Algorithms and Computing
Department of Computer Engineering (DCE)
College of E&ME
NUST
 Computer
– Device capable of performing computations and making
logical decisions
 Computer programs
– Sets of instructions that control computer’s processing of
data
 Hardware
– Various devices comprising computer
• Keyboard, screen, mouse, disks, memory, CD-ROM,
processing units, …
 Software
– Programs that run on computer, Instructions to command
computer to perform actions and make decisions
Computer Organization
 Six logical units of computer
1. Input unit
•
•
“Receiving” section
Obtains information from input devices
– Keyboard, mouse, microphone, scanner,… etc
2. Output unit
•
•
•
“Shipping” section
Takes information processed by computer
Places information on output devices
– Screen, printer,… etc
– Information used to control other devices
Computer Organization
 Six logical units of computer
3. Memory unit
•
•
•
•
Rapid access, relatively low capacity “warehouse” section
Retains information from input unit
– Immediately available for processing
Retains processed information
– Until placed on output devices
Memory / Primary memory
4. Arithmetic and logic unit (ALU)
•
•
“Manufacturing” section
Performs arithmetic calculations and logic decisions
Computer Organization
 Six logical units of computer
5. Central processing unit (CPU)
•
•
“Administrative” section
Supervises and coordinates other sections of computer
6. Secondary storage unit
•
•
•
•
•
Long-term, high-capacity “warehouse” section
Storage
– Inactive programs or data
Secondary storage devices
– Disks
Longer to access than primary memory
Less expensive per unit than primary memory
Machine Languages, Assembly Languages,
and High-level Languages
 Three types of computer languages
1. Machine language
•
•
•
•
•
•
•
Only language computer directly understands
“Natural language” of computer
Defined by hardware design
– Machine-dependent
Generally consist of strings of numbers
– Ultimately 0s and 1s
Instruct computers to perform elementary operations
– One at a time
Cumbersome for humans
Example:
+1300042774
+1400593419
+1200274027
Machine Languages, Assembly Languages,
and High-level Languages
 Three types of computer languages
2. Assembly language
•
•
•
•
English-like abbreviations representing elementary computer
operations
Clearer to humans
Incomprehensible to computers
– Translator programs (assemblers)
• Convert to machine language
Example:
LOAD PURCHASE PRICE
ADD
SALES TAX
STORE RETAIL PRICE
Machine Languages, Assembly Languages,
and High-level Languages
 Three types of computer languages
3. High-level languages
•
•
•
Similar to everyday English, use common mathematical
notations
Single statements accomplish substantial tasks
– Assembly language requires many instructions to
accomplish simple tasks
Translator programs (compilers)
– Convert to machine language
• Example:
RETAIL PRICE = PURCHASE PRICE + SALES TAX
History of C and C++
 History of C
– Evolved from two other programming languages
• BCPL and B
– Dennis Ritchie (Bell Laboratories)
• Added data typing, other features
– Development language of UNIX
– Hardware independent
• Portable programs
– 1989: ANSI standard
– 1990: ANSI and ISO standard published
History of C and C++
 History of C++
–
–
–
–
Extension of C
Early 1980s: Bjarne Stroustrup (Bell Laboratories)
“Spruces up” C
Provides capabilities for object-oriented programming
• Objects: reusable software components
– Model items in real world
• Object-oriented programs
– Easy to understand, correct and modify
– Hybrid language
• C-like style
• Object-oriented style
• Both
C++ Standard Library
 Standardized version of C++
– United States
• American National Standards Institute (ANSI)
– Worldwide
• International Organization for Standardization (ISO)
 C++ programs
– Built from pieces called classes and functions
 C++ standard library
– Rich collections of existing classes and functions
 “Building block approach” to creating programs
– “Software reuse”
Other High-level Languages
 FORTRAN
– FORmula TRANslator
– 1954-1957: IBM
– Complex mathematical computations
• Scientific and engineering applications
 COBOL
– COmmon Business Oriented Language
– 1959: computer manufacturers, government and industrial
computer users
– Precise and efficient manipulation of large amounts of data
• Commercial applications
Other High-level Languages
 Pascal
– Prof. Niklaus Wirth
– Academic use
Basics of a Typical C++ Environment
 C++ systems
– Program-development environment
– Language
– C++ Standard Library
Basics of a Typical C++ Environment
Phases of C++ Programs:
1. Edit
2. Preprocess
Editor
Preprocessor
Compiler
Linker
3. Compile
Disk
Program is created in
the editor and stored
on disk.
Disk
Preprocessor program
processes the code.
Disk
Compiler creates
object code and stores
it on disk.
Disk
Primary
Memory
4. Link
Loader
5. Load
Disk
6. Execute
Linker links the object
code with the libraries,
Creates an executable
file and stores it on disk
Loader puts program
in memory.
..
..
..
Primary
Memory
CPU
..
..
..
CPU takes each
instruction and
executes it, possibly
storing new data
values as the program
executes.
A Simple Program:
Printing a Line of Text
 Input/output
– cin
• Standard input stream
• Normally keyboard
– cout
• Standard output stream
• Normally computer screen
A Simple Program:
Printing a Line of Text
 Comments
–
–
–
–
Document programs
Improve program readability
Ignored by compiler
Single-line comment
• Begin with //
 Preprocessor directives
– Processed by preprocessor before compiling
– Begin with #
A Simple Program:
Printing a Line of Text
 Standard output stream object
– std::cout
– “Connected” to screen
– <<
• Stream insertion operator
• Value to right (right operand) inserted into output stream
 Escape characters
– \
– Indicates “special” character output
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// A first program in C++.
Function main
#include <iostream.h>
Single-line comments.
returns an
directive to
integer
value.
Left brace
{ begins Preprocessor
function
include
input/output Statements
stream
begins
execution
Function
main appears
body. program
end with a
header
file
<iostream>.
exactly once in every C++ semicolon ;.
program..
// function main
int main()
{
cout << "Welcome to C++!\n";
return 0;
//
} // end function
Welcome to C++!
Corresponding right brace }
indicate
thatbody.
program ended successfully
ends
function
Stream
insertion
Name cout
belongs
to operator.
main namespace std.
Keyword return is one of
several means to exit
function; value 0 indicates
program terminated
successfully.
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// Printing a line with multiple statements.
#include <iostream.h>
// function main begins program execution
int main()
{
cout << "Welcome ";
cout << "to C++!\n";
return 0;
// indicate that program ended successfully
} // end function main
Welcome to C++!
Multiple stream insertion
statements produce one line
of output.
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// Printing multiple lines with a single statement
#include <iostream.h>
// function main begins program execution Using newline characters
print on multiple lines.
int main()
{
cout << "Welcome\nto\n\nC++!\n";
return 0;
// indicate that program ended successfully
} // end function main
Welcome
to
C++!
to
Another Simple Program:
Adding Two Integers
 Variables
– Location in memory where value can be stored
– Common data types
• int - integer numbers
• char - characters
• double - floating point numbers
– Declare variables with name and data type before use
int integer1;
int integer2;
int sum;
– Can declare several variables of same type in one declaration
• Comma-separated list
int integer1, integer2, sum;
Another Simple Program:
Adding Two Integers
 Variables
– Variable names
• Valid identifier
– Series of characters (letters, digits, underscores)
– Cannot begin with digit
– Case sensitive
Another Simple Program:
Adding Two Integers
 Input stream object
– >> (stream extraction operator)
• Used with std::cin
• Waits for user to input value, then press Enter (Return) key
• Stores value in variable to right of operator
– Converts value to variable data type
 = (assignment operator)
– Assigns value to variable
– Binary operator (two operands)
– Example:
sum = variable1 + variable2;
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// Addition program.
#include <iostream.h>
// function main begins program execution
int main()
Declare integer variables.
{
int integer1; // first number to be input by user
int integer2; // second number to be input by user
Usewhich
stream
extraction
int sum;
// variable in
sum
will be stored
cout << "Enter first
cin >> integer1;
operator with standard input
stream to obtain
user input.
integer\n";
// prompt
// read an integer
cout << "Enter second integer\n"; // prompt
cin >> integer2;
// read an integer
sum = integer1 + integer2;
// assign result to sum
cout << "Sum is " << sum << endl; // print sum
return 0;
Stream manipulator
std::endl outputs a
newline, then “flushes output
buffer.”
// indicate that program ended successfully
} // end function main
Concatenating, chaining or
cascading stream insertion
operations.
Enter first integer
45
Enter second integer
72
Sum is 117
Memory Concepts
 Variable names
– Correspond to actual locations in computer's memory
– Every variable has name, type, size and value
– When new value placed into variable, overwrites previous
value
– Reading variables from memory nondestructive
Memory Concepts
std::cin >> integer1;
integer1
45
std::cin >> integer2;
integer1
45
– Assume user entered 72
integer2
72
integer1
45
integer2
72
– Assume user entered 45
sum = integer1 + integer2;
sum
117
Arithmetic
 Arithmetic calculations
– *
• Multiplication
– /
• Division
• Integer division truncates remainder
– 7 / 5 evaluates to 1
– %
• Modulus operator returns remainder
– 7 % 5 evaluates to 2
Arithmetic
 Rules of operator precedence
– Operators in parentheses evaluated first
• Nested/embedded parentheses
– Operators in innermost pair first
– Multiplication, division, modulus applied next
• Operators applied from left to right
– Addition, subtraction applied last
Operator(s)
Operation(s)
• Operators
applied fromOrder
left oftoevaluation
right (precedence)
()
Parentheses
*, /, or %
Multiplication Division Evaluated second. If there are several, they re
Modulus
evaluated left to right.
+ or -
Addition
Subtraction
Evaluated first. If the parentheses are nested, the
expression in the innermost pair is evaluated first. If
there are several pairs of parentheses “on the same level”
(i.e., not nested), they are evaluated left to right.
Evaluated last. If there are several, they are
evaluated left to right.
Decision Making: Equality and Relational
Operators
 if structure
– Make decision based on truth or falsity of condition
• If condition met, body executed
• Else, body not executed
 Equality and relational operators
Decision Making: Equality and Relational
Operators
Sta nd a rd a lg eb ra ic
eq ua lity op era tor or
rela tiona l op era tor
C++ eq ua lity
or rela tiona l
op era tor
Exa m p le
of C++
c ond ition
Mea ning of
C++ c ond ition
>
>
x > y
x is greater than y
<
<
x < y
x is less than y

>=
x >= y
x is greater than or equal to y

<=
x <= y
x is less than or equal to y
=
==
x == y
x is equal to y

!=
x != y
x is not equal to y
Relational operators
Equality operators
Decision Making: Equality and Relational
Operators
 if ( x == y )
cout << x << " is equal to " << y << endl;
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// Using if statements, relational
// operators, and equality operators.
#include <iostream.h>
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variables.
// function main begins programDeclare
execution
int main()
{
Can write
cout
cin
int num1; // first number
to be
readand
from
user
without
std::
prefix.
int num2; // second number to be read from user
cout << "Enter two integers, and I will tell you\n"
if structure compares values
<< "the relationships they satisfy: ";
of num1
and num2
to test for
If condition
is true
cin >> num1 >> num2;
// read
two integers
if ( num1 == num2 )
cout << num1 << " is
(i.e.,
equality.
values are equal), execute this
if structure compares
values
statement.
If condition
is true (i.e.,
of num1
andnum2
num2
test for
equal
to " <<
<< toendl;
values are not equal), execute
inequality.
this statement.
if ( num1 != num2 )
cout << num1 << " is not equal to " << num2 << endl;
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if ( num1 < num2 )
cout << num1 << " is less than " << num2 << endl;
if ( num1 > num2 )
cout << num1 << " is greater than " << num2 << endl;
if ( num1 <= num2 )
cout << num1 << " is less than or equal to "
<< num2 << endl;
if ( num1 >= num2 )
cout << num1 << " is greater than or equal to "
<< num2 << endl;
return 0;
// indicate that program ended successfully
} // end function main
Enter two integers, and I will tell you
the relationships they satisfy: 22 12
22 is not equal to 12
22 is greater than 12
22 is greater than or equal to 12
Statements may be split over
several lines.
Enter two integers, and I will tell you
the relationships they satisfy: 7 7
7 is equal to 7
7 is less than or equal to 7
7 is greater than or equal to 7
Algorithms
 Before writing a program
– Have a thorough understanding of problem
– Carefully plan your approach for solving it
Algorithms
 Computing problems
– Solved by executing a series of actions in a specific order
 Algorithm a procedure determining
– Actions to be executed
– Order to be executed
– Example: recipe
 Program control
– Specifies the order in which statements are executed
Pseudocode
 Pseudocode
– Artificial, informal language used to develop algorithms
– Similar to everyday English
 Not executed on computers
– Used to think out program before coding
• Easy to convert into C++ program
– Only executable statements
• No need to declare variables
Control Structures
 Sequential execution
– Statements executed in order
 Transfer of control
– Next statement executed not next one in sequence
 3 control structures
– Sequence structure
• Programs executed sequentially by default
– Selection structures
• if, if/else, switch
– Repetition structures
• while, do/while, for
Control Structures
 Flowchart
– Graphical representation of an algorithm
– Special-purpose symbols connected by arrows (flowlines)
– Rectangle symbol (action symbol)
• Any type of action
– Oval symbol
• Beginning or end of a program
if Selection Structure
 Selection structure
– Choose among alternative courses of action
– Pseudocode example:
If student’s grade is greater than or equal to 60
Print “Passed”
– If the condition is true
• Print statement executed, program continues to next statement
– If the condition is false
• Print statement ignored, program continues
– Indenting makes programs easier to read
• C++ ignores whitespace characters (tabs, spaces, etc.)
if Selection Structure
 Translation into C++
If student’s grade is greater than or equal to 60
Print “Passed”
if ( grade >= 60 )
cout << "Passed";
 Diamond symbol (decision symbol)
– Indicates decision is to be made
– Contains an expression that can be true or false
• Test condition, follow path
if Selection Structure
 Flowchart of pseudocode statement
grade >= 60
false
true
print “Passed”
if/else Selection Structure
 if
– Performs action if condition true
 if/else
– Different actions if conditions true or false
 Pseudocode
if student’s grade is greater than or equal to 60
print “Passed”
else
print “Failed”
 C++ code
if ( grade >= 60 )
cout << "Passed";
else
cout << "Failed";
Selection Structure
 Ternary conditional operator (?:)
– Three arguments (condition, value if true, value if false)
 Code could be written:
cout << ( grade >= 60 ? “Passed” : “Failed” );
Condition
false
print “Failed”
Value if true
grade >= 60
Value if false
true
print “Passed”
if/else Selection Structure
 Nested if/else structures
– One inside another, test for multiple cases
– Once condition met, other statements skipped
if student’s grade is greater than or equal to 90
Print “A”
else
if student’s grade is greater than or equal to 80
Print “B”
else
if student’s grade is greater than or equal to 70
Print “C”
else
if student’s grade is greater than or equal to 60
Print “D”
else
Print “F”
if/else Selection Structure
 Example
if ( grade >= 90 )
cout << "A";
else if ( grade >= 80 )
cout << "B";
else if ( grade >= 70 )
cout << "C";
else if ( grade >= 60 )
cout << "D";
else
cout << "F";
// 90 and above
// 80-89
// 70-79
// 60-69
// less than 60
if/else Selection Structure
 Compound statement
– Set of statements within a pair of braces
if ( grade
cout <<
else {
cout <<
cout <<
>= 60 )
"Passed.\n";
"Failed.\n";
"You must take this course again.\n";
}
– Without braces,
cout << "You must take this course again.\n";
always executed
 Block
– Set of statements within braces
Even or Odd
int num;
cout<<"Enter any number"<<endl;
cin>>num;
if(num%2==0)
cout<<"The number is even"<<endl;
else
cout<<"The number is odd"<<endl;
Dangling Else Problem
if ( x > 5)
if ( y > 5)
cout << “x and y are > 5”;
else
cout << “x is <= 5”;
Dangling Else Problem
if ( x > 5)
if ( y > 5)
cout << “x and y are > 5”;
else
cout << “x is <= 5”;
Dangling Else Problem
if ( x > 5)
{
if ( y > 5)
cout << “x and y are > 5”;
}
else
cout << “x is <= 5”;
 else associated with the first if
Guess Number
#include <iostream.h>
#include <cstdlib.h>
int main()
{
int magic;
int guess;
magic = rand();
// get a random number
cout << "Enter your guess: ";
cin >> guess;
if (guess == magic) {
cout << "** Right **\n";
cout << magic << " is the magic number.\n";
}
else {
cout << "...Sorry, you're wrong.";
if(guess > magic)
cout <<" Your guess is too high.\n";
else
cout << " Your guess is too low.\n";
}
return 0;
}
while Repetition Structure
 Repetition structure
– Action repeated while some condition remains true
– Psuedocode
while there are more items on my shopping list
Purchase next item and cross it off my list
– while loop repeated until condition becomes false
 Example
int product = 2;
while ( product <= 1000 )
product = 2 * product;
The while Repetition Structure
 Flowchart of while loop
true
product <= 1000
false
product = 2 * product
Formulating Algorithms (Counter-Controlled
Repetition)
 Counter-controlled repetition
– Loop repeated until counter reaches certain value
 Definite repetition
– Number of repetitions known
 Example
A class of ten students took a quiz. The grades (integers in
the range 0 to 100) for this quiz are available to you.
Determine the class average on the quiz.
Formulating Algorithms (Counter-Controlled
Repetition)
 Pseudocode for example:
Set total to zero
Set grade counter to one
While grade counter is less than or equal to ten
Input the next grade
Add the grade into the total
Add one to the grade counter
Set the class average to the total divided by ten
Print the class average
 Next: C++ code for this example
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// Class average program with counter-controlled repetition.
#include <iostream>
// function main begins
int main()
{
int total;
//
int gradeCounter; //
int grade;
//
int average;
//
program execution
sum of grades input by user
number of grade to be entered next
grade value
average of grades
// initialization phase
total = 0;
// initialize total
gradeCounter = 1;
// initialize loop counter
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// processing phase
while ( gradeCounter <= 10 ) {
cout << "Enter grade: ";
cin >> grade;
total = total + grade;
gradeCounter = gradeCounter + 1;
}
// termination phase
average = total / 10;
//
//
//
//
//
loop 10 times
prompt for input
read grade from user
add grade to total
increment counter
// integer division
// display result
cout << "Class average is The
" <<counter
average
<<incremented
endl;
gets
return 0;
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Class
time the loop executes.
// indicate program
ended
Eventually,
thesuccessfully
counter causes
} // end function main
grade: 98
grade: 76
grade: 71
grade: 87
grade: 83
grade: 90
grade: 57
grade: 79
grade: 82
grade: 94
average is 81
each
loop to end.
the
Formulating Algorithms (Sentinel-Controlled
Repetition)
 Suppose problem becomes:
Develop a class-averaging program that will process an
arbitrary number of grades each time the program is run
– Unknown number of students
– How will program know when to end?
 Sentinel value
– Indicates “end of data entry”
– Loop ends when sentinel input
– Sentinel chosen so it cannot be confused with regular input
• -1 in this case
Formulating Algorithms (Sentinel-Controlled
Repetition)
 Top-down, stepwise refinement
– Begin with pseudocode representation of top
Determine the class average for the quiz
– Divide top into smaller tasks, list in order
Initialize variables
Input, sum and count the quiz grades
Calculate and print the class average
Formulating Algorithms (Sentinel-Controlled
Repetition)
 Many programs have three phases
– Initialization
• Initializes the program variables
– Processing
• Input data, adjusts program variables
– Termination
• Calculate and print the final results
– Helps break up programs for top-down refinement
Formulating Algorithms (Sentinel-Controlled
Repetition)
 Refine the initialization phase
Initialize variables
becomes:
Initialize total to zero
Initialize counter to zero
 Processing
Input, sum and count the quiz grades
becomes:
Input the first grade (possibly the sentinel)
While the user has not as yet entered the sentinel
Add this grade into the running total
Add one to the grade counter
Input the next grade (possibly the sentinel)
Formulating Algorithms (Sentinel-Controlled
Repetition)
 Termination
Calculate and print the class average
becomes:
If the counter is not equal to zero
Set the average to the total divided by the counter
Print the average
Else
Print “No grades were entered”
 Next: C++ program
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// Class average program with sentinel-controlled repetition.
#include <iostream>
#include <iomanip>
// parameterized stream manipulators
using std::setprecision;
// sets numeric output precision
// function main begins program execution
int main()
Data type double used to represent
{
int total;
// sum of grades decimal numbers.
int gradeCounter; // number of grades entered
int grade;
// grade value
double average;
// number with decimal point for average
// initialization phase
total = 0;
// initialize total
gradeCounter = 0; // initialize loop counter
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// processing phase
// get first grade from user
cout << "Enter grade, -1 to end: ";
cin >> grade;
// prompt for input
// read grade from user
// loop until sentinel value read from user
treats total
while ( grade != -1 )static_cast<double>()
{
double temporarily
(casting).
total = total + grade;
// add
grade to total
gradeCounter = gradeCounter + 1; // increment counter
as a
Required because dividing two integers truncates the
cout << "Enter grade, -1 to end: ";
remainder.
cin >> grade;
} // end while
// prompt for input
// read next grade
gradeCounter is an int, but it gets promoted to
double.
// termination phase
// if user entered at least one grade ...
if ( gradeCounter != 0 ) {
// calculate average of all grades entered
average = static_cast< double >( total ) / gradeCounter;
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// display average with two digits of precision
cout << "Class average is " << setprecision( 2 )
<< average << endl;
} // end if part of if/else
else // if no grades were entered, output appropriate message
cout << "No grades were entered" << endl;
return 0;
// indicate program ended successfully
} // end function main
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Enter
Class
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
grade, -1 to end:
average is 82.50
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-1
setprecision(2)prints two digits past
decimal point (rounded to fit precision).
Programs that use this must include <iomanip>
Nested Control Structures
 Problem statement
A college has a list of test results (1 = pass, 2 = fail) for 10
students. Write a program that analyzes the results. If more
than 8 students pass, print “Hardworking Class”.
 Notice that
– Program processes 10 results
• Fixed number, use counter-controlled loop
– Two counters can be used
• One counts number that passed
• Another counts number that fail
– Each test result is 1 or 2
• If not 1, assume 2
Nested Control Structures
 Top level outline
Analyze exam results and decide if class was hardworking
 First refinement
Initialize variables
Input the ten quiz grades and count passes and failures
Print a summary of the exam results and decide if class was
hardworking
 Refine
Initialize variables
becomes:
Initialize passes to zero
Initialize failures to zero
Initialize student counter to one
Nested Control Structures
 Refine
Input the ten quiz grades and count passes and failures
becomes:
While student counter is less than or equal to ten
Input the next exam result
If the student passed
Add one to passes
Else
Add one to failures
Add one to student counter
Nested Control Structures
 Refine
Print a summary of the exam results and decide if class was
hardworking
becomes:
Print the number of passes
Print the number of failures
If more than eight students passed
Print “Hardworking Class”
 Program next
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// Analysis of examination results.
#include <iostream>
// function main begins program execution
int main()
{
// initialize variables in declarations
int passes = 0;
// number of passes
int failures = 0;
// number of failures
int studentCounter = 1;
// student counter
int result;
// one exam result
// process 10 students using counter-controlled loop
while ( studentCounter <= 10 ) {
// prompt user for input and obtain value from user
cout << "Enter result (1 = pass, 2 = fail): ";
cin >> result;
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// if result 1, increment passes; if/else nested in while
if ( result == 1 )
// if/else nested in while
passes = passes + 1;
else // if result not 1, increment failures
failures = failures + 1;
// increment studentCounter so loop eventually terminates
studentCounter = studentCounter + 1;
} // end while
// termination phase; display number of passes and failures
cout << "Passed " << passes << endl;
cout << "Failed " << failures << endl;
// if more than eight students passed, print "raise tuition"
if ( passes > 8 )
cout << “Hardworking Class" << endl;
return 0;
// successful termination
} // end function main
Enter result
Enter result
Enter result
Enter result
Enter result
Enter result
Enter result
Enter result
Enter result
Enter result
Passed 6
Failed 4
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(1
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Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Enter result (1 =
Passed 9
Failed 1
Hardworking Class
pass,
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