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226 Methods Chapter 6 The programmer can write methods to define specific tasks that may be used at many points in a program. These methods sometimes are referred to as programmer-defined methods. The actual statements defining the method are written only once and are hidden from other methods. Methods are called by writing the name of the method (sometimes preceded by the class name and a dot operator), followed by a left parenthesis, the method s argument (or a comma-separated list of arguments) and a right parenthesis. All variables declared in method definitions are local variables they are known only in the method in which they are defined. Packaging code as a method allows that code to be executed from several locations in a program when the method is called. The return statement in a method passes the results of the method back to the calling method. The format of a method definition is return-value-type method-name( parameter-list ) { declarations and statements } The first line of a method definition is sometimes known as the method header. The attributes and modifiers in the method header are used to specify information about the method. The method return-value-type is the data type of the result that is returned from the method to the caller. Methods can return one value at most. The parameter-list is a comma-separated list containing the declarations of the parameters received by the called method. There must be one argument in the method call for each parameter in the method definition. The declarations and statements within the braces that follow the method header form the method body. Variables can be declared in any block, and blocks can be nested. A method cannot be defined inside another method. In many cases, an argument value that does not correspond precisely to the parameter types in the method definition is converted to the proper type before the method is called. When an argument is passed by value, a copy of the argument s value is made and passed to the called method. With pass-by-reference, the caller enables the called method to access the caller s data directly and to modify that data if the called method chooses. The class Random can be used to generate random numbers. An event is a signal that is sent to a program when some action takes place, such as when the user clicks a button. The programmer writes the application to perform tasks when these events occur. An event handler is a method that executes when an event occurs (or is raised ). An identifier s duration (its lifetime) is the period during which that identifier exists in memory. Identifiers that represent local variables in a method (i.e., parameters and variables declared in the method body) have automatic duration. Automatic-duration variables are created when program control reaches the variable s declaration. They exist while the block in which they are declared is active, and they are destroyed when the block in which they are declared is exited. The scope (sometimes called a declaration space) of an identifier for a variable, reference or method is the portion of the program in which that identifier can be referenced.
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Chapter 6 Methods 225 So far, the logical names of methods that have been used by the compiler have not mentioned the methods return types. This is because method calls cannot be distinguished by return type. The program in Fig. 6.19 illustrates the syntax error that is generated when two methods have the same signature and different return types. Overloaded methods with different parameter lists can have different return types. Overloaded methods need not have the same number of parameters. Common Programming Error 6.17 Creating overloaded methods with identical parameter lists and different return types is a syntax error. SUMMARY The best way to develop and maintain a large program is to construct it from small pieces, or modules. This technique is called divide and conquer. Modules can be created with methods and classes. Programs are written by combining new methods and classes that the programmer writes with prepackaged methods and classes in the .NET Framework Library, and in various other method and class libraries. The .NET Framework Library provides a rich collection of classes and methods for performing common mathematical calculations, string manipulations, character manipulations, input/output, error checking and other useful operations. 1 // Fig. 6.19: InvalidMethodOverload.cs 2 // Demonstrating incorrect method overloading. 3 4 public class InvalidMethodOverload 5 { 6 public int Square( double x ) 7 { 8 return x * x; 9 } 10 11 // ERROR! Second Square method takes same number, order 12 // and types of arguments. 13 public double Square( double y ) 14 { 15 return y * y; 16 } 17 } Fig. 6.19 Syntax error generated from overloaded methods with identical parameter lists and different return types.
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224 Methods Chapter 6 29 // main entry point for the application 30 [STAThread] 31 static void Main() 32 { 33 Application.Run( new MethodOverload() ); 34 } 35 36 private void showOutputButton_Click( object sender, 37 System.EventArgs e ) 38 { 39 // call both versions of Square 40 outputLabel.Text = 41 “The square of integer 7 is ” + Square( 7 ) + 42 “nThe square of double 7.5 is ” + Square ( 7.5 ); 43 } 44 45 } // end of class MethodOverload Fig. 6.18 Using overloaded methods. (Part 2 of 2.) The compiler distinguishes overloaded methods by their signatures. A method s signature is a combination of the method s name and parameter types. If the compiler looked only at method names during compilation, the code in Fig. 6.18 would be ambiguous the compiler would not know how to distinguish the two Square methods. The compiler uses overload resolution to determine which method to call. This process first searches for all the methods that can be used in the context, based on the number and type of arguments that are present. It might seem that only one method would match, but recall that C# can convert variable values to other data types implicitly. Once all matching methods are found, the closest match is chosen. This match is based on a best-fit algorithm, which analyzes the implicit conversions that will take place. Let us look at an example. In Fig. 6.18, the compiler might use the logical name Squareof int for the Square method that specifies an int parameter (line 30) and Squareof double for the Square method that specifies a double parameter (line 36). If a method Foo s definition begins as void Foo( int a, float b ) the compiler might use the logical name Foo of int and float. If the parameters are specified as void Foo( float a, int b ) the compiler might use the logical name Fooof float and int. The order of the parameters is important to the compiler; it considers the preceding two Foo methods distinct.
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Chapter 6 Methods 223 Common Programming Error 6.16 Accidentally having a nonrecursive method call itself through another method can cause infinite recursion. Most programming textbooks introduce recursion much later than we have done in this book. We feel that recursion is a sufficiently rich and complex topic that it is better to introduce it early and spread its examples over the remainder of the text. 6.17 Method Overloading C# enables several methods of the same name to be defined in the same class, as long as these methods have different sets of parameters (number of parameters, types of parameters or order of the parameters). This is called method overloading. When an overloaded method is called, the C# compiler selects the proper method by examining the number, types and order of the call s arguments. Method overloading commonly is used to create several methods with the same name that perform similar tasks, but on different data types. Figure 6.18 uses overloaded method Square to calculate the square of an int and a double. Good Programming Practice 6.6 Overloading methods that perform closely related tasks can make programs more readable and understandable. 1 // Fig. 6.18: MethodOverload.cs 2 // Using overloaded methods. 3 using System; 4 using System.Drawing; 5 using System.Collections; 6 using System.ComponentModel; 7 using System.Windows.Forms; 8 using System.Data; 9 10 public class MethodOverload : System.Windows.Forms.Form 11 { 12 private System.Windows.Forms.Button showOutputButton; 13 private System.Windows.Forms.Label outputLabel; 14 15 // Visual Studio .NET generated code 16 17 // first version, takes one integer 18 public int Square ( int x ) 19 { 20 return x * x; 21 } 22 23 // second version, takes one double 24 public double Square ( double y ) 25 { 26 return y * y; 27 } 28 Fig. 6.18 Using overloaded methods. (Part 1 of 2.)
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222 Methods Chapter 6 see, the number of calls to Fibonacci increases quickly 1,664,080 additional calls between the Fibonacci values of 30 and 31, and 2,692,538 additional calls between the Fibonacci values of 31 and 32. This difference in number of calls made between the Fibonacci values of 31 and 32 is more than 1.5 times the difference for Fibonacci values of 30 and 31. Problems of this nature humble even the world s most powerful computers! In the field called complexity theory, computer scientists determine how hard algorithms work to do their jobs. Complexity issues are discussed in detail in the upper-level computer science curriculum course generally called Algorithms. Performance Tip 6.1 Avoid Fibonacci-style recursive programs, which result in an exponential explosion of method calls. 6.16 Recursion vs. Iteration In the previous sections, we studied two methods that can be implemented either recursively or iteratively. In this section, we compare the two approaches and discuss why the programmer might choose one approach over the other. Both iteration and recursion are based on a control structure iteration uses a repetition structure (such as for, whileor do/while) and recursion uses a selection structure (such as if, if/elseor switch). Both iteration and recursion involve repetition iteration explicitly uses a repetition structure and recursion achieves repetition through repeated method calls. Iteration and recursion each involve a termination test iteration terminates when the loop-continuation condition fails and recursion terminates when a base case is recognized. Iteration with counter-controlled repetition and recursion both gradually approach termination iteration keeps modifying a counter until the counter assumes a value that makes the loop-continuation condition fail and recursion keeps producing simpler versions of the original problem until a base case is reached. Both iteration and recursion can execute infinitely an infinite loop occurs with iteration if the loop-continuation test never becomes false and infinite recursion occurs if the recursion step does not reduce the problem in a manner that converges on a base case. Recursion has disadvantages as well. It repeatedly invokes the mechanism, and consequently the overhead, of method calls. This can be costly in both processor time and memory space. Each recursive call creates another copy of the method (actually, only the method s variables); this can consume considerable memory. Iteration normally occurs within a method, so the overhead of repeated method calls and extra memory assignment is omitted. Why then would a programmer choose recursion? Software Engineering Observation 6.11 Any problem that can be solved recursively also can be solved iteratively (nonrecursively). A recursive approach normally is chosen in preference to an iterative approach when the recursive approach more naturally mirrors the problem and results in a program that is easier to understand and debug. Recursive solutions also are chosen when iterative solutions are not apparent. Performance Tip 6.2 Avoid using recursion in performance situations. Recursive calls take time and consume additional memory.
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Chapter 6 Methods 221 Fibonacci( 3 ) return return + + return 1 return 1 return 0 Fibonacci( 2 ) Fibonacci( 1 ) Fibonacci( 1 ) Fibonacci( 0 ) Fig. 6.17 Set of recursive calls to method Fibonacci. This figure raises some issues about the order in which C# compilers will evaluate operands. Figure 6.17 shows that, during the evaluation of Fibonacci(3), two recursive calls will be made Fibonacci(2) and Fibonacci(1). In what order will these calls be made? Most programmers assume the operands will be evaluated from left to right; in C# this is indeed true. The C and C++ languages (on which many of C# s features are based) do not specify the order in which the operands of most operators (including +) are evaluated. Therefore, in those languages, the programmer can make no assumption about the order in which these calls execute. The calls could, in fact, execute Fibonacci(2), then Fibonacci(1), or they could execute in the reverse order (Fibonacci(1), then Fibonacci(2)). In this program and in most other programs, the final result would be the same. However, in some programs, the evaluation of an operand could have side effects that would affect the expression s final result. C# specifies that the order of evaluation of the operands is from left to right. Thus, the method calls are first Fibonacci(2), then Fibonacci(1). Good Programming Practice 6.5 Do not write expressions that depend on the order of evaluation of the operator s operands. Doing so often results in programs that are difficult to read, debug, modify and maintain. A word of caution about using a recursive program to generate Fibonacci numbers: each invocation of the Fibonacci method that does not match one of the base cases (i.e., 0 or 1) results in two recursive calls to the Fibonacci method. This quickly results in many method invocations. Calculating the Fibonacci value of 20 using the program in Fig. 6.16 requires 21,891 calls to the Fibonacci method; calculating the Fibonacci value of 30 requires 2,692,537 calls to the Fibonacci method. As the programmer tries larger values, each consecutive Fibonacci number that the program is asked to calculate results in a substantial increase in the number of calls to the Fibonaccimethod and hence in calculation time. For example, the Fibonacci value 31 requires 4,356,617 calls, and the Fibonacci value of 32 requires 7,049,155 calls. As you can
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220 Methods Chapter 6 15 16 private System.Windows.Forms.Label displayLabel; 17 private System.Windows.Forms.Label promptLabel; 18 19 // Visual Studio .NET generated code 20 21 // call Fibonacci and display results 22 protected void calculateButton_Click( 23 object sender, System.EventArgs e ) 24 { 25 int number = Convert.ToInt32( inputTextBox.Text ); 26 int fibonacciNumber = Fibonacci( number ); 27 displayLabel.Text = 28 “Fibonacci Value is ” + fibonacciNumber; 29 } 30 31 // calculates Fibonacci number 32 public int Fibonacci( int number ) 33 { 34 if ( number == 0 || number == 1 ) 35 return number; 36 else 37 return Fibonacci( number - 1 ) + Fibonacci( number -2 ); 38 } 39 40 // main entry point for the application 41 [STAThread] 42 static void Main() 43 { 44 Application.Run( new FibonacciTest() ); 45 } 46 47 } // end of class FibonacciTest Fig. 6.16 Recursively generating Fibonacci numbers. (Part 2 of 2.) The call to Fibonacci (line 26) from calculateButton_Click is not a recursive call, but all subsequent calls to Fibonacci from line 37 are recursive. Each time Fibonacci is invoked, it immediately tests for the base case number equal to 0 or 1 (line 34). If this is true, Fibonacci returns number(fibonacci(0) is 0 and fibonacci(1) is 1). Interestingly, if number is greater than 1, the recursion step generates two recursive calls (line 37), each of which is for a slightly simpler problem than the original call to Fibonacci. Figure 6.17 shows how method Fibonacci would evaluate Fibonacci(3).
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Chapter 6 Methods 219 Common Programming Error 6.15 Omitting the base case or writing the recursion step so that it does not converge on the base case will cause infinite recursion, eventually exhausting memory. Infinite recursion is analogous to the problem of an infinite loop in an iterative (nonrecursive) solution. 6.15 Example Using Recursion: The Fibonacci Series The Fibonacci series 0,1, 1, 2, 3, 5, 8, 13, 21, begins with 0 and 1 and has the property that each subsequent Fibonacci number is the sum of the previous two Fibonacci numbers. The series occurs in nature and, in particular, describes a form of spiral. The ratio of successive Fibonacci numbers converges on a constant value of 1.618 . This number, too, repeatedly occurs in nature and has been called the golden ratio or the golden mean. Humans tend to find the golden mean aesthetically pleasing. Architects often design windows, rooms and buildings whose length and width are in the ratio of the golden mean. Postcards often are designed with a golden mean width-to-height ratio. The recursive definition of the Fibonacci series is as follows: Fibonacci( 0 ) = 0 Fibonacci( 1 ) = 1 Fibonacci( n ) = Fibonacci( n 1 ) + Fibonacci( n 2 ) Note that there are two base cases for the Fibonacci calculation fibonacci(0) evaluates to 0, and fibonacci(1) evaluates to 1. The application in Fig. 6.16 calculates the ith Fibonacci number recursively using method Fibonacci. The user enters an integer in the text box, indicating the ith Fibonacci number to calculate, and clicks the calculateButton (which displays the text Calculate Fibonacci). Method calculateButton_Click (lines 22 29) executes in response to the user interface event and calls recursive method Fibonacci to calculate the specified Fibonacci number. In Fig. 6.16, the screen captures show the results of calculating several Fibonacci numbers. 1 // Fig. 6.16: FibonacciTest.cs 2 // Recursive fibonacci method. 3 using System; 4 using System.Drawing; 5 using System.Collections; 6 using System.ComponentModel; 7 using System.Windows.Forms; 8 using System.Data; 9 10 public class FibonacciTest : System.Windows.Forms.Form 11 { 12 private System.Windows.Forms.Button calculateButton; 13 14 private System.Windows.Forms.TextBox inputTextBox; Fig. 6.16 Recursively generating Fibonacci numbers. (Part 1 of 2.)
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218 Methods Chapter 6 26 // main entry point for the application 27 [STAThread] 28 static void Main() 29 { 30 Application.Run( new FactorialTest()); 31 } 32 33 private void showFactorialsButton_Click( object sender, 34 System.EventArgs e ) 35 { 36 outputLabel.Text = “”; 37 38 for ( long i =0; i <= 10; i++ ) 39 outputLabel.Text += i + "! = " + 40 Factorial( i ) + "n"; 41 } 42 43 } // end of class FactorialTest Fig. 6.15 Calculating factorials with a recursive method. (Part 2 of 2.) Method Factorial receives a parameter of type long and returns a result of type long. As seen in Fig. 6.15, factorial values become large quickly. We choose data type long so the program can calculate factorials greater than 20!. Unfortunately, the Factorial method produces large values so quickly, even long does not help us print many more factorial values before the size of even the long variable is exceeded. Factorials of larger numbers require the program to use float and double variables. This points to a weakness in most programming languages, namely, that the languages are not easily extended to handle the unique requirements of various applications. As we will see in our treatment of object-oriented programming beginning in Chapter 8, C# is an extensible language programmers with unique requirements can extend the language with new data types (called classes). A programmer could create a HugeInteger class, for example, that would enable a program to calculate the factorials of arbitrarily large numbers. Common Programming Error 6.14 Forgetting to return a value from a recursive method can result in syntax and/or logic errors.
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Chapter 6 Methods 217 5! 5 * 4! 4 * 3! 3 * 2! 2 * 1! 1 5! 5 * 4! 4 * 3! 3 * 2! 2 * 1! 1 Final value = 120 5! = 5 * 24 = 120 is returned 4! = 4 * 6 = 24 is returned 3! = 3 * 2 = 6 is returned 2! = 2 * 1 = 2 is returned 1 returned (a) Procession of recursive calls (b) Values returned from each recursive call Fig. 6.14 Recursive evaluation of 5!. returns. If number is greater than 1, line 23 expresses the problem as the product of number and a recursive call to Factorial, evaluating the factorial of number -1. Note that Factorial( number -1 ) is a slightly simpler problem than the original calculation Factorial( number). 1 // Fig. 6.15: FactorialTest.cs 2 // Calculating factorials with recursion. 3 using System; 4 using System.Drawing; 5 using System.Collections; 6 using System.ComponentModel; 7 using System.Windows.Forms; 8 using System.Data; 9 10 public class FactorialTest : System.Windows.Forms.Form 11 { 12 private System.Windows.Forms.Button showFactorialsButton; 13 private System.Windows.Forms.Label outputLabel; 14 15 // Visual Studio .NET generated code 16 17 public long Factorial( long number ) 18 { 19 if ( number <= 1 ) // base case 20 return 1; 21 22 else 23 return number * Factorial( number - 1 ); 24 } 25 Fig. 6.15 Calculating factorials with a recursive method. (Part 1 of 2.)
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