1. CS1101: Programming Methodology http://www.comp.nus.edu.sg/~cs1101x/
CS1101X Programming Methodology
CS1101: Programming Methodology
Aaron Tan

2. CS1101X Programming Methodology
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.
CS1101X Introduction

3. CS1101X Programming Methodology
History of Computers
Websites
ACM Timeline of Computing History (
The Virtual Museum of Computing (
IEEE Annals of the History of Computing (
and others (surf the web)
CS1101X Introduction

4. Computers as Information Processors (1/2)
CS1101X Programming Methodology
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.
CS1101X Introduction

5. Computers as Information Processors (2/2)
CS1101X Programming Methodology
Computers as Information Processors (2/2)
Computer are Information Processors
Computer system
Raw data
Processed information
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).
CS1101X Introduction

6. Components of a Computer (1/2)
CS1101X Programming Methodology
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 – brain’s reasoning powers
Memory – brain’s memory
Input Devices – eyes, ears, sensory sub-system
Output Devices – mouth, hands, facial and body expressions
CS1101X Introduction

7. Components of a Computer (2/2)
CS1101X Programming Methodology
Components of a Computer (2/2)
Monitor (Output)
Mouse and Keyboard (Input)
Headphone (Output)
Hardware box (contains processor, memory, buses etc.)
CS1101X Introduction

8. CS1101X Programming Methodology
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:
… …
Example: The digit in each position is multiplied by the corresponding weight:
5     = (593.68)10
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9. CS1101X Programming Methodology
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.
CS1101X Introduction

10. Base-R to Decimal Conversion
CS1101X Programming Methodology
Base-R to Decimal Conversion
( )2 = 1     = = (13.625)10
(572.6)8 = 5    = = (378.75)10
(2A.8)16 = 2   = = (42.5)10
(341.24)5 = 3     = = (96.56)10
CS1101X Introduction

11. Decimal to Binary Conversion (1/2)
CS1101X Programming Methodology
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
CS1101X Introduction

12. Decimal to Binary Conversion (2/2)
CS1101X Programming Methodology
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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13. CS1101X Programming Methodology
Mathematics
A-level Mathematics assumed.
Common concepts encountered in programming: prime numbers, complex numbers, polynomials, matrices.
Mathematical maturity desirable.
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14. CS1101X Programming Methodology
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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15. CS1101X Programming Methodology
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:
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16. CS1101X Programming Methodology
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 language for coding machine language instructions.
Example: ADD A, B, C
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17. CS1101X Programming Methodology
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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18. CS1101X Programming Methodology
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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19. CS1101X Programming Methodology
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.
Java’s clean design and wide availability make it an suitable language for teaching the fundamentals of computer programming.
CS1101X Introduction
Acknowledgement: Cohoon and Davidson

20. CS1101X Programming Methodology
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
CS1101X Introduction
Acknowledgement: Cohoon and Davidson

21. CS1101X Programming Methodology
Task
Ask for user’s name and display a welcome message.
Hi <name>.
Welcome to CS1101!
CS1101X Introduction
Acknowledgement: Cohoon and Davidson

22. CS1101X Programming Methodology
Sample output
Compilation
Interpretation
Program output
CS1101X Introduction

23. CS1101X Programming Methodology
Welcome.java (1/4)
// Author: Aaron Tan
// Purpose: Ask for user’s 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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24. CS1101X Programming Methodology
Welcome.java (2/4)
// Author: Aaron Tan
// Purpose: Ask for user’s 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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25. CS1101X Programming Methodology
Welcome.java (3/4)
// Author: Aaron Tan
// Purpose: Ask for user’s 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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26. CS1101X Programming Methodology
Welcome.java (4/4)
// Author: Aaron Tan
// Purpose: Ask for user’s 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().
CS1101X Introduction

27. Problem Solving Process (1/3)
CS1101X Programming Methodology
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.
CS1101X Introduction

28. Problem Solving Process (1/3)
CS1101X Programming Methodology
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
CS1101X Introduction

29. Problem Solving Process (1/3)
CS1101X Programming Methodology
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
CS1101X Introduction

30. Problem Solving Process (1/3)
CS1101X Programming Methodology
Problem Solving Process (1/3)
Analysis
Design
Implementation
Testing
Test the components individually and collectively.
CS1101X Introduction

31. Problem Solving Process (2/3)
CS1101X Programming Methodology
Problem Solving Process (2/3)
CS1101X Introduction

32. Problem Solving Process (3/3)
CS1101X Programming Methodology
Problem Solving Process (3/3)
Refer also to Jumpstart to SoC on course website, “Misc…”, “For Freshmen”.
CS1101X Introduction

33. Pólya: How to Solve It (1/2)
CS1101X Programming Methodology
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
CS1101X Introduction

34. Pólya: How to Solve It (2/2)
CS1101X Programming Methodology
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
CS1101X Introduction

35. Pólya: How to Solve It (2/2)
CS1101X Programming Methodology
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.
CS1101X Introduction

36. Pólya: How to Solve It (2/2)
CS1101X Programming Methodology
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 can’t solve it, solve a more general version, or a special case, or part of it.
CS1101X Introduction

37. Pólya: How to Solve It (2/2)
CS1101X Programming Methodology
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?
CS1101X Introduction

38. Pólya: How to Solve It (2/2)
CS1101X Programming Methodology
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?
CS1101X Introduction

39. Algorithmic Problem Solving
CS1101X Programming Methodology
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.
Algorithm
Input
Output
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40. CS1101X Programming Methodology
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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41. CS1101X Programming Methodology
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 > 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 < B
Note that we have 0 ≤ r < B < A and GCD(A,B) = GCD(B,r).
Replace A by B, and B by r. Go to step 2.
CS1101X Introduction

42. Find minimum, maximum and average (1/3)
CS1101X Programming Methodology
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.
CS1101X Introduction

43. Find minimum, maximum and average (2/3)
CS1101X Programming Methodology
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 < min then min  num
if num > max then max  num
ave  sum / count
CS1101X Introduction

44. Find minimum, maximum and average (3/3)
CS1101X Programming Methodology
Find minimum, maximum and average (3/3)
start
sum  count  0
min  ?
max  ?
end of input?
increment count
sum  sum + num
num < min?
min  num
Yes No
num > max?
max  num
ave  sum/count
end
Terminator box
Process box
Decision box
Flowchart
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45. CS1101X Programming Methodology
Control structures
Sequence
Branching (selection)
Loop (repetition)
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46. CS1101X Programming Methodology
Examples (1/4)
Example 1: Compute the average of three integers.
A possible algorithm:
enter values for num1, num2, num3
ave  ( num1 + num2 + num3 ) / 3
print ave
num1
Variables used:
num2
num3
ave
Another possible algorithm:
enter values for num1, num2, num3
total  ( num1 + num2 + num3 )
ave  total / 3
print ave
num1
Variables used:
num2
num3
ave
total
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47. CS1101X Programming Methodology
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 < 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
Variables used:
num1
num2
final1
final2
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48. CS1101X Programming Methodology
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 < num1
then temp  num1
num1  num2
num2  temp
// Display sorted integers */
print num1, num2
Variables used:
num1
num2
temp
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49. CS1101X Programming Methodology
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 <= n do the following
ans  ans + count // add count to ans
count  count + 1 // increase count by 1
// Display answer
print ans
Variables used: n
count
ans
CS1101X Introduction

50. Task 1: Area of a circle (1/2)
CS1101X Programming Methodology
Task 1: Area of a circle (1/2) 2a
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?
CS1101X Introduction

51. Task 1: Area of a circle (2/2)
CS1101X Programming Methodology
Task 1: Area of a circle (2/2) a r
Pythagoras’ theorem: r2 = 2 * a2
Area of circle C =  * r =  * 2 * a2
CS1101X Introduction

52. Task 2: Pascal’s triangle
CS1101X Programming Methodology
Task 2: Pascal’s triangle 1
1 1
Compute nCk or C(n,k)
nCk = n! / (k! * (n – k)!)
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53. CS1101X Programming Methodology
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? C A A A A
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54. CS1101X Programming Methodology
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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55. CS1101X Programming Methodology
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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56. CS1101X Programming Methodology
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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57. CS1101X Programming Methodology
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CS1101X Introduction