Algorithms and Computing Department of Computer Engineering (DCE) College of E&ME NUST.

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 computer1. 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


Six logical units of computer3. 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


Six logical units of computer5. 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



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 PRICEADD SALES TAXSTORE RETAIL PRICE



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

3. Compile

4. Link

5. Load

6. Execute

Loader

PrimaryMemory

Program is created inthe editor and storedon disk.

Preprocessor programprocesses the code.

Loader puts programin memory.

CPU takes eachinstruction andexecutes it, possiblystoring new datavalues as the programexecutes.

CompilerCompiler createsobject code and storesit on disk.

Linker links the objectcode with the libraries,Creates an executablefile and stores it on disk

Editor

Preprocessor

Linker

CPU

PrimaryMemory

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Disk

Disk

Disk

Disk

Disk

A Simple Program:Printing a Line of Text

Input/output

– cin• Standard input stream

• Normally keyboard

– cout• Standard output stream

• Normally computer screen


Comments– Document programs

– Improve program readability

– Ignored by compiler

– Single-line comment• Begin with //

Preprocessor directives– Processed by preprocessor before compiling

– Begin with #


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

12 // A first program in C++.3 #include <iostream.h>4 5 // function main begins program execution6 int main()7 {8 cout << "Welcome to C++!\n";9 10 return 0; // indicate that program ended successfully11 12 } // end function main

Welcome to C++!

Single-line comments.

Preprocessor directive to include input/output stream header file <iostream>.

Function main appears exactly once in every C++ program..

Function main returns an integer value.Left brace { begins function body.

Corresponding right brace } ends function body.

Statements end with a semicolon ;.

Name cout belongs to namespace std.

Stream insertion operator.

Keyword return is one of several means to exit function; value 0 indicates program terminated successfully.

12 // Printing a line with multiple statements.3 #include <iostream.h>4 5 // function main begins program execution6 int main()7 {8 cout << "Welcome "; 9 cout << "to C++!\n";10 11 return 0; // indicate that program ended successfully12 13 } // end function main

Welcome to C++!

Multiple stream insertion statements produce one line of output.

12 // Printing multiple lines with a single statement3 #include <iostream.h>4 5 // function main begins program execution6 int main()7 {8 cout << "Welcome\nto\n\nC++!\n";9 10 return 0; // indicate that program ended successfully11 12 } // end function main

Welcome

to

C++!

Using newline characters to print on multiple lines.

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 useint integer1;

int integer2;

int sum;

– Can declare several variables of same type in one declaration• Comma-separated list

int integer1, integer2, sum;


Variables– Variable names

• Valid identifier

– Series of characters (letters, digits, underscores)

– Cannot begin with digit

– Case sensitive


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;

12 // Addition program.3 #include <iostream.h>4 5 // function main begins program execution6 int main()7 {8 int integer1; // first number to be input by user 9 int integer2; // second number to be input by user 10 int sum; // variable in which sum will be stored11 12 cout << "Enter first integer\n"; // prompt13 cin >> integer1; // read an integer14 15 cout << "Enter second integer\n"; // prompt16 cin >> integer2; // read an integer17 18 sum = integer1 + integer2; // assign result to sum19 20 cout << "Sum is " << sum << endl; // print sum21 22 return 0; // indicate that program ended successfully23 24 } // end function main

Declare integer variables.

Use stream extraction operator with standard input stream to obtain user input.

Stream manipulator std::endl outputs a newline, then “flushes output buffer.”

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;– Assume user entered 45

std::cin >> integer2;– Assume user entered 72

sum = integer1 + integer2;

integer1 45

integer1 45

integer2 72

integer1 45

integer2 72

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• Operators applied from left to rightOperator(s) Operation(s) Order of evaluation (precedence)

() Parentheses 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.

*, /, or % Multiplication Division Modulus

Evaluated second. If there are several, they re evaluated left to right.

+ or - Addition Subtraction

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


Standard algebraic equality operator or relational operator

C++ equality or relational operator

Example of C++ condition

Meaning of C++ condition

Relational operators

> > 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

Equality operators

= == x == y x is equal to y

!= x != y x is not equal to y


if ( x == y )

cout << x << " is equal to " << y << endl;

12 // Using if statements, relational3 // operators, and equality operators.4 #include <iostream.h>5 6 78 9 10 // function main begins program execution11 int main()12 {13 int num1; // first number to be read from user14 int num2; // second number to be read from user15 16 cout << "Enter two integers, and I will tell you\n"17 << "the relationships they satisfy: ";18 cin >> num1 >> num2; // read two integers19 20 if ( num1 == num2 ) 21 cout << num1 << " is equal to " << num2 << endl;22 23 if ( num1 != num2 )24 cout << num1 << " is not equal to " << num2 << endl;25

Can write cout and cin without std:: prefix.

Declare variables.

if structure compares values of num1 and num2 to test for equality.

If condition is true (i.e., values are equal), execute this statement.if structure compares values

of num1 and num2 to test for inequality.

If condition is true (i.e., values are not equal), execute this statement.

26 if ( num1 < num2 )27 cout << num1 << " is less than " << num2 << endl;28 29 if ( num1 > num2 )30 cout << num1 << " is greater than " << num2 << endl;31 32 if ( num1 <= num2 )33 cout << num1 << " is less than or equal to "34 << num2 << endl;35 36 if ( num1 >= num2 )37 cout << num1 << " is greater than or equal to "38 << num2 << endl;39 40 return 0; // indicate that program ended successfully41 42 } // 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.)


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


Flowchart of pseudocode statement

true

false

grade >= 60

print “Passed”

if/else Selection Structure

if– Performs action if condition true

if/else– Different actions if conditions true or false

Pseudocodeif student’s grade is greater than or equal to 60

print “Passed”else

print “Failed”

C++ codeif ( 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” );

truefalse

print “Failed” print “Passed”

grade >= 60

Condition Value if true Value if false


Nested if/else structures– One inside another, test for multiple cases

– Once condition met, other statements skippedif 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”


Example

if ( grade >= 90 ) // 90 and above cout << "A";else if ( grade >= 80 ) // 80-89 cout << "B";else if ( grade >= 70 ) // 70-79 cout << "C"; else if ( grade >= 60 ) // 60-69 cout << "D";else // less than 60 cout << "F";


Compound statement– Set of statements within a pair of braces if ( grade >= 60 )

cout << "Passed.\n";else { cout << "Failed.\n"; cout << "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;

elsecout<<"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”;

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

– Psuedocodewhile there are more items on my shopping list

Purchase next item and cross it off my list

– while loop repeated until condition becomes false

Exampleint product = 2;

while ( product <= 1000 )

product = 2 * product;

The while Repetition Structure

Flowchart of while loop

product <= 1000 product = 2 * producttrue

false

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 tenInput the next gradeAdd the grade into the totalAdd one to the grade counter

Set the class average to the total divided by tenPrint the class average

Next: C++ code for this example

12 // Class average program with counter-controlled repetition.3 #include <iostream>4 5678 9 // function main begins program execution10 int main()11 {12 int total; // sum of grades input by user13 int gradeCounter; // number of grade to be entered next14 int grade; // grade value15 int average; // average of grades16 17 // initialization phase18 total = 0; // initialize total19 gradeCounter = 1; // initialize loop counter20

21 // processing phase22 while ( gradeCounter <= 10 ) { // loop 10 times23 cout << "Enter grade: "; // prompt for input24 cin >> grade; // read grade from user25 total = total + grade; // add grade to total26 gradeCounter = gradeCounter + 1; // increment counter27 }28 29 // termination phase30 average = total / 10; // integer division31 32 // display result33 cout << "Class average is " << average << endl; 34 35 return 0; // indicate program ended successfully36 37 } // end function main

Enter grade: 98

Enter grade: 76

Enter grade: 71

Enter grade: 87

Enter grade: 83

Enter grade: 90

Enter grade: 57

Enter grade: 79

Enter grade: 82

Enter grade: 94

Class average is 81

The counter gets incremented each time the loop executes. Eventually, the counter causes the loop to end.

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


Top-down, stepwise refinement– Begin with pseudocode representation of top

Determine the class average for the quiz

– Divide top into smaller tasks, list in orderInitialize variables

Input, sum and count the quiz grades

Calculate and print the class average


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


Refine the initialization phaseInitialize variables

becomes:

Initialize total to zero

Initialize counter to zero

ProcessingInput, 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)


TerminationCalculate 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

12 // Class average program with sentinel-controlled repetition.3 #include <iostream>4 56789 10 #include <iomanip> // parameterized stream manipulators11 12 using std::setprecision; // sets numeric output precision 13 14 // function main begins program execution15 int main()16 {17 int total; // sum of grades18 int gradeCounter; // number of grades entered19 int grade; // grade value20 21 double average; // number with decimal point for average22 23 // initialization phase24 total = 0; // initialize total25 gradeCounter = 0; // initialize loop counter

Data type double used to represent decimal numbers.

26 27 // processing phase28 // get first grade from user29 cout << "Enter grade, -1 to end: "; // prompt for input30 cin >> grade; // read grade from user31 32 // loop until sentinel value read from user33 while ( grade != -1 ) { 34 total = total + grade; // add grade to total35 gradeCounter = gradeCounter + 1; // increment counter36 37 cout << "Enter grade, -1 to end: "; // prompt for input38 cin >> grade; // read next grade39 40 } // end while41 42 // termination phase43 // if user entered at least one grade ...44 if ( gradeCounter != 0 ) {45 46 // calculate average of all grades entered47 average = static_cast< double >( total ) / gradeCounter;48

static_cast<double>() treats total as a double temporarily (casting).

Required because dividing two integers truncates the remainder.

gradeCounter is an int, but it gets promoted to double.

49 // display average with two digits of precision50 cout << "Class average is " << setprecision( 2 )51 << average << endl;52 53 } // end if part of if/else54 55 else // if no grades were entered, output appropriate message56 cout << "No grades were entered" << endl;57 58 return 0; // indicate program ended successfully59 60 } // end function main

Enter grade, -1 to end: 75








Enter grade, -1 to end: -1

Class average is 82.50

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


Top level outlineAnalyze exam results and decide if class was hardworking

First refinementInitialize variables

Input the ten quiz grades and count passes and failures

Print a summary of the exam results and decide if class was hardworking

RefineInitialize variables

becomes:

Initialize passes to zero

Initialize failures to zero

Initialize student counter to one


RefineInput the ten quiz grades and count passes and failures

becomes:

While student counter is less than or equal to tenInput the next exam result

If the student passed

Add one to passesElse Add one to failures

Add one to student counter


RefinePrint 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

12 // Analysis of examination results.3 #include <iostream>4 5678 9 // function main begins program execution10 int main()11 {12 // initialize variables in declarations13 int passes = 0; // number of passes14 int failures = 0; // number of failures15 int studentCounter = 1; // student counter16 int result; // one exam result17 18 // process 10 students using counter-controlled loop19 while ( studentCounter <= 10 ) {20 21 // prompt user for input and obtain value from user22 cout << "Enter result (1 = pass, 2 = fail): ";23 cin >> result;24

25 // if result 1, increment passes; if/else nested in while26 if ( result == 1 ) // if/else nested in while27 passes = passes + 1; 28 29 else // if result not 1, increment failures 30 failures = failures + 1; 31 32 // increment studentCounter so loop eventually terminates33 studentCounter = studentCounter + 1; 34 35 } // end while36 37 // termination phase; display number of passes and failures38 cout << "Passed " << passes << endl; 39 cout << "Failed " << failures << endl;40 41 // if more than eight students passed, print "raise tuition"42 if ( passes > 8 )43 cout << “Hardworking Class" << endl; 44 45 return 0; // successful termination46 47 } // end function main

Enter result (1 = pass, 2 = fail): 1










Passed 6

Failed 4











Passed 9

Failed 1

Hardworking Class

Algorithms and Computing Department of Computer Engineering (DCE) College of E&ME NUST.

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Transcript of Algorithms and Computing Department of Computer Engineering (DCE) College of E&ME NUST.