COMP101: Introduction to Programming in JAVA. Reading: Morelli Chapter 0, Chapter 2, Chapter 3, Cohoon and Davidson Chapter 1. For pseudocode see

Transcription

1 Lecture 10 Algorithm Design COMP101: Introduction to Programming in JAVA Reading: Morelli Chapter 0, Chapter 2, Chapter 3, Cohoon and Davidson Chapter 1. For pseudocode see users.csc.calpoly.edu/ jdalbey/swe/pdl_std.html Russell Martin with some materials from Clare Dixon, Michele Zito, and Frans Coenen Department of Computer Science Russell.Martin(at)liv.ac.uk www2.csc.liv.ac.uk/ martin/teaching/comp101 Russell Martin Algorithm Design 1 / 81

2 Introduction We are describing a process that should be used when solving a given programming problem in Java. First, we talked about problem decomposition into classes and their attributes and representing these using class diagrams. Several questions are still unanswered: How do we find out what computation is needed to solve a particular problem? How do we describe such computation? How do we translate such descriptions into working Java code? Russell Martin Algorithm Design 2 / 81

3 Describing Computations The underlying assumption in our approach is that any computation (in fact almost any process you can think of) can be described by a sequence of steps each being, in turn, a (simpler) computation. Thus, processes like: Go to the local shop to buy milk Prepare spaghetti carbonara Search through a list of items to find a particular one Write a book Create the best video-game ever Write a Java program can all be described in terms of a sequence of steps that need to be completed to achieve the particular goal. Russell Martin Algorithm Design 3 / 81

4 Pseudocode standards The pseudocode language is a kind of structured English for describing processes. It allows the designer to focus on the logic of the process without being distracted by details of language syntax. A pseudocode description needs to be complete: it should describe the entire logic of the particular process so that implementation becomes a mechanical task of translating line by line into source code. The vocabulary used should be that of the problem domain, not of Java. The pseudocode is a narrative for someone who knows the requirements (problem domain), and is trying to learn how the solution is organised. Russell Martin Algorithm Design 4 / 81

5 Pseudocode conventions Each textbook and each individual designer may have their own personal style of pseudocode. There is no universal standard. Remember it is intended to be read by humans not computers. The format below inspired by jdalbey/swe/pdl_std.html is recommended for COMP101. Russell Martin Algorithm Design 5 / 81

6 Pseudocode conventions There are three main ways of doing things: sequence a process described as a sequence of steps occurring one after the other. I do this, then that, then that. selection a process described in terms of alternatives. If this happens, then I do this otherwise I do that. iteration a process described in terms of repeated executions of particular actions, sometimes subject to a termination condition. While there is still a coin in my purse, I pick one, remove it from the purse and add its value to a running total. We will look at pseudocode for selection and iteration in later weeks when we cover these issues in Java. Russell Martin Algorithm Design 6 / 81

7 Sequence A sequential process is indicated by writing one action after another, each action on a line by itself, and all actions aligned with the same indentation. The actions are performed in the sequence (top to bottom) that they are written. Example (non-computer) Example Brush teeth Wash face Comb hair Smile in mirror READ height of rectangle READ width of rectangle COMPUTE area as height multiplied by width Russell Martin Algorithm Design 7 / 81

8 Common Action Keywords Several keywords are often used to indicate common input, output, and processing operations. Input: READ, OBTAIN, GET Output: PRINT, DISPLAY, SHOW Compute: COMPUTE, CALCULATE, DETERMINE Initialize: SET Add one: INCREMENT Russell Martin Algorithm Design 8 / 81

9 Object Interactions Method invocation and message exchanging are achieved by specifying, in plain English, the name of the object that is called into action, the service (method, operation, functionality) asked from the named object, and the data needed to carry out the particular task. Examples. The Swimming Pool object mypool computes the volume of the pool. [The current object is to] Generate an instance of the Swimming Pool of length 5, width 4 and depth 2. Debit the Client account with ChequeAmount. Russell Martin Algorithm Design 9 / 81

10 Method definition Methods are defined by specifying their name, their input data, and the type of result they produce. Example. Carrying on from one of the examples on the previous slide, one may define METHOD Debit Account INPUT ChequeAmount : double OUTPUT None... <pseudocode describing the processing>... Russell Martin Algorithm Design 10 / 81

11 Golden Rules The main purpose of using pseudocode is to describe the system processing at an abstract level. (!) Rule 1 As mentioned before, one should avoid language specific constructs. The description should be in the language of the problem domain. Rule 2 If a pseudocode description is about the same length as the corresponding actual code it is probably too long! A pseudocode description for a method involving essentially a single Java statement is NOT NEEDED! Carefully chosen names for the method and its parameter list give enough information about its purpose. Russell Martin Algorithm Design 11 / 81

12 Approaches How do we find out what computation is needed to solve a particular programming task? For relatively simple programming tasks (similar to those that we will consider), one possible approach is to perform a two-level step-wise refinement process: 1 Decompose the task at hand in a number (usually much less than ten) of sub-tasks. 2 Reduce the sub-tasks to Java instructions. For complex tasks (these are not the type of problems we will consider in this module), usually people apply patterns. A number of computational problems have been studied in the literature. Given a new programming task, it is often possible to reduce it to a combination of well-known tasks that are then solved by applying standard well-known techniques. Russell Martin Algorithm Design 12 / 81

13 Examples: Computing timetofill() Problem Write a program to input the length, width and depth of a rectangular swimming pool of uniform depth and calculate the time it takes to fill it. Assume the rate of flow of water into the pool is 50 litres per minute and that 1 cubic metre has a capacity of 1,000 litres of water. SwimmingPoolUser + main(string[]) SwimmingPool - RATEOFFLOW: double = UNITCAPACITY: double = length: double - width: double - depth: double +timetofill(): double Russell Martin Algorithm Design 13 / 81

14 Initial Analysis From our verb analysis, we decided we needed the calculation of the time it takes to fill the pool. This will be a number, resulting from some calculations. We need to: 1 decide who is going to have responsibility of computing this; 2 think about its input data, return value and their types; 3 define a method that will perform such computation (let s call it timetofill). Russell Martin Algorithm Design 14 / 81

15 Responsibilities The responsibility for computing this could be either given to the SwimmingPoolUser class, in which case the method needs to get the values for length, width, and depth from somewhere else as the attributes in the SwimmingPool class are private to that class. Alternatively, the operation could be assigned to the SwimmingPool class, in which case the pool sizes would be available to the operation and no additional input data is needed. This looks like part of the behaviour of SwimmingPool so we will put it there. Thus if SwimmingPool is re-used in other programs, all the relevant methods will be provided. Russell Martin Algorithm Design 15 / 81

16 Scenarios 1 If the swimming pool contained 1 cubic metre of water its capacity would be 1,000 litres (this is in the problem statement!). If it takes a minute to pour 50 litres of water in the pool it would take 1, = 20 minutes to fill such a pool. 2 By a similar argument, if the swimming pool contained 5 cubic metres of water it would take 5 1, = 100 minutes to fill it. 3 Generalising, if the swimming pool contained x cubic metres of water this number should be multiplied by the unit capacity and divided by the rate of flow to give the correct answer. Thus, we get the answer (in minutes) from the Java expression: x * UNITCAPACITY / RATEOFFLOW Russell Martin Algorithm Design 16 / 81

17 Technical Issue Conceptually, X is the volume of the pool. Since the problem statement talks of a rectangular swimming pool of uniform depth, we see that x is the volume of a cuboid. Instead of x lets use poolvolume poolvolume = length * width * depth We assume that input lengths are in metres. Russell Martin Algorithm Design 17 / 81

18 Pseudocode for timetofill() As length, width and depth are all doubles, given the calculation involved, we probably want timetofill also to output a double. Here s the full specification of the required method: METHOD timetofill INPUT OUTPUT double COMPUTE the volume of the pool poolvolume as length x width x depth RETURN (poolvolume x UNITCAPACITY) / RATEOFFLOW Remark. It is arguable whether the given pseudocode is actually needed. In effect timetofill is formed by a single line of code. A pseudocode description is a bit of an overkill. (It was given here for pedagogical reasons.) Russell Martin Algorithm Design 18 / 81

19 The main method Assuming SwimmingPool gets the responsibility of running the method timetofill, the pseudocode for the main method is as follows. METHOD main INPUT args OUTPUT LOCAL DATA lth, wth and dth (all real numbers) READ lth, wth and dth from the keyboard SET up an instance mypool of Swimming Pool setting length=lth, width=wth and depth=dth PRINT the result of calling timetofill() on mypool. Russell Martin Algorithm Design 19 / 81

20 Another Example: Average Fuel Consumption Problem Write a program to input the cost of fuel put in the car each day of the (working) week, then compute the total cost and the average cost, and display the results of the two computations. FuelCostUser + main(string[]) FuelCost - moncost: double - tuescost: double - wedcost: double - thurscost: double - fricost: double +totalcost(): double +averagecost(): double Russell Martin Algorithm Design 20 / 81

21 Behaviours Write a program to input the cost of fuel put in the car each day of the (working) week, then compute the total cost and the average cost, and display the results of the two computations. We decided that we needed two methods totalcost and averagecost. Where are these located? For similar reasons as with timetofill() we will put them in the FuelCost class. What is their return type? Probably double as we need to perform calculations on values that are doubles. What pseudocode is needed for these methods? What pseudocode is needed for the main method? Russell Martin Algorithm Design 21 / 81

22 Summary We have shown how to use pseudocode to write down the behaviour of parts of the program. We have applied this to examples. Russell Martin Algorithm Design 24 / 81

23 Lecture 11 More About Methods COMP101: Introduction to Programming in JAVA Reading: Morelli Chapter 3, Cohoon and Davidson Chapters 2 and 4 Russell Martin with some materials from Clare Dixon, Michele Zito, and Frans Coenen Department of Computer Science Russell.Martin(at)liv.ac.uk www2.csc.liv.ac.uk/ martin/teaching/comp101 Russell Martin More About Methods 25 / 81

24 Overview In this lecture we have a closer look at methods. We look at the flow of control when using methods and how to pass information to the methods. We also discuss the scope and lifetime of identifiers. We give the implementation of the timetofill() method from the SwimmingPool class. Russell Martin More About Methods 26 / 81

25 Methods One of the core features of the objects in an object-oriented system is that they should be able to do things. Methods specify the things that objects in a given class can do. A method is a group of self-contained declarations and executable statements that performs a specific task or operation. As we have already seen, Java methods have the following format: Modifiers ReturnType Name (ParamList) { StatementList } Russell Martin More About Methods 27 / 81

26 Methods: Example The following was a method in the Rectangle class to calculate the area of the rectangle. // Method that returns the area of the rectangle. public int calculatearea() { return length * width; } We could add a method to the Rectangle class that prints out the rectangle s length and width. // Print out rectangle s length and width public void printdimensions() { System.out.println("Length: " + getlength() + " Width: " + getwidth()); System.out.println(); } Russell Martin More About Methods 28 / 81

27 Methods Control Flow // program to demonstrate how to call a // programmer-defined method public class TestMethodsControlFlow { } public static void main(string [] args) { System.out.println("Execution starts in [main] method;"); display(); System.out.println("back to the [main] method."); } // method to display a message public static void display() { System.out.println(" method [display] is then called;"); } >>>How does it work?<<< Russell Martin More About Methods 29 / 81

28 Running it! The first statement in the main method will print the message starting Execution starts... to the screen. Then Java executes display(). It does so by jumping inside the body of the method display at the bottom of the listing and running the method s single statement. The sentence method [display] is then called; appears on the screen. Then execution of the method ends, and the next statement that is executed is the one immediately following the call to display. The final line back to the [main] method. will appear on the screen. $ java TestMethodsControlFlow Execution starts in [main] method; method [display] is then called; back to the [main] method. $ Russell Martin More About Methods 30 / 81

29 The return Keyword // program to demonstrate calling a method that returns // a value import java.util.scanner; public class TestMethodsWithReturnValue { public static void main(string[] args) { System.out.println("The sum is " + sum()); } } public static int sum() { int first, second; // numbers to input Scanner input = new Scanner(System.in); System.out.print("First number? "); first = input.nextint(); System.out.print("Second number? "); second = input.nextint(); return first+second; } Russell Martin More About Methods 31 / 81

30 Remarks $ java TestMethodsWithReturnValue First number? 10 Second number? 5 The sum is 15 $ The invocation to sum() in the main program creates a new execution environment with its own memory, allocates space in this memory for the variables defined inside the method, and starts executing the method s code. The statement return expression is used to assign a value to the method and return the control to the calling method. If the method type is void there is no need to use a return statement, but one may be used to force the control back to the calling method. It is syntactically legal to have many return statements inside a method... but not a very good practice for maintenance as it may become difficult to trace all of them. Russell Martin More About Methods 32 / 81

31 Parameters Methods can receive data from the calling method in several ways. We will comment on each of the available possibilities by referring to the same basic piece of code. Russell Martin More About Methods 33 / 81

32 Class or Instance Variables // program to demonstrate calling a method that // uses class or instance variables. import java.util.scanner; public class TestMethodsWithClassVars { private static int first, second; // numbers to input public static void main(string[] args) { Scanner input = new Scanner(System.in); System.out.print("First number? "); first = input.nextint(); System.out.print("Second number? "); second = input.nextint(); System.out.println("Sum of numbers is " + sum()); System.out.println("First number is now " + first); } } public static int sum() { first = first + second; return first; } Russell Martin More About Methods 34 / 81

33 Remarks As first and second are class variables they are accessible throughout the class, even in the method sum(). Assigning first + second to first in sum() means the value of first will have changed in the main method. What is output if we input 10 and 5? The static modifier was added to the declarations of first and second otherwise Java would complain as follows: TestMethodsWithReturnValue.java:12: non-static variable first cannot be referenced from a static context first = input.nextint(); ˆ What happens if the declarations of first and second are moved inside main? Russell Martin More About Methods 35 / 81

34 Method Parameters // program to demonstrate calling a method that receives its // data through a parameter list. import java.util.scanner; public class TestMethodsWithParameterPassing { public static int first, second; // numbers to input public static void main(string[] args) { Scanner input = new Scanner(System.in); System.out.print("First number? "); first = input.nextint(); System.out.print("Second number? "); second = input.nextint(); System.out.println("Sum of numbers is " + sum(first, second)); System.out.println("First number is now " + first); } public static int sum( int f, int s) { f = f+s; return f; } } Russell Martin More About Methods 38 / 81

35 Remarks How do things work in this case? Here parameters are variables of primitive data type. The parameter list in the method call must contain the same number of elements, in the same order and of the same type as the parameter list in the method definition. When sum(first, second) is called from the main method the values of the actual parameters (first and second) are evaluated and copied as values for the formal parameters (f and s). This is known as passing by value. Any changes to the formal parameters (assigning f+s to f) will not affect the actual parameters, i.e. here first and second are not affected by the method call. Question: what would happen if the parameters were called first and second? Russell Martin More About Methods 39 / 81

36 Reference Parameters I Note that for items of data that are stored by reference (e.g. objects or arrays), the parameter mechanism has slightly different effects. In such cases the actual address of the variable is passed to the calling method. Consequently, any change that happens to the parameters inside the called method will remain after the control is returned to the caller. This is similar to what happens when we assign one object to another. Rectangle rect2 = new Rectangle(); Rectangle bigrect = new Rectangle(100,35); rect2 = bigrect; Both bigrect and rect2 will refer to the same object. Russell Martin More About Methods 41 / 81

37 Reference Parameters II public class TestMethodsWithObjectParameters { // METHODS /* Main Method */ public static void main(string[] args) { // Instantiate up bigrect Rectangle bigrect = new Rectangle(100,35); // Print out its length and width System.out.println("The Big Rectangle s dimensions"); bigrect.printdimensions(); // Call changerectangle using bigrect as parameter and print Rectangle newrect = changerectangle(bigrect); System.out.println("After calling changerectangle(bigrect) "); newrect.printdimensions(); Russell Martin More About Methods 42 / 81

38 Reference Parameters III } // Print out the Big Rectangle s length and width again System.out.println("The Big Rectangle s dimensions "); bigrect.printdimensions(); } public static Rectangle changerectangle(rectangle therect) { therect.setlength(50); return therect; } This has the following output: $ java TestMethodsWithObjectParameters The Big Rectangle s dimensions Length: 100 Width: 35 After calling changerectangle(bigrect) Length: 50 Width: 35 The Big Rectangle s dimensions Length: 50 Width: 35 $ Russell Martin More About Methods 43 / 81

39 Reference Parameters IV bigrect length = 100 width =35 bigrect length = 50 width =35 bigrect length = 100 width =35 therect therect bigrect length = 50 width = 35 newrect Russell Martin More About Methods 44 / 81

40 Scope and Lifetime of Identifiers 1 The scope of an identifier refers to the region of a program in which an identifier can be used. 2 An identifier with class scope is accessible throughout the entire class and anywhere in the program where an object X of the given class is defined, prefixed by X. (dependent on modifiers e.g. public). 3 A block is any segment of code beginning with a { and ending with a }. 4 An identifier with block or local scope is accessible from its point of declaration throughout the entire block in which it is defined. Russell Martin More About Methods 45 / 81

41 Remarks Method parameters can be thought of as having block or local scope. They are only accessible within the body of the method they refer to. Class attributes are examples of variables having class scope. Method names give another example of identifiers having class scope. Russell Martin More About Methods 46 / 81

42 Scope of Identifiers // program to demonstrate calling a method that receives its // data through a parameter list. import java.util.scanner; class TestMethodsWithParameterPassing { private static int first, second; // numbers to input public static void main(string[] args) { System.out.print("First number? "); first = new Scanner(System.in).nextInt(); System.out.print("Second number? "); second = new Scanner(System.in).nextInt(); System.out.println("Sum of numbers is " + sum1(first, second)); System.out.println("First number is now " + first); } first, second and sum() have class scope } public static int sum( int f, int s) { f = f+s; return f; } f, s have local or block scope Russell Martin More About Methods 47 / 81

43 Lifetime The lifetime of an identifier is the period during which the value of the identifier exists in the computer memory. identifiers with block scope only exist during the execution of the particular block. When an object goes out of scope, garbage collection takes place. (Garbage collection is the process of reclaiming memory for re-use.) Russell Martin More About Methods 48 / 81

44 Back to the Swimming Pool Recall we had the following pseudocode for the method timetofill located in the SwimmingPool class. METHOD timetofill INPUT OUTPUT double COMPUTE the volume of the pool poolvolume as length x width x depth RETURN (poolvolume x UNITCAPACITY) / RATEOFFLOW Russell Martin More About Methods 49 / 81

45 Implementation of the method TimeToFill() /** * Compute the pool s volume as the result of * volume x UNITCAPACITY / RATEOFFLOW * and return double */ public double timetofill( ) { double mypool; } mypool = length * width * depth; return mypool * UNITCAPACITY / RATEOFFLOW; Russell Martin More About Methods 50 / 81

46 FuelCost: Pseudocode for totalcost and averagecost METHOD totalcost INPUT OUTPUT double COMPUTE the total fuel cost as moncost + tuescost + wedcost + thurscost + fricost RETURN the computed value METHOD averagecost INPUT OUTPUT double CALL totalcost() to obtain the total cost of fuel COMPUTE totalcost() / 5 RETURN the computed value How can we implement these? Russell Martin More About Methods 51 / 81

47 Summary We had a closer look at methods with respect to flow of control and parameter passing. We mentioned scope of lifetime of identifiers. We gave the implementation of the timetofill() method from the SwimmingPool class. Russell Martin More About Methods 53 / 81

48 Lecture 12 Arithmetic and the Math Class COMP101: Introduction to Programming in JAVA Morelli chapter 5, Cohoon and Davidson Chapter 2 Russell Martin with some materials from Clare Dixon, Michele Zito, and Frans Coenen Department of Computer Science Russell.Martin(at)liv.ac.uk www2.csc.liv.ac.uk/ martin/teaching/comp101 Russell Martin Arithmetic and the Math Class 54 / 81

49 Overview We introduce some of the features of the Math Class. We consider the analysis and design, implementation and testing of a program to calculate area and circumference of a circle given its radius. We discuss arithmetic testing with respect to this program. Russell Martin Arithmetic and the Math Class 55 / 81

50 Expressions Java supports the standard binary algebraic operators +, -, and / (plus the remainder operator). Recall that Java expressions may look different from their algebraic counterpart: Operator Java Algebra + x+2 x m-2 m 2 m * 2 2m or 2 m x / x / y x y or y remainder x % y x mod y Russell Martin Arithmetic and the Math Class 56 / 81

51 Division and Remainder Recall when applied to two integers / uses integer division. The result is the integer part of the usual division result. In Java 11/2 evaluates to 5, 6/2 evaluates to 3 as does 7/2. x % y gives the remainder after dividing x by y. In Java 11 % 2 evaluates to 1, 6 % 2 evaluates to 0, and 7 % 2 evaluates to 1. What is the result of 12/6 and 13/6? What is the result of 12 % 6 and 13 % 6? Russell Martin Arithmetic and the Math Class 57 / 81

52 Abbreviations: The Increment Operators Java provides a number of unary operators that are used to increment or decrement an integer variable. So k++ (or, resp. k--) has the effect of adding (resp. subtracting) one to (from) the variable k and assigning the resulting value to k. Both ++k and k++ (or --k and k--) are valid increment expressions, but with different meanings: here s the explanation in the case of positive increment, The expression j = ++k corresponds to an increment of k and then the assignment of the resulting value to j. On the other hand in j = k++ the initial value of k is assigned to variable j first and then k is increased. Be careful when using these. Russell Martin Arithmetic and the Math Class 58 / 81

53 Other Shortcut Operators Similarly, Java supplies a number of shortcut assignment operators. Their format and interpretation is given in the following table: concise form a += b a -= b a *= b a /= b a %= b equivalent verbose expression a = a + b a = a - b a = a * b a = a / b a = a % b Note that expressions such as a =* b are not allowed. Russell Martin Arithmetic and the Math Class 60 / 81

54 Operator Precedence In the next table the operators we have seen so far are listed according to precedence order, the closer to the top of the table, the higher its precedence. Operators with higher precedence are evaluated before operators with lower precedence. Operators on the same line have equal precedence. When operators of equal precedence appear in the same expression all binary operators, except for the assignment operators, are evaluated from left to right; assignment operators are evaluated right to left. Russell Martin Arithmetic and the Math Class 61 / 81

55 Operator Precedence Operators Precedence postfix expr++ expr-- unary ++expr --expr multiplicative * / % additive + - assignment = += -= *= /= %= Thus result = 3 * will evaluate to the same as result = ((3 * 8) + 2). To ensure clarity and prevent errors, use parentheses. Russell Martin Arithmetic and the Math Class 62 / 81

56 Dividing by Zero When programming, always take care to avoid dividing by zero. In Java System.out.println("5 /0 " + 5/ 0); will result in the following run-time error. Exception in thread "main" java.lang.arithmeticexception: / by zero at TestNaN.main(TestNaN.java:41) System.out.println("5.0 / 0.0 " / 0.0); System.out.println("0.0 / 0.0 " / 0.0); will result in 5.0 / 0.0 Infinity 0.0 / 0.0 NaN NaN is short for is not a number. Russell Martin Arithmetic and the Math Class 63 / 81

57 The Math class More advanced mathematical computations can be achieved using operations defined in the Math class. This class is contained in the java.lang package, included implicitly in all Java programs (no explicit import needed!). The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions. The Math class cannot be instantiated and all its methods are static class methods. Hence, they are invoked through the class name e.g. Math.round(34.2) to call the method round. For more details, see docs.oracle.com/javase/8/docs/api/java/lang/math.html Russell Martin Arithmetic and the Math Class 64 / 81

58 Approximation Functions double ceil(double a) Returns the smallest double value that is greater than or equal to the argument and is equal to a mathematical integer. E.g. Math.ceil(10.2) returns 11.0 double floor(double a) Returns the greatest double value that is less than or equal to the argument and is equal to a mathematical integer. E.g. Math.floor(10.2) returns 10.0 long round(double a) (int) Returns the long integer closest to its argument. E.g. Math.round(10.2) returns 10 double rint(double a) Returns the double value that is closest in value to the argument and is equal to a mathematical integer. E.g. Math.rint(10.2) returns 10.0 Russell Martin Arithmetic and the Math Class 65 / 81

59 Abs, Max, Min double abs(double a) It returns the absolute value of its input. E.g. Math.abs( ) returns and Math.abs(743.97) returns double max(double a, double b) Returns the greater of a and b. E.g. Math.max(543.2,532.0) returns double min(double a, double b) Returns the smaller of a and b. E.g. Math.min(543.2,532.0) returns Note abs, max, min also have versions for int, long and float which take and return parameters of the appropriate types. Russell Martin Arithmetic and the Math Class 67 / 81

60 Powers, Square Roots etc double pow(double a, double b) The expression Math.pow(a,b) computes and returns the value a b (as a double). double sqrt(double a) Returns the square root of its argument. E.g. Math.sqrt(25.0) returns 5.0 double cbrt(double a) Returns the cube root of its argument. E.g. Math.cbrt(8.0) returns 2.0 Russell Martin Arithmetic and the Math Class 68 / 81

61 Trigonometric functions double sin(double a) Returns the trigonometric sine of its argument (considered as an angle measured in radians). double cos(double a) Returns the trigonometric cosine of its argument (considered as an angle measured in radians). double tan(double a) Returns the trigonometric tangent of its argument (considered as an angle measured in radians). double double todegrees(double angrad) Converts an angle measured in radians to an approximately equivalent angle measured in degrees. toradians(double angdeg) Converts an angle measured in degrees to an approximately equivalent angle measured in radians. Russell Martin Arithmetic and the Math Class 69 / 81

62 More About the Math class Many other trigonometric functions, e.g. the inverse functions asin, acos, and atan are also provided. The following useful numbers are denoted by the constants in the Math class: e = is Math.E; and π = is Math.PI. This is only a very short review of the Math class. We did not cover all its methods and even when we did cover a method, we only provided a very short description of its behaviour. For more details read the full description available from docs.oracle.com/javase/8/docs/api/java/lang/math.html Russell Martin Arithmetic and the Math Class 70 / 81

63 Example: Circle Calculation Problem Write a program that calculates and outputs the circumference and area of a circle given its radius. radius Hints: assume that the radius is input by the user as a double; the area of a circle = π radius 2 ; Circumference = π diameter = 2 π radius; Use the constant PI from the Math class. Russell Martin Arithmetic and the Math Class 71 / 81

64 Class Analysis Very little analysis needed. The statement talks of a Circle (a class) which has a radius (an attribute). The system is supposed to calculate the circumference and the area of the circle. The use of the word calculate should lead us to believe that we will need to define methods for doing this. We assume that Circle does the relevant calculations, and we have a CircleUser class that allows the input of the circumference, instantiates Circle, and displays the results of the calculations. A possible class diagram is on the next slide. Russell Martin Arithmetic and the Math Class 72 / 81

65 Class Diagram CircleUser + main(string[]) Circle - radius: double +circumference(): double +area(): double Note that we are assigning the responsibility of computing circumference and area of the circle to the Circle class. Russell Martin Arithmetic and the Math Class 73 / 81

66 Processing The main method has the usual simple task of setting up all relevant variables, then calling the area and circumference methods, and finally displaying the result of the computation. METHOD main INPUT args OUTPUT LOCAL DATA rad READ rad from the keyboard SET up an instance mycircle of Circle using rad as radius of the structure PRINT the result of calculating the circumference and area of mycircle Russell Martin Arithmetic and the Math Class 74 / 81

67 Active Behaviours The class Circle is responsible for computing the circumference and the area of the circle Recall that the circumference of a circle having radius r is 2 π r, whereas the area of the circle is πr 2. We will not need to write any pseudocode for this. When this will become Java code, we may use the constant Math.PI to get an (approximate) value for π = , and we may use Math.pow to compute r 2 needed in the formula for the area of the circle, or we could just use the expression radius * radius. Russell Martin Arithmetic and the Math Class 75 / 81

68 The Circle Class /** * Circle.java - michele * Fri Oct :36:59 * Edited by Clare Dixon June 2010 **/ public class Circle { // attributes private double radius; // constructors public Circle(double r) { radius = r; } // calculates the circumference of a circle given radius public double circumference() { return 2*Math.PI*radius; } // calculates the area of a circle given radius public double area() { return Math.PI*radius*radius; } } Russell Martin Arithmetic and the Math Class 76 / 81

69 The CircleUser Class /** * CircleUser.java - michele * Fri Oct :35:59 * Edited by Clare Dixon June 2010 **/ import java.util.scanner; public class CircleUser { public static void main(string [] args) { Circle mycircle; Scanner input = new Scanner(System.in); double rad; System.out.print("What s the circle radius? "); rad = input.nextdouble(); mycircle = new Circle(rad); System.out.println("Circumference = " + mycircle.circumference()); System.out.println("Area = " + mycircle.area()); } } Russell Martin Arithmetic and the Math Class 77 / 81

70 Arithmetic Testing Given an arithmetic statement, it is always a good idea to test the effect that negative, positive and zero sample values will have on the outcome. In this case, there is only one numeric input, we should therefore test, negative and positive inputs as well as zero. If there is more than one input, we should test every possible combination of positive, negative and zero input. Thus, if we have two inputs we would have 3 3 possible combinations, with three inputs possible combinations (and so on). This form of testing is known as arithmetic testing. Russell Martin Arithmetic and the Math Class 78 / 81

71 Arithmetic Testing: The Circle Test Case Expected Result Radius Circumference Area Note that when we input a negative number we produce a negative circumference - this is probably not the desired result. We should return to the requirements phase and determine what action we should take in the event of a negative radius. What might this be? However, with our current level of programming skills, we will just have to live with this undesirable result. Russell Martin Arithmetic and the Math Class 79 / 81

72 Arithmetic Testing: Output The following is the actual output. $ java CircleUser What s the circle radius? 10.0 Circumference = Area = $ java CircleUser What s the circle radius? 0.0 Circumference = 0.0 Area = 0.0 $ java CircleUser What s the circle radius? Circumference = Area = $ How could we improve on the presentation of this output? Russell Martin Arithmetic and the Math Class 80 / 81

73 Summary We introduced some of the features of the Math Class We considered the analysis and design of a program to calculate some values of a circle given its radius. We gave the implementation of these classes. We discussed arithmetic testing with respect to our program. Russell Martin Arithmetic and the Math Class 81 / 81