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CS1101: Programming Methodology http://www.comp.nus.edu.sg/~cs1101x/ Aaron Tan 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 2 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/museu ms/computing.html) IEEE Annals of the History of Computing (http://www.computer.org/annals/) and others (surf the web) CS1101X Introduction 3 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 4 Computers as Information Processors (2/2) Computer are Information Processors Raw data Computer system 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 5 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 6 Components of a Computer (2/2) Headphone (Output) Monitor (Output) Hardware box (contains processor, memory, buses etc.) Mouse and Keyboard (Input) CS1101X Introduction 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, (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: 5102 + 9101 + 3100 + 610-1 + 810-2 = (593.68)10 CS1101X Introduction 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-of16. 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 9 Base-R to Decimal Conversion (1101.101)2 = 123 + 122 + 120 + 12-1 + 12-3 = 8 + 4 + 1 + 0.5 + 0.125 = (13.625)10 (572.6)8 = 582 + 781 + 280 + 68-1 = 320 + 56 + 2 + 0.75 = (378.75)10 (2A.8)16 = 2161 + 10160 + 816-1 = 32 + 10 + 0.5 = (42.5)10 (341.24)5 = 352 + 451 + 150 + 25-1 + 45-2 = 75 + 20 + 1 + 0.4 + 0.16 = (96.56)10 CS1101X Introduction 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 CS1101X Introduction 2 2 2 2 2 2 43 21 10 5 2 1 0 rem 1 LSB rem 1 rem 0 rem 1 rem 0 rem 1 MSB 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 CS1101X Introduction 0.31252=0.625 0.6252=1.25 0.252=0.50 0.52=1.00 Carry 0 1 0 1 MSB LSB 12 Mathematics A-level Mathematics assumed. Common concepts encountered in programming: prime numbers, complex numbers, polynomials, matrices. Mathematical maturity desirable. CS1101X Introduction 13 Software (1/4) Program Execution Performing the instruction sequence Programming language Sequence of instruction that tells a computer what to do Language for writing instructions to a computer Major flavors Machine language or object code Assembly language High-level CS1101X Introduction 14 Software (2/4) Program Execution Performing the instruction sequence Programming language Sequence of instruction that tells a computer what to do Language for writing instructions to a computer Major flavors Machine language or object code Program to which computer Assembly language can respond directly. Each High-level instruction is a binary code that corresponds to a native instruction. Example: 0001001101101110 CS1101X Introduction 15 Software (3/4) Program Execution Performing the instruction sequence Programming language Sequence of instruction that tells a computer what to do Language for writing instructions to a computer Major flavors Machine language or object code Assembly language Symbolic language High-level for coding machine language instructions. Example: ADD A, B, C CS1101X Introduction 16 Software (4/4) Program Execution Performing the instruction sequence Programming language Sequence of instruction that tells a computer what to do Language for writing instructions to a computer Major flavors Machine language or object code Assembly language Detailed knowledge of the High-level machine is not required. Uses a vocabulary and structure closer to the problem being solved. Examples: Java, C, C++, Prolog, Scheme. CS1101X Introduction 17 Translation High-level language programs (source programs) must be translated into machine code for execution Translator Compiler Accepts a program written in a source language and translates it to a program in a target language Standard name for a translator whose source language is a high-level language Interpreter A translator that both translates and executes a source program CS1101X Introduction 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. CS1101X Introduction Acknowledgement: Cohoon and Davidson 19 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 20 Task Ask for user’s name and display a welcome message. Hi <name>. Welcome to CS1101! CS1101X Introduction Acknowledgement: Cohoon and Davidson 21 Sample output Compilation Interpretation Program output CS1101X Introduction 22 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"); } } CS1101X Introduction 23 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. CS1101X Introduction 24 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"); } } CS1101X Introduction A method is a named piece of code that performs some action or implements a behavior. 25 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"); } } CS1101X Introduction An application program is required to have a public static void method named main(). 26 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 27 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 28 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 29 Problem Solving Process (1/3) Analysis Design Implementation Testing Test the components individually and collectively. CS1101X Introduction 30 Problem Solving Process (2/3) CS1101X Introduction 31 Problem Solving Process (3/3) Refer also to Jumpstart to SoC on course website, “Misc…”, “For Freshmen”. CS1101X Introduction 32 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 33 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 34 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 35 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 36 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 37 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 38 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. Input CS1101X Introduction Algorithm Output 39 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. CS1101X Introduction 40 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 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 41 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 42 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 43 Find minimum, maximum and average (3/3) start Terminator box Flowchart Process box sum count 0 min ? max ? Yes Decision box end of input? No increment count sum sum + num num < min? ave sum/count Yes min num Yes max num No num > max? No CS1101X Introduction end 44 Control structures Sequence Branching (selection) Loop (repetition) CS1101X Introduction 45 Examples (1/4) Example 1: Compute the average of three integers. Variables used: A possible algorithm: num1 enter values for num1, num2, num3 ave ( num1 + num2 + num3 ) / 3 print ave Variables used: num1 CS1101X Introduction num3 ave Another possible algorithm: enter values for num1, num2, num3 total ( num1 + num2 + num3 ) ave total / 3 print ave num2 num2 num3 total ave 46 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 Variables used: num1 num2 final1 final2 // Transfer values in final1, final2 back to num1, num2 num1 final1 num2 final2 // Display sorted integers */ print num1, num2 CS1101X Introduction 47 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 Variables used: num1 num2 temp // Display sorted integers */ print num1, num2 CS1101X Introduction 48 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 Variables used: n count ans // Display answer print ans CS1101X Introduction 49 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? 2a CS1101X Introduction 50 Task 1: Area of a circle (2/2) a r Pythagoras’ theorem: r2 = 2 * a2 a Area of circle C = * r2 = * 2 * a2 CS1101X Introduction 51 Task 2: Pascal’s triangle 1 1 1 Compute nCk or C(n,k) 1 2 1 nC = n! / (k! * (n – k)!) 1 3 3 1 k 1 4 6 4 1 1 5 10 10 5 1 CS1101X Introduction 52 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 CS1101X Introduction 53 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? CS1101X Introduction 54 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? CS1101X Introduction 55 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. CS1101X Introduction 56 End of File CS1101X Introduction 57