Lecture 2. CS118 Term planner. Refinement. Recall our first Java program. Program skeleton GCD. For your first seminar. For your second seminar

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1 2 Lecture 2 CS118 Term planner For your first seminar Meet at CS reception Bring The Guide Bring your CS account details Finish the problem sheet in your own time Talk to each other about the questions For your second seminar Complete Problem Sheet 2 Put your name and seminar tutors name on your solutions Post in the CS118-marked submission box in room hours before your seminar Meet at the classroom indicated on your timetable, not the lab You are here 3 Recall our first Java program Refinement /* A java program that uses Euclid s algorithm to calculate the GCD */ How did we go from this specification int a = IO.readint("Enter first number: "); int b = IO.readint("Enter second number: "); Program which calculates the GCD using Euclid s algorithm To compute the GCD of a and b, check to see if a and b are equal. If so, print one of them and then stop. Otherwise, replace the larger // while a and b not equal if (a > b ) a = a- b; else b = b- a; // replace larger by the to high-level program code? This process of conversion (in a programming context) is known as refinement 4 5 Program skeleton GCD Most of our early Java programs will have the following form The file name (S.java) should correspond to the class name File named GCD.java public class S // P // A program that calculates the GCD of two numbers a and b using // Euclid s algorithm 6 15

2 23 Understanding the specification GCD To compute the GCD of a and b, check to see if a and b are equal. If so, print one of them and then stop. Otherwise, replace the larger Precondition: Input: Calculates: Output: When should the program work? Does the program need any input? What should the program calculate? Is there any output? Postcondition: What is the state after execution? // Input: takes two numbers a and b 24 Input for GCD program GCD with input Using the Warwick IO library To input an Integer use the readint method int a=io.readint( Enter first number: ); This code performs four functions it declares an integer variable called a it prompts the user for some input using IO.readint an integer is read from input (keyboard) it assigns the integer value to a int a= IO.readint( Enter first number: ); int b= IO.readint( Enter second number: ); Note: int a; // Declaration without assignment Integers in Java Ariane 5 When you use a data type like int, you should know what values it can represent. The data type int represents the numbers European Space Agency rocket which was launched on June at the cost of approx. $7 billion Ariane 5 re-used the code from the thrust control unit of the Ariane 4-2,147,483,648 to +2,147,483,647 How did I know this? Does it really matter? The speed of A5 was greater than A4, but designers did not check the range of values which the software could represent 1. What happens if I ignore this detail? 2. OK, then how do I remember this detail? Once A5 reached a certain speed there was an overflow - at which time the processor shut down This caused the rocket to jump sideways

3 35 Number Systems The byte number type Positive numbers The smallest number type in Java is byte Base 10 (3 digits) s 10s 1s It uses one byte of storage space = (3 * 100) + (5 * 10) + (2 *1) Base 2 (3 digits) One byte on a computer is made up of 8 bits s 2s 1s Therefore, range (in 2s-comp) is -128 to = (1 *4) + (0 *2) + (1 *1) Negative numbers Use left-most digit as negative 352 = (3* -100) + (5*10) + (2*1) = = and = = (1* -4) + (0*2) + (1*1) = -3 Remember this range as -2 7 to Other Java number types Strengthen the precondition Type Size Range byte 1 byte -128 to to short 2 bytes to to // provided <= a,b <= int a= IO.readint( Enter first number: ); int b= IO.readint( Enter second number: ); int 4 bytes to long 8 bytes a large range! to to OK, so a and b have a restricted range so what? Equality is decided using the == (equals) and!= (not equals) operators e.g. 3 == 3 will result in the answer true 3 == 4 will result in the answer false 3!= 4 will result in the answer true So we can use a!=b to tell if they are different While the numbers are not the same we replace the larger one by their difference if (a > b) a = a - b; else b = b - a; // replace larger by 49 50

4 51 GCD with calculation part if (a > b) a = a - b; else b = b - a; // replace larger by Execution order 1. Check equality between a and b 2. If they are the same don t do anything 3. While they are different, repeat the code in the s 4. If a is greater than b then assign a the difference, else assign b the difference //...provided <= a,b <= int a = IO.readint("Enter first number: "); int b = IO.readint("Enter second number: "); if (a > b) a = a - b; else b = b - a; // replace larger by 56 Is the precondition correct? Output part for GCD Precondition: <= a,b <= If the inputs are in this range can we ensure that the program works every time? if (a > b) a = a - b; else b = b - a; What happens after one iteration of the loop? Will you need to strengthen the precondition? Java also has built-in library functions for output System.out.println( prints this text followed by a carriage return ); System.out.print( prints this text ); System.out.print(a); // prints the value of the variable a Output part for GCD And finally We could have used the format System.out.println("The GCD is: " + a); to gain the same result The + here stands for append; not for addition The compiler resolved this overloading using the following rules: when the two arguments are integers, it is addition when one of the arguments is a string, it is append 60 //...provided 0 < a,b <= int a = IO.readint("Enter first number: "); int b = IO.readint("Enter second number: "); if (a > b) a = a - b; else b = b - a; // replace larger by 62

5 63 is the postcondition correct? How do we check? 1. Start with the precondition 2. User enters some numbers in this range 3. Some code is repeated until the values are equal 4. Euclid has ensured that a and b converge to 1 5. When the values are equal, one of them is printed on the screen