homogeneous
– You can use an array to implement a stack
• Can dynamically allocate array
– Enables user to specify size of the array
• The class stackType implements the
functions of the abstract class
stackADT
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Implementation of Stacks as Arrays
(cont'd.)
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Implementation of Stacks as Arrays
(cont'd.)
• C++ arrays begin with the index 0
– Must distinguish between:
• The value of stackTop
• The array position indicated by stackTop
• If stackTop is 0, the stack is empty
• If stackTop is nonzero, the stack is not
empty
– The top element is given by stackTop - 1
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Implementation of Stacks as Arrays
(cont'd.)
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Initialize Stack
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Empty Stack
• If stackTop is 0, the stack is empty
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Full Stack
• The stack is full if stackTop is equal to
maxStackSize
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Push
• Store the newItem in the array
component indicated by stackTop
• Increment stackTop
• Must avoid an overflow
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Push (cont'd.)
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Return the Top Element
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Pop
• Simply decrement stackTop by 1
• Must check for underflow condition
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Pop (cont’d.)
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Pop (cont’d.)
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Copy Stack
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Constructor and Destructor
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Constructor and Destructor
(cont'd.)
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Copy Constructor
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Overloading the Assignment
Operator (=)
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Stack Header File
• Place definitions of class and functions
(stack operations) together in a file
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Programming Example: Highest
GPA
• Input: program reads an input file with
each student’s GPA and name
3.5
3.6
2.7
3.9
3.4
3.9
3.4
Bill
John
Lisa
Kathy
Jason
David
Jack
• Output: the highest GPA and all the names
associated with the highest GPA
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Programming Example: Problem
Analysis and Algorithm Design
• Read the first GPA and name of the student
– This is the highest GPA so far
• Read the second GPA and student name
– Compare this GPA with highest GPA so far
• New GPA is greater than highest GPA so far
– Update highest GPA, initialize stack, add to stack
• New GPA is equal to the highest GPA so far
– Add name to stack
• New GPA is smaller than the highest GPA
– Discard
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Programming Example: Problem
Analysis and Algorithm Design (cont’d.)
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Programming Example: Problem
Analysis and Algorithm Design (cont’d.)
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Linked Implementation of
Stacks
• Array only allows fixed number of
elements
• If number of elements to be pushed
exceeds array size
– Program may terminate
• Linked lists can dynamically organize data
• In a linked representation, stackTop is
pointer to top element in stack
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Linked Implementation of
Stacks (cont’d.)
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Default Constructor
• Initializes the stack to an empty state
when a stack object is declared
– Sets stackTop to NULL
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Empty Stack and Full Stack
• In the linked implementation of stacks, the
function isFullStack does not apply
– Logically, the stack is never full
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Initialize Stack
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Push
• The newElement is added at the
beginning of the linked list pointed to by
stackTop
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Push (cont'd.)
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Push (cont'd.)
• We do not need to check whether the
stack is full before we push an element
onto the stack
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Return the Top Element
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Pop
• Node pointed to by stackTop is removed
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Pop (cont'd.)
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Pop (cont'd.)
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Copy Stack
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Copy Stack (cont'd.)
• Notice that this function is similar to the
definition of copyList for linked lists
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Constructors and Destructors
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Overloading the Assignment
Operator (=)
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Stack as Derived from the class
unorderedLinkedList
• Our implementation of push is similar to
insertFirst (discussed for general lists)
– Other functions are similar too:
• initializeStack and initializeList
• isEmptyList and isEmptyStack
• linkedStackType can be derived from
linkedListType
– class linkedListType is abstract
• Must implement pop as described earlier
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Derived Stack (cont’d.)
• unorderedLinkedListType is derived
from linkedListType
– Provides the definitions of the abstract
functions of the class linkedListType
• We can derive the linkedStackType
from unorderedLinkedListType
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Application of Stacks: Postfix
Expressions Calculator
• Infix notation: usual notation for writing
arithmetic expressions
– The operator is written between the operands
– Example: a + b
– The operators have precedence
• Parentheses can be used to override precedence
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Prefix (Polish) notation: the operators are
written before the operands
– Introduced by the Polish mathematician Jan
Lukasiewicz
• Early 1920s
– The parentheses can be omitted
– Example: + a b
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Reverse Polish notation: the operators
follow the operands (postfix operators)
– Proposed by the Australian philosopher and
early computer scientist Charles L. Hamblin
• Late 1950's
– Advantage: the operators appear in the order
required for computation
– Example: a + b * c
• In a postfix expression: a b c * +
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Postfix notation has important applications
in computer science
– Many compilers first translate arithmetic
expressions into postfix notation and then
translate this expression into machine code
• Evaluation algorithm:
– Scan expression from left to right
– When an operator is found, back up to get the
operands, perform the operation, and
continue
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Example: 6 3 + 2 * =
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Symbols can be numbers or anything else:
– +, -, *, and / are operators
• Pop stack twice and evaluate expression
• If stack has less than two elements  error
– If symbol is =, the expression ends
• Pop and print answer from stack
• If stack has more than one element  error
– If symbol is anything else
• Expression contains an illegal operator
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• Examples:
7 6 + 3 ; 6 - =
• ; is an illegal operator
14 + 2 3 * =
• Does not have enough operands for +
14 2 3 + =
• Error: stack will have two elements when we
encounter equal (=) sign
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Application of Stacks: Postfix
Expressions Calculator (cont'd.)
• We assume that the postfix expressions
are in the following form:
#6 #3 + #2 * =
– If symbol scanned is #, next input is a number
– If the symbol scanned is not #, then it is:
• An operator (may be illegal) or
• An equal sign (end of expression)
• We assume expressions contain only +, -,
*, and / operators
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Main Algorithm
• Pseudocode:
• We will write four functions:
– evaluateExpression, evaluateOpr,
discardExp, and printResult
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Function evaluateExpression
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Function evaluateOpr
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Function evaluateOpr (cont’d.)
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Function discardExp
• This function is called whenever an error is
discovered in the expression
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Function printResult
• If the postfix expression contains no
errors, the function printResult prints
the result
– Otherwise, it outputs an appropriate message
• The result of the expression is in the stack
and the output is sent to a file
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Function printResult (cont’d.)
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Removing Recursion: Nonrecursive
Algorithm to Print a Linked List
Backward
• To print the list backward, first we need to get
to the last node of the list
– Problem: how do we get back to previous node?
• Links go in only one direction
– Solution: save a pointer to each of the nodes with
info 5, 10, and 15
• Use a stack (LIFO)
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Removing Recursion:
Nonrecursive Algorithm to Print a
Linked List Backward (cont’d.)
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Removing Recursion:
Nonrecursive Algorithm to Print a
Linked List Backward (cont’d.)
• Let us now execute the following
statements:
• Output:
20 15 10 5
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Queues
• 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
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Queue Operations
• Some of the queue operations are:
–
–
–
–
–
–
–
initializeQueue
isEmptyQueue
isFullQueue
front
back
addQueue
deleteQueue
• Abstract class queueADT defines these
operations
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Implementation of Queues as
Arrays
• You need at least four (member) 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
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Implementation of Queues as
Arrays (cont'd.)
• 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
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Implementation of Queues as
Arrays (cont'd.)
• To delete an element from the queue:
– Retrieve element pointed to by queueFront
– Advance queueFront to next queue element
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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...
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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
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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
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Implementation of Queues as
Arrays (cont'd.)
• To advance the index in a (logically)
circular array:
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Implementation of Queues as
Arrays (cont'd.)
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Implementation of Queues as
Arrays (cont'd.)
• Case 1:
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Implementation of Queues as
Arrays (cont'd.)
• Case 2:
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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?
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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
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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
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Implementation of Queues as
Arrays (cont'd.)
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Empty Queue and Full Queue
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Initialize Queue
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Front
• Returns the first element of the queue
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Back
• Returns the last element of the queue
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addQueue
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deleteQueue
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Constructors and Destructors
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Constructors and Destructors
(cont'd.)
• The array to store the queue elements is
created dynamically
– When the queue object goes out of scope, the
destructor simply deallocates the memory
occupied by the array
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Linked Implementation of
Queues
• Array size is fixed: only a finite number of queue
elements can be stored in it
• The array implementation of the queue requires
array to be treated in a special way
– Together with queueFront and queueRear
• The linked implementation of a queue simplifies
many of the special cases of the array
implementation
– In addition, the queue is never full
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Linked Implementation of Queues
(cont'd.)
• Elements are added at one end and
removed from the other
– We need to know the front of the queue and
the rear of the queue
• Two pointers: queueFront and queueRear
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Empty and Full Queue
• The queue is empty if queueFront is
NULL
• The queue is never full
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Initialize Queue
• Initializes queue to an empty state
– Must remove all the elements, if any
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addQueue
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front and back Operations
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deleteQueue
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Default Constructor
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Queue Derived from the class
unorderedLinkedListType
• The linked implementation of a queue is
similar to the implementation of a linked
list created in a forward manner
–
–
–
–
–
–
addQueue is similar to insertFirst
initializeQueue is like initializeList
isEmptyQueue is similar to isEmptyList
deleteQueue can be implemented as before
queueFront is the same as first
queueRear is the same as last
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Queue Derived from the class
unordered LinkedListType
(cont'd.)
• We can derive the class to implement the
queue from linkedListType
– Abstract class: does not implement all the
operations
• However, unorderedLinkedListType
is derived from linkedListType
– Provides the definitions of the abstract
functions of the linkedListType
– Therefore, we can derive linkedQueueType
from unorderedLinkedListType
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Application of Queues:
Simulation
• Simulation: a technique in which one
system models the behavior of another
system
• Computer simulations using queues as the
data structure are called queuing systems
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Designing a Queuing System
• Server: the object that provides the service
• Customer: the object receiving the service
• Transaction time: service time, or the time
it takes to serve a customer
• Model: system that consists of a list of
servers and a waiting queue holding the
customers to be served
– Customer at front of queue waits for the next
available server
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Designing a Queuing System
(cont'd.)
• We need to know:
– Number of servers
– Expected arrival time of a customer
– Time between the arrivals of customers
– Number of events affecting the system
• Performance of system depends on:
– How many servers are available
– How long it takes to serve a customer
– How often a customer arrives
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Designing a Queuing System
(cont'd.)
• If it takes too long to serve a customer and
customers arrive frequently, then more
servers are needed
• System can be modeled as a time-driven
simulation
• Time-driven simulation: the clock is a
counter
– The passage of, say, one minute can be
implemented by incrementing the counter by 1
– Simulation is run for a fixed amount of time
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Customer
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Server
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Server List
• A server list is a set of servers
– At a given time, a server is either free or busy
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Waiting Customers Queue
• When a customer arrives, he/she goes to the
end of the queue
• When a server becomes available, the
customer at front of queue leaves to conduct
the transaction
• After each time unit, the waiting time of each
customer in the queue is incremented by 1
• We can use queueType but must add the
operation of incrementing the waiting time
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Waiting Customers Queue
(cont'd.)
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Main Program
• Algorithm:
– Declare and initialize the variables
– Main loop (see next slide)
– Print results
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Main Program (cont'd.)
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Summary
• Stack: items are added/deleted from one
end
– Last In First Out (LIFO) data structure
– Operations: push, pop, initialize, destroy,
check for empty/full stack
– Can be implemented as array or linked list
– Middle elements should not be accessed
• Postfix notation: operators are written after
the operands (no parentheses needed)
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Summary (cont'd.)
• Queue: items are added at one end and
removed from the other end
– First In First Out (FIFO) data structure
– Operations: add, remove, initialize, destroy,
check if queue is empty/full
– Can be implemented as array or linked list
– Middle elements should not be accessed
– Restricted versions of arrays and linked lists
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