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182 Methods Chapter 6 Method Description Example Abs( x ) absolute value of x Abs( 23.7 )is 23.7 Abs( 0 )is 0 Abs( -23.7 )is 23.7 Ceiling( x ) rounds x to the smallest integer Ceiling( 9.2 ) is 10.0 not less than x Ceiling( -9.8 )is -9.0 Cos( x ) trigonometric cosine of x Cos( 0.0 ) is 1.0 (x in radians) Exp( x ) exponential method ex Exp( 1.0 ) is approximately 2.7182818284590451 Exp( 2.0 ) is approximately 7.3890560989306504 Floor( x ) rounds x to the largest integer Floor( 9.2 )is 9.0 not greater than x Floor( -9.8 )is -10.0 Log( x ) natural logarithm of x (base e) Log( 2.7182818284590451 ) is approximately 1.0 Log( 7.3890560989306504 ) is approximately 2.0 Max( x, y ) larger value of x and y Max( 2.3, 12.7 )is 12.7 (also has versions for float, Max( -2.3, -12.7 )is -2.3 intand long values) Min( x, y ) smaller value of x and y Min( 2.3, 12.7 )is 2.3 (also has versions for float, Min( -2.3, -12.7 )is -12.7 intand long values) Pow( x, y ) x raised to power y (xy) Pow( 2.0, 7.0 )is 128.0 Pow( 9.0, .5 ) is 3.0 Sin( x ) trigonometric sine of x Sin( 0.0 ) is 0.0 (x in radians) Sqrt( x ) square root of x Sqrt( 900.0 )is 30.0 Sqrt( 9.0 )is 3.0 Tan( x ) trigonometric tangent of x Tan( 0.0 ) is 0.0 (x in radians) Fig. 6.2 Commonly used Math class methods. There are several motivations for modularizing a program with methods. The divideand- conquer approach makes program development more manageable. Another motivation is software reusability using existing methods (and classes) as building blocks to create new programs. With proper method naming and definition, we can create programs from standardized methods, rather than building customized code. For example, we did not have to define how to convert strings to integers The .NET Framework Class Library already defines such methods for us (Int32.Parse). A third motivation is to avoid repeating code in a program. Packaging code as a method allows that code to be executed from several locations in a program we simply have to call that method.
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Chapter 6 Methods 181 6.3 Math Class Methods Math class methods allow the programmer to perform certain common mathematical calculations. We use various Math class methods to introduce the concept of methods in general. Throughout the book, we discuss many other methods from the classes of the Framework Class Library. Methods are called by writing the name of the method, followed by a left parenthesis, the argument (or a comma-separated list of arguments) of the method and a right parenthesis. The parentheses may be empty, if we are calling a method that needs no information to perform its task. For example, a programmer wishing to calculate and print the square root of 900.0 might write Console.WriteLine( Math.Sqrt( 900.0 ) ); When this statement executes, the method Math.Sqrt calculates the square root of the number in parentheses (900.0). The number 900.0 is the argument to the Math.Sqrt method. The Math.Sqrt method takes an argument of type double and returns a result of type double. The preceding statement uses the result of method Math.Sqrt as the argument to method Console.WriteLine and displays 30.0. Note that all Math class methods must be invoked by preceding the method name with the class name Math and a dot (.) operator (also called the member access operator). Software Engineering Observation 6.3 It is not necessary to add an assembly reference to use the Math class methods in a program. Class Math is located in namespace System, which is available to every program. Common Programming Error 6.1 Forgetting to invoke a Math class method by preceding the method name with the class name Math and a dot operator (.) results in a syntax error. Method arguments may be constants, variables or expressions. If c1=13.0, d=3.0 and f=4.0, then the statement Console.WriteLine( Math.Sqrt( c1 + d * f ) ); calculates and displays the square root of 13.0+3.0*4.0=25.0, which is 5.0. Figure 6.2 summarizes some Mathclass methods. In this figure, the variables x and y are of type double; however, many of the methods provide versions that take values of other data types as arguments. The Mathclass also defines two commonly used mathematical constants Math.PI (3.14159265358979323846) and Math.E (2.7182818284590452354). The constant Math.PI of class Mathis the ratio of a circle s circumference to its diameter. The constant Math.E is the base value for natural logarithms (calculated with the Math.Log method). 6.4 Methods Methods allow programmers to modularize programs. Variables declared in method definitions are local variables only the method that defines them knows they exist. Most methods have a list of parameters that enable method calls to communicate information between methods. A method s parameters are also variables local to that method and are not visible in any other methods.
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180 Methods Chapter 6 operations, error checking and many other useful operations. This set of modules makes the programmer s job easier, because the modules provide many of the capabilities programmers need. The FCL methods are part of the .NET Framework, which includes FCL classes Console and MessageBox used in earlier examples. Software Engineering Observation 6.1 Familiarize yourself with the rich collection of classes and methods in the FCL. Software Engineering Observation 6.2 When possible, use .NET Framework classes and methods instead of writing new classes and methods. This reduces program development time and avoids the introduction of new errors. The programmer can write methods to define specific tasks that may be used at many points in a program. Such methods are known as programmer-defined (or user-defined) methods. The actual statements defining the method are written only once and are hidden from other methods. A method is invoked (i.e., made to perform its designated task) by a method call. The method call specifies the name of the method and may provide information (as arguments) that the called method requires to perform its task. When the method call completes, the method either returns a result to the calling method (or caller) or simply returns control to the calling method. A common analogy for this is the hierarchical form of management. A boss (the calling method or caller) asks a worker (the called method) to perform a task and report back (i.e., return) the results after completing the task. The boss method does not know how the worker method performs its designated tasks. The worker may also call other worker methods, and the boss will be unaware of these calls. We will see how this hiding of implementation details promotes good software engineering. Figure 6.1 shows a boss method communicating with worker methods worker1, worker2 and worker3 in a hierarchical manner. Note that worker1 acts as a boss method to worker4 and worker5 in this particular example. Boss Worker3 Worker2 Worker1 Worker4 Worker5 Fig. 6.1 Hierarchical boss method/worker method relationship.
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Chapter 6 Methods 179 Outline 6.1 Introduction 6.2 Program Modules in C# 6.3 Math Class Methods 6.4 Methods 6.5 Method Definitions 6.6 Argument Promotion 6.7 C# Namespaces 6.8 Value Types and Reference Types 6.9 Passing Arguments: Pass-by-Value vs. Pass-by-Reference 6.10 Random-Number Generation 6.11 Example: Game of Chance 6.12 Duration of Variables 6.13 Scope Rules 6.14 Recursion 6.15 Example Using Recursion: The Fibonacci Series 6.16 Recursion vs. Iteration 6.17 Method Overloading Summary Terminology Self-Review Exercises Answers to Self-Review Exercises Exercises 6.1 Introduction Most computer programs that solve real-world problems are much larger than the programs presented in the first few chapters of this text. Experience has shown that the best way to develop and maintain a large program is to construct it from small, simple pieces, or modules. This technique is known as divide and conquer. This chapter describes many key features of the C# language that facilitate the design, implementation, operation and maintenance of large programs. 6.2 Program Modules in C#1 Modules in C# are called methods and classes. C# programs are written by combining new methods and classes that the programmer writes with prepackaged methods and classes available in the .NET Framework Class Library (FCL). In this chapter, we concentrate on methods. We discuss classes in detail in Chapter 8, Object-Based Programming. The FCL provides a rich collection of classes and methods for performing common mathematical calculations, string manipulations, character manipulations, input/output 1. It is important to note that we are discussing modules in an abstract sense. In C#, there is another form of code packaging (other than assemblies), called modules. This is not what we are discussing in this chapter, but the reader should know that this term can be used in two ways.
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6 Methods Objectives To construct programs modularly from small pieces called methods. To introduce the common math methods available in the Framework Class Library. To be able to create new methods. To understand the mechanisms for passing information between methods. To introduce simulation techniques that use random number generation. To understand how the visibility of identifiers is limited to specific regions of programs. To understand how to write and use methods that call themselves. Form ever follows function. Louis Henri Sullivan E pluribus unum. (One composed of many.) Virgil O! call back yesterday, bid time return. William Shakespeare Call me Ishmael. Herman Melville When you call me that, smile. Owen Wister
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Chapter 5 Control Structures: Part 2 177 5.6 (Pythagorean Triples) A right triangle can have sides that are all integers. A set of three integer values for the sides of a right triangle is called a Pythagorean triple. These three sides must satisfy the relationship that the sum of the squares of the two sides is equal to the square of the hypotenuse. Write a program to find all Pythagorean triples for side1, side2and hypotenuse, none larger than 30. Use a triple-nested for loop that tries all possibilities. This is an example of brute force computing. You will learn in more advanced computer science courses that there are several problems for which there is no other known algorithmic approach. 5.7 Write a program that displays the following patterns separately, one below the other. Use for loops to generate the patterns. All asterisks (*) should be printed by a single statement of the form Console.Write(’*');(this causes the asterisks to print side by side). A statement of the form Console.WriteLine(); can be used to position to the next line. A statement of the form Console.Write('’); can be used to display spaces for the last two patterns. There should be no other output statements in the program. [Hint: The last two patterns require that each line begin with an appropriate number of blanks.] (A) (B) (C) (D) * ********** ********** * ** ********* ********* ** *** ******** ******** *** **** ******* ******* **** ***** ****** ****** ***** ****** ***** ***** ****** ******* **** **** ******* ******** *** *** ******** ********* ** ** ********* ********** * * ********** 5.8 Modify Exercise 5.7 to combine your code from the four separate triangles of asterisks into a single program that prints all four patterns side by side, making clever use of nested for loops. 5.9 Write a program that prints the following diamond shape. You may use output statements that print a single asterisk (*), a single space or a single newline character. Maximize your use of repetition (with nested for structures) and minimize the number of output statements. * *** ***** ******* ********* ******* ***** *** * 5.10 Modify the program you wrote in Exercise 5.9 to read an odd number in the range from 1 to 19 to specify the number of rows in the diamond. Your program should then display a diamond of the appropriate size.
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176 Control Structures: Part 2 Chapter 5 b) Math.Pow( 2.5, 3 ) c) x = 1; while ( x <= 20 ) { Console.Write( x ); if ( x % 5 ==0 ) Console.WriteLine(); else Console.Write( 't' ); ++x; } d) for ( x = 1; x <= 20; x++ ) { Console.Write( x ); if ( x % 5 ==0 ) Console.WriteLine(); else Console.Write( 't' ); } or for ( x = 1; x <= 20; x++ ) if ( x % 5 ==0 ) Console.WriteLine( x ); else Console.Write( x + "t" ); EXERCISES 5.4 The factorial method is used frequently in probability problems. The factorial of a positive integer n (written n! and pronounced n factorial ) is equal to the product of the positive integers from 1 to n. Write a program that evaluates the factorials of the integers from 1 to 20 with different integer data types. Display the results in a three-column output table. [Hint: create a Windows application, using Labels as the columns and the 'n' character to line up rows.] The first column should display the n values (1-20). The second column should display n!, calculated with int (Int32, a 32bit integer value). The third column should display n!, calculated with long(Int64, a 64-bit integer value). What happens when int (Int32) is too small in size to hold the result of a factorial calculation? 5.5 Write two programs that each print a table of the binary, octal, and hexadecimal equivalents of the decimal numbers in the range 1 256. If you are not familiar with these number systems, read Appendix C, Number Systems, first. a) For the first program, print the results to the console without using any string formats. b) For the second program, print the results to the console using both the decimal and hexadecimal string formats (there are no formats for binary and octal in C#).
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Chapter 5 Control Structures: Part 2 175 i) The break statement, when executed in a repetition structure, causes immediate exit from the repetition structure. j) The || operator has a higher precedence than the && operator. 5.2 Fill in the blanks in each of the following statements: a) Specifying the order in which statements are to be executed in a computer program is called . b) Placing a semicolon after a for statement typically results in a error. c) A forloop should count with values. d) Using the < relational operator instead of <=in a while-repetition condition that should loop 10 times (as shown below) causes an error: int x =1; while ( x < 10 ) e) A control variable initialized within a for loop can be used only in the body of the loop. This is called the of the variable. f) In a for loop, incrementing occurs the body of the structure is performed each time. g) Multiple initializations in the for structure header should be separated by . h) Placing expressions whose values do not change inside can lead to poor per formance. i) The four types of MessageBox icons are exclamation, information, error and . j) The value in parentheses immediately following the keyword switch is called the . 5.3 Write a C# statement or a set of C# statements to accomplish each of the following tasks: a) Sum the odd integers between 1 and 99, using a forstructure. Assume that the integer variables sum and counthave been declared. b) Calculate the value of 2.5 raised to the power of 3, using the Math.Powmethod. c) Print the integers from 1 to 20, using a while loop and the counter variable x. Assume that the variable x has been declared, but not initialized. Print only five integers per line. [Hint: Use the calculation x % 5. When the value of this is 0, print a newline character; otherwise, print a tab character. Use the Console.WriteLine() method to output the newline character, and use the Console.Write('t') method to output the tab character.] d) Repeat part c, using a for structure. ANSWERS TO SELF-REVIEW EXERCISES 5.1 a) False. The default case is optional. If no default action is required, then there is no need for a default case. b) True. c) False. Both of the relational expressions must be true for the entire expression to be true. d) True. e) False. The expression (x<=y&&y>4) is true if x is less than or equal to yand y is greater than 4. f) False. A for loop requires two semicolons in its header. g) False. Infinite loops are caused when the loop-continuation condition is always true. h) True. i) True. j) False. The &&operator has higher precedence than the || operator. 5.2 a) program control. b) logic. c) integral. d) off-by-one. e) scope. f) after. g) comma. h) loops. i) question. j) controlling expression. 5.3 a) sum = 0; for ( count = 1; count <= 99; count += 2 ) sum += count;
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174 Control Structures: Part 2 Chapter 5 hexadecimal (base16) number system nested building block icons for message dialogs nested control structure if structure nesting rule if/else structure off-by-one error increment expression one-based counting infinite loop optimization initialization section of a for structure overlapped building block iteration of a loop Pow method of class Math labels in a switch structure program-construction principles levels of nesting rectangle symbol logical AND operator (&) repetition logical exclusive OR operator (^) scope of a variable logical negation (!) selection logical NOT or logical negation operator (!) sequence logical operators short-circuit evaluation logical OR operator (|) side effect loop body simple condition loop counter simplest flowchart loop-continuation condition single selection Math class single-entry/single-exit control structure message-dialog buttons small circle symbol message-dialog icons stacking MessageBoxButton.AbortRetryIgnorestacking rule MessageBoxButton.OK string formatting codes MessageBoxButton.OKCancel structured programming MessageBoxButton.RetryCancel switch structure MessageBoxButton.YesNo title bar string MessageBoxButton.YesNoCancel truth table MessageBoxIcon.Error unary operator MessageBoxIcon.Exclamation unstructured flowchart MessageBoxIcon.Information while structure MessageBoxIcon.Question X formatting code multiple-selection structure zero-based counting N formatting code SELF-REVIEW EXERCISES 5.1 State whether each of the following is true or false. If false, explain why. a) The default case is required in the switch selection structure. b) If there is more than one statement in the body of the for, braces ({ and }) are needed to define the body of the loop. c) The expression (x >y&& ay is true or a 4) is true if x is less than or equal to y or y is greater than 4. f) A forloop requires two commas in its header. g) Infinite loops are caused when the loop-termination condition is always true. h) The following syntax continues iterating the loop while 10 < x < 100: while ( x > 10&& x < 100 );
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