CS1101: Programming Methodology http://www.comp.nus.edu.sg/~cs1101x/

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CS1101 Programming Methodology
http//www.comp.nus.edu.sg/cs1101x/
Aaron Tan
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Week 1 Introduction

• History of computers
• Components of a computer
• Binary numbers
• Introduce high-level programming languages
• Introduce Java programming, compilation and
  execution.
• Present useful problem-solving strategies.
• Writing algorithms in pseudo-codes.

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History of Computers

• Websites
• ACM Timeline of Computing History
  (http//www.computer.org/computer/timeline)
• The Virtual Museum of Computing
  (http//www.comlab.ox.ac.uk/archive/other/museums/
  computing.html)
• IEEE Annals of the History of Computing
  (http//www.computer.org/annals/)
• and others (surf the web)

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Computers as Information Processors (1/2)

• Unlike previous inventions, computers are special
  because they are general-purpose.
• Could be used to perform a variety of tasks.
• Computer Hardware Software.
• Hardware physical components for
  computation/processing should be simple, fast,
  reliable.
• Software set of instructions to perform tasks to
  specifications should be flexible,
  user-friendly, sophisticated.

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Computers as Information Processors (2/2)

• Computer are Information Processors

Data Units 1 bit (binary digit) one of
two values (0 or 1). 1 byte 8 bits.
1 word 1, 2, or 4 bytes, or more (depends on
ALU).
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Components of a Computer (1/2)

• Main Components
• CPU (Central Processing Unit controls devices
  and processes data).
• Memory stores programs and intermediate data.
• Input Devices accept data from outside world.
• Output Devices presents data to the outside
  world.
• An analogy with Human Information Processors
• CPU brains reasoning powers
• Memory brains memory
• Input Devices eyes, ears, sensory sub-system
• Output Devices mouth, hands, facial and body
  expressions

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Components of a Computer (2/2)
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Decimal Number System

• Also called the base-10 number system.
• 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• In general, (anan-1 a0 . f1f2 fm)10
  (an x 10n) (an-1x10n-1) (a0 x
  100) (f1 x 10-1) (f2 x 10-2)
  (fm x 10-m)
• Weighting factors (or weights) are in
  powers-of-10
• 103 102 101 100.10-1 10-2 10-3 10-4
• Example 593.68. The digit in each position is
  multiplied by the corresponding weight
• 5?102 9?101 3?100 6?10-1 8?10-2
  (593.68)10

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Other Number Systems

• Binary (base 2) weights in powers-of-2.
• Binary digits (bits) 0,1.
• Essential in computing.
• Octal (base 8) weights in powers-of-8.
• Octal digits 0,1,2,3,4,5,6,7.
• Hexadecimal (base 16) weights in powers-of-16.
• Hexadecimal digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,
  F.
• Base R weights in powers-of-R.

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Base-R to Decimal Conversion

• (1101.101)2 1?23 1?22 1?20 1?2-1
  1?2-3 8 4 1 0.5 0.125 (13.625)10
• (572.6)8 5?82 7?81 2?80 6?8-1
  320 56 2 0.75 (378.75)10
• (2A.8)16 2?161 10?160 8?16-1
  32 10 0.5 (42.5)10
• (341.24)5 3?52 4?51 1?50 2?5-1
  4?5-2 75 20 1 0.4 0.16
  (96.56)10

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Decimal to Binary Conversion (1/2)

• Whole number repeated division-by-2 method.
• To convert a whole number to binary, use
  successive division by 2 until the quotient is 0.
  The remainders form the answer, with the first
  remainder as the least significant bit (LSB) and
  the last as the most significant bit (MSB).
• (43)10 (101011)2

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Decimal to Binary Conversion (2/2)

• Fractions repeated multiply-by-2 method.
• To convert decimal fractions to binary, repeated
  multiplication by 2 is used, until the fractional
  product is 0 (or until the desired number of
  decimal places). The carried digits, or carries,
  produce the answer, with the first carry as the
  MSB, and the last as the LSB.
• (0.3125)10 (.0101)2

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Mathematics

• A-level Mathematics assumed.
• Common concepts encountered in programming prime
  numbers, complex numbers, polynomials, matrices.
• Mathematical maturity desirable.

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Software (1/4)

• Program
• Sequence of instruction that tells a computer
  what to do
• Execution
• Performing the instruction sequence
• Programming language
• Language for writing instructions to a computer
• Major flavors
• Machine language or object code
• Assembly language
• High-level

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Software (2/4)

• Program
• Sequence of instruction that tells a computer
  what to do
• Execution
• Performing the instruction sequence
• Programming language
• Language for writing instructions to a computer
• Major flavors
• Machine language or object code
• Assembly language
• High-level

Program to which computer can respond directly.
Each instruction is a binary code that
corresponds to a native instruction. Example
0001001101101110
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Software (3/4)

• Program
• Sequence of instruction that tells a computer
  what to do
• Execution
• Performing the instruction sequence
• Programming language
• Language for writing instructions to a computer
• Major flavors
• Machine language or object code
• Assembly language
• High-level

Symbolic languagefor coding machinelanguage
instructions. Example ADD A, B, C
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Software (4/4)

• Program
• Sequence of instruction that tells a computer
  what to do
• Execution
• Performing the instruction sequence
• Programming language
• Language for writing instructions to a computer
• Major flavors
• Machine language or object code
• Assembly language
• High-level

Detailed knowledge of the machine is not
required. Uses a vocabulary and structure closer
to the problem being solved. Examples Java, C,
C, Prolog, Scheme.
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Translation

• High-level language programs (source programs)
  must be translated into machine code for
  execution
• Translator
• Accepts a program written in a source language
  and translates it to a program in a target
  language
• Compiler
• Standard name for a translator whose source
  language is a high-level language
• Interpreter
• A translator that both translates and executes a
  source program

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Java

• A high-level object-oriented language developed
  by Sun.
• Two types of Java programs
• Applet runs within a web browser.
• Application a complete stand-alone program.
• Javas clean design and wide availability make it
  an suitable language for teaching the
  fundamentals of computer programming.

Acknowledgement Cohoon and Davidson
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Java translation

• Two-step process
• First step
• Translation from Java to bytecodes
• Bytecodes are architecturally neutral object code
• Bytecodes are stored in a file with extension
  .class
• Second step
• An interpreter translates the bytecodes into
  machine instructions and executes them
• Interpreter is known as a Java Virtual Machine
  (JVM), a program that mimics the operation of a
  real machine
• JVM reads the bytecodes produced by Java compiler
  and executes the bytecodes

Acknowledgement Cohoon and Davidson
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Task

• Ask for users name and display a welcome
  message.
• Hi ltnamegt.
• Welcome to CS1101!

Acknowledgement Cohoon and Davidson
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Sample output
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Welcome.java (1/4)
// Author Aaron Tan // Purpose Ask for users
name and display a welcome message. import
java.util. public class Welcome public
static void main(String args) Scanner
scanner new Scanner(System.in)
System.out.print(What is your name? ")
String name scanner.next()
System.out.println("Hi " name ".")
System.out.println("Welcome to CS1101!\n")
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Welcome.java (2/4)
// Author Aaron Tan // Purpose Ask for users
name and display a welcome message. import
java.util. public class Welcome public
static void main(String args) Scanner
scanner new Scanner(System.in)
System.out.print(What is your name? ")
String name scanner.next()
System.out.println("Hi " name ".")
System.out.println("Welcome to CS1101!\n")
These statements make up the action of method
main(). Method main() is part of class Welcome.
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Welcome.java (3/4)
// Author Aaron Tan // Purpose Ask for users
name and display a welcome message. import
java.util. public class Welcome public
static void main(String args) Scanner
scanner new Scanner(System.in)
System.out.print(What is your name? ")
String name scanner.next()
System.out.println("Hi " name ".")
System.out.println("Welcome to CS1101!\n")
A method is a named piece of code that performs
some action or implements a behavior.
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Welcome.java (4/4)
// Author Aaron Tan // Purpose Ask for users
name and display a welcome message. import
java.util. public class Welcome public
static void main(String args) Scanner
scanner new Scanner(System.in)
System.out.print(What is your name? ")
String name scanner.next()
System.out.println("Hi " name ".")
System.out.println("Welcome to CS1101!\n")
An application program is required to have a
public static void method named main().
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Problem Solving Process (1/3)

• Analysis
• Design
• Implementation
• Testing

Determine the inputs, outputs, and other
components of the problem. Description should be
sufficiently specific to allow you to solve the
problem.
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Problem Solving Process (1/3)

• Analysis
• Design
• Implementation
• Testing

Describe the components and associated processes
for solving the problem. Straightforward and
flexible Method process Object component and
associated methods
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Problem Solving Process (1/3)

• Analysis
• Design
• Implementation
• Testing

Develop solutions for the components and use
those components to produce an overall
solution. Straightforward and flexible
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Problem Solving Process (1/3)

• Analysis
• Design
• Implementation
• Testing

Test the components individually and collectively.
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Problem Solving Process (2/3)
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Problem Solving Process (3/3)

• Refer also to Jumpstart to SoC on course website,
  Misc, For Freshmen.

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Pólya How to Solve It (1/2)
A great discovery solves a great problem but
there is a grain of discovery in the solution of
any problem. Your problem may be modest but if
it challenges your curiosity and brings into play
your inventive faculties, and if you solve it by
your own means, you may experience the tension
and enjoy the triumph of discovery. Such
experiences at a susceptible age may create a
taste for mental work and leave their imprint on
mind and character for a lifetime. --
George Pólya
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Pólya How to Solve It (2/2)

• Phase 1 Understanding the problem
• Phase 2 Devising a plan
• Phase 3 Carrying out the plan
• Phase 4 Looking back

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Pólya How to Solve It (2/2)

• Phase 1 Understanding the problem
• Phase 2 Devising a plan
• Phase 3 Carrying out the plan
• Phase 4 Looking back

• What is the unknown? What are the data?
• What is the condition? Is it possible to satisfy
  the condition? Is the condition sufficient to
  determine the unknown?
• Draw a figure. Introduce suitable notation.

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Pólya How to Solve It (2/2)

• Phase 1 Understanding the problem
• Phase 2 Devising a plan
• Phase 3 Carrying out the plan
• Phase 4 Looking back

• Have you seen the problem before? Do you know a
  related problem?
• Look at the unknown. Think of a problem having
  the same or similar unknown.
• Split the problem into smaller sub-problems.
• If you cant solve it, solve a more general
  version, or a special case, or part of it.

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Pólya How to Solve It (2/2)

• Phase 1 Understanding the problem
• Phase 2 Devising a plan
• Phase 3 Carrying out the plan
• Phase 4 Looking back

• Carry out your plan of the solution. Check each
  step.
• Can you see clearly that the step is correct?
• Can you prove that it is correct?

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Pólya How to Solve It (2/2)

• Phase 1 Understanding the problem
• Phase 2 Devising a plan
• Phase 3 Carrying out the plan
• Phase 4 Looking back

• Can you check the result?
• Can you derive the result differently?
• Can you use the result, or the method, for some
  other problem?

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Algorithmic Problem Solving

• An algorithm is a well-defined computational
  procedure consisting of a set of instructions,
  that takes some value or set of values, as input,
  and produces some value or set of values, as
  output.

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Algorithm

• Each step of an algorithm must be exact.
• An algorithm must terminate.
• An algorithm must be effective.
• An algorithm must be general.
• Can be presented in pseudo-code or flowchart.

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Euclidean algorithm

• First documented algorithm by Greek mathematician
  Euclid in 300 B.C.
• To compute the GCD (greatest common divisor) of
  two integers.

• Let A and B be integers with A gt B 0.
• If B 0, then the GCD is A and algorithm ends.
• Otherwise, find q and r such that
• A q.B r where 0 r lt B
• Note that we have 0 r lt B lt A and GCD(A,B)
  GCD(B,r).
• Replace A by B, and B by r. Go to step 2.

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Find minimum, maximum and average (1/3)

• Version 1

First, you initialise sum to zero, min to a very
big number, and max to a very small number. Then,
you enter the numbers, one by one. For each
number that you have entered, assign it to num
and add it to the sum. At the same time, you
compare num with min, if num is smaller than min,
let min be num instead. Similarly, you compare
num with max, if num is larger than max, let max
be num instead. After all the numbers have been
entered, you divide sum by the numbers of items
entered, and let ave be this result. End of
algorithm.
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Find minimum, maximum and average (2/3)

• Version 2

sum ? count ? 0 // sum sum of numbers //
count how many numbers are entered? min ? ? //
min to hold the smallest value eventually max ?
? // max to hold the largest value eventually
for each num entered, increment count sum ?
sum num if num lt min then min ? num if num gt
max then max ? num ave ? sum / count
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Find minimum, maximum and average (3/3)

• Flowchart

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Control structures

• Sequence
• Branching (selection)
• Loop (repetition)

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Examples (1/4)

• Example 1 Compute the average of three integers.

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Examples (2/4)

• Example 2 Arrange two integers in increasing
  order (sort).

Algorithm A enter values for num1, num2 //
Assign smaller number into final1, // larger
number into final2 if num1 lt num2 then
final1 ? num1 final2 ? num2 else
final1 ? num2 final2 ? num1 // Transfer
values in final1, final2 back to num1, num2
num1 ? final1 num2 ? final2 // Display
sorted integers / print num1, num2
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Examples (3/4)

• Example 2 Arrange two integers in increasing
  order (sort).

Algorithm B enter values for num1, num2 //
Swap the values in the variables if necessary
if num2 lt num1 then temp ? num1
num1 ? num2 num2 ? temp // Display sorted
integers / print num1, num2
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Examples (4/4)

• Example 3 Find the sum of positive integers up
  to n (assuming that n is a positive integer).

Algorithm enter value for n // Initialise a
counter count to 1, and ans to 0 count ? 1 ans
? 0 while count lt n do the following ans
? ans count // add count to ans count ?
count 1 // increase count by 1 // Display
answer print ans
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Task 1 Area of a circle (1/2)

• What is the data? Side of square 2a
• What is the unknown? Area of circle, C.
• What is the condition? If radius r is known, C
  can be calculated.
• How to obtain r?

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Task 1 Area of a circle (2/2)

• Pythagoras theorem r2 2 a2
• Area of circle C ? r2 ? 2 a2

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Task 2 Pascals triangle
1 1 1 1 2 1 1 3 3 1 1 4 6 4
1 1 5 10 10 5 1
Compute nCk or C(n,k)
nCk n! / (k! (n k)!)
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Task 3 NE-paths

• To find the number of north-east paths between
  any two points.
• North-east (NE) path you may only move northward
  or eastward.
• How many NE-paths between A and C?

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Task 4 Finding maximum

• Given three numbers, find the maximum value.
• Example 4, 7, 3. Answer 7

• Can you extend the algorithm to four numbers,
  five numbers, in general, n numbers?

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Task 5 Palindrome

• A word is a palindrome if it reads the same
  forward and backward.
• Examples NOON, RADAR.
• How do you determine if a word is a palindrome?

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Task 6 Coin change

• Given this list of coin denominations 1, 50
  cents, 20 cents, 10 cents, 5 cents, 1 cent, find
  the smallest number of coins needed for a given
  amount. You do not need to list out what coins
  are used.
• Example 1 For 3.75, 6 coins are needed.
• Example 2 For 5.43, 10 coins are needed.

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