CS1101: Programming Methodology

Week 1: Introduction  Chapter 0: Introduction to Computers and Programming Languages  Binary numbers  High-level programming languages  Useful problem-solving strategies.  Writing algorithms in pseudo-codes. © CS1101 (AY Semester 1)Week1 - 2

Chapter 0: Introduction to Computers and Programming Languages  From Thomas Wu’s book.  Please read up on your own. © CS1101 (AY Semester 1)Week1 - 3

Computers as Information Processors (1/2)  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. © CS1101 (AY Semester 1)Week1 - 4

Computers as Information Processors (2/2) Computer are Information Processors Data Units: 1 bit (binary digit): 0 or 1. 1 byte: 8 bits. 1 word: 1, 2, or 4 bytes, or more (depends on computer). Computer system Raw data Processed information © CS1101 (AY Semester 1) Week1 - 5

Components of a Computer (1/2)  Main Components:  Processor (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:  Processor – brain’s reasoning powers  Memory – brain’s memory  Input Devices – eyes, ears, sensory sub-system  Output Devices – mouth, hands, facial and body expressions © CS1101 (AY Semester 1) Week1 - 6

Components of a Computer (2/2) Monitor (Output) Mouse and Keyboard (Input) Headphone (Output) Hardware box (contains processor, memory, buses etc.) © CS1101 (AY Semester 1) Week1 - 7

Decimal Number System Also called the base-10 number system. 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In general, (a n a n-1 … a 0. f 1 f 2 … f m ) 10 = (a n x 10 n ) + (a n-1 x10 n-1 ) + … + (a 0 x 10 0 ) + (f 1 x ) + (f 2 x ) + … + (f m 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 © CS1101 (AY Semester 1) Week1 - 8

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. © CS1101 (AY Semester 1) Week1 - 9

Base-R to Decimal Conversion  ( ) 2 = 1      2 -3 = = (13.625) 10  (572.6) 8 = =  (2A.8) 16 = =  (341.24) 5 = = © CS1101 (AY Semester 1) Week1 - 10

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 © CS1101 (AY Semester 1) Week1 - 11

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 © CS1101 (AY Semester 1) Week1 - 12

Mathematics  A-level Mathematics assumed.  Common concepts encountered in programming: prime numbers, complex numbers, polynomials, matrices.  Mathematical maturity desirable. © CS1101 (AY Semester 1) Week1 - 13

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 © CS1101 (AY Semester 1) Week1 - 14

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: © CS1101 (AY Semester 1) Week1 - 15

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 © CS1101 (AY Semester 1) Week1 - 16

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. © CS1101 (AY Semester 1) Week1 - 17

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 © CS1101 (AY Semester 1) Week1 - 18

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. Acknowledgement: Cohoon and Davidson © CS1101 (AY Semester 1) Week We will focus on this.

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 © CS1101 (AY Semester 1) Week1 - 20

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. © CS1101 (AY Semester 1) Week1 - 21

Problem Solving Process (1/3) Analysis Design Implementation Testing Describe the components and associated processes for solving the problem. © CS1101 (AY Semester 1) Week1 - 22

Problem Solving Process (1/3) Analysis Design Implementation Testing Develop solutions for the components and use those components to produce an overall solution. © CS1101 (AY Semester 1) Week1 - 23

Problem Solving Process (1/3) Analysis Design Implementation Testing Test the components individually and collectively. © CS1101 (AY Semester 1) Week1 - 24

Problem Solving Process (2/3) © CS1101 (AY Semester 1) Week1 - 25

Problem Solving Process (3/3) Refer also to Jumpstart to SoC on course website, “Misc…”, “For Freshmen”. © CS1101 (AY Semester 1) Week1 - 26

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 © CS1101 (AY Semester 1) Week1 - 27

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 © CS1101 (AY Semester 1) Week1 - 28

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. © CS1101 (AY Semester 1) Week1 - 29

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. © CS1101 (AY Semester 1) Week1 - 30

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? © CS1101 (AY Semester 1) Week1 - 31

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? © CS1101 (AY Semester 1) Week1 - 32

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 InputOutput © CS1101 (AY Semester 1) Week1 - 33

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. © CS1101 (AY Semester 1) Week1 - 34

Euclidean algorithm First documented algorithm by Greek mathematician Euclid in 300 B.C.  To compute the GCD (greatest common divisor) of two integers. 1.Let A and B be integers with A > B ≥ 0. 2.If B = 0, then the GCD is A and algorithm ends. 3.Otherwise, find q and r such that A = q.B + r where 0 ≤ r < B 4. Replace A by B, and B by r. Go to step 2. © CS1101 (AY Semester 1) Week1 - 35

Find maximum and average of a list of numbers (1/3) Version 1 Declare variables sum, count and max. First, you initialise sum, count and max to zero. Then, you enter the input numbers, one by one. For each number that you have entered, assign it to num and add it to the sum. Increase count by 1. At the same time, 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. Print max and ave. End of algorithm. © CS1101 (AY Semester 1) Week1 - 36

Find maximum and average of a list of numbers (2/3) Version 2 sum  count  0// sum = sum of numbers // count = how many numbers are entered? max  0// max to hold the largest value eventually for each num entered, count  count + 1 sum  sum + num if num > max then max  num ave  sum / count print max, ave © CS1101 (AY Semester 1) Week1 - 37

Find maximum and average of a list of numbers (3/3) Flowchart © CS1101 (AY Semester 1) Week start sum  count  0 max  0 end of input? increment count sum  sum + num Yes No num > max? Yes No max  num ave  sum/count end Terminator box Process box Decision box print max, ave

Handling a list (1/2) In the previous example, we compute the maximum as we read in the input numbers one by one. In many applications, it might be desirable to read in the whole list of numbers first, then we work on the list. To do this, we need to introduce some notation. Given a list A with n items, we may refer to the individual items as A 0, A 1, A 2, …, A n-1 © CS1101 (AY Semester 1) Week1 - 39

Handling a list (2/2) We can then write version 3: © CS1101 (AY Semester 1) Week count  0// count = how many numbers are entered? while not end of input enter value for A count count  count + 1 sum  0// sum = sum of numbers max  0// max to hold the largest value eventually for i from 0 to count – 1 sum  sum + A i if A i > max then max  A i ave  sum / count print max, ave

Control structures Sequence Branching (selection) Loop (repetition) © CS1101 (AY Semester 1) Week1 - 41

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: num2num3 ave Another possible algorithm: enter values for num1, num2, num3 total  ( num1 + num2 + num3 ) ave  total / 3 print ave num1 Variables used: num2num3 ave total © CS1101 (AY Semester 1) Week1 - 42

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: num1num2 final1final2 © CS1101 (AY Semester 1) Week1 - 43

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: num1num2 temp © CS1101 (AY Semester 1) Week1 - 44

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 © CS1101 (AY Semester 1) Week1 - 45

Step-wise Refinement (1/2) From preceding examples, we can see that in general an algorithm comprises three steps:  Input (read data (at the moment from user))  Compute (process the input data to generate some answers)  Output (display the answers) The ‘compute’ step is in general the most complex. Step-wise refinement – breaking down a complex step into smaller steps. © CS1101 (AY Semester 1) Week1 - 46

Step-wise Refinement (2/2) Example: Given a list A containing n integers, how would you find the second largest value in the list? Before we begin, remember Phase 1 of “How To Solve It”: Understanding the problem.  Is the problem clear? If not, ask questions! One possible algorithm: © CS1101 (AY Semester 1) Week read values into A// step 1: input sort A in descending order// step 2: compute print A 1 // step 3: output

Step-wise Refinement (3/3) We can actually stop here, if we are clear about how to do each step. If not, we need to refine the step. For instance, step 2, how do we sort?  We won’t discuss this now as sorting will be covered later. Can you solve this problem without using sorting? © CS1101 (AY Semester 1) Week1 - 48

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? 2a2a © CS1101 (AY Semester 1) Week1 - 49

Task 1: Area of a circle (2/2) Pythagoras’ theorem: r 2 = 2 * a 2 Area of circle C =  * r 2 =  * 2 * a 2 a a r © CS1101 (AY Semester 1) Week1 - 50

Task 2: Pascal’s triangle Compute n C k or C(n,k) © CS1101 (AY Semester 1) Week n C k = n-1 C k-1 + n-1 C k 1, if k=0 or k=n 0C00C0 1C01C0 1C11C1 3C13C1 5C35C3

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 © CS1101 (AY Semester 1) Week1 - 52

Task 4: Palindrome A word is a palindrome if it reads the same forward and backward.  Examples: NOON, RADAR. How do you determine if a word W is a palindrome? © CS1101 (AY Semester 1) Week1 - 53

Task 5: Anagrams Two phrases are anagrams if one is formed by rearranging the letters of the other, disregarding spaces and punctuation marks.  Examples: “Debit card” = “Bad credit”; “The eyes” = “They see”; “Astronomer” = “Moon starer”; “A telescope” = “To see place”; “A decimal point” = “I’m a dot in place”. For our purpose, we’ll do a simpler version on words without spaces or punctuation marks, and all letters are in capital.  Example: “LISTEN” = “SILENT”. How do you determine if two words X and Y are anagrams? © CS1101 (AY Semester 1) Week1 - 54

Task 6: Coin change Given this list of coin denominations: 1¢, 5¢, 10¢, 20¢, 50¢, and $1, 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. For simplicity, assume that the input data is in cents. © CS1101 (AY Semester 1) Week1 - 55

Algorithm before coding Preceding examples show that we can discuss problems and their solutions (algorithms) without writing out the codes. A sample program development process:  Understanding the problem (if in doubt, ask questions!): 5 minutes  Writing the algorithm: 30 minutes  Testing the algorithm: 20 minutes  Writing the program: 20 minutes  Testing and debugging the program: 30 minutes to 3 hours or more For more complex problems, time spent in thinking about the algorithm could far exceed time spent in writing the program. The more time you invest in writing a good algorithm, the more time you will save in debugging your program. © CS1101 (AY Semester 1) Week1 - 56

Summary for Today Today’s most important lessons  Module objectives and resources  Module website, IVLE, This CS1101 Handy Handbook, etc.  Problem-solving  As a systematic, logical process  Steps in problem-solving  Algorithms  How to write pseudo-codes  Control structures: sequence, selection, repetition © CS1101 (AY Semester 1) Week1 - 57

Announcements/Things-to-do Discussion classes start in week 3. Check out IVLE regularly for announcements and updates. To prepare for next week:  Visit module website and IVLE  Read “This CS1101 Handy Handbook”  Read Chapters 1 and 2 and their PowerPoint files before you come for lecture © CS1101 (AY Semester 1) Week1 - 58

End of File © CS1101 (AY Semester 1) Week1 - 59