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216 Methods Chapter 6 only the simplest case(s), or base case(s). If the method is called with a base case, the method returns a result. If the method is called with a more complex problem, the method divides the problem into two conceptual pieces a piece that the method knows how to perform (base case) and a piece that the method does not know how to perform. To make recursion feasible, the latter piece must resemble the original problem, but be a slightly simpler or smaller version of it. The method invokes (calls) a fresh copy of itself to work on the smaller problem this is referred to as a recursive call, or a recursion step. The recursion step also normally includes the keyword return, because its result will be combined with the portion of the problem that the method knew how to solve. Such a combination will form a result that will be passed back to the original caller. The recursion step executes while the original call to the method is still open (i.e., it has not finished executing). The recursion step can result in many more recursive calls, as the method divides each new subproblem into two conceptual pieces. Each time the method calls itself with a slightly simpler version of the original problem, the sequence of smaller and smaller problems must converge on the base case, so the recursion can eventually terminate. At that point, the method recognizes the base case and returns a result to the previous copy of the method. A sequence of returns ensues up the line until the original method call returns the final result to the caller. As an example of these concepts, let us write a recursive program to perform a popular mathematical calculation. The factorial of a nonnegative integer n, written n! (and pronounced n factorial ), is the product n ( n - 1 ) ( n - 2 ) 1 with 1! equal to 1, and 0! defined as 1. For example, 5! is the product 5 4 3 2 1, which is equal to 120. The factorial of an integer number greater than or equal to 0 can be calculated iteratively (nonrecursively) using for as follows: factorial = 1; for ( int counter = number; counter >= 1; counter– ) factorial *= counter; We arrive at a recursive definition of the factorial method with the following relationship: n! = n ( n - 1 )! For example, 5! is clearly equal to 5 * 4!, as shown by the following: 5! = 5 4 3 2 1 5! = 5 ( 4 3 2 1 ) 5! = 5 ( 4! ) A recursive evaluation of 5! would proceed as in Fig. 6.14. Figure 6.14a shows how the succession of recursive calls proceeds until 1! is evaluated to be 1, which terminates the recursion. Each rectangle represents a method call. Figure 6.14 shows the values returned from each recursive call to its caller until the final value is calculated and returned. Figure 6.15 uses recursion to calculate and print the factorials of the integers 0 10. The recursive method Factorial (lines 17 24) first determines whether its terminating condition is true (i.e., number is less than or equal to 1). If number is less than or equal to 1, factorial returns 1, no further recursion is necessary and the method
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Chapter 6 Methods 215 69 Application.Run( new Scoping() ); 70 } 71 72 } // end of class Scoping Fig. 6.13 Scoping. (Part 3 of 3.) The program defines two other methods MethodA and MethodB that take no arguments and return nothing. The program calls each method twice from method Scoping. MethodA defines local variable x (line 21) and initializes it to 25. Each call to MethodA displays the variable s value in outputLabel, increments the variable and displays it again before exiting the method. Each call to MethodA recreates automatic variable x and initializes it to 25. Method MethodB does not declare any variables. Therefore, when it refers to variable x, the instance variable x is used. Each call to MethodB displays the instance variable in outputLabel, multiplies it by 10 (line 40) and displays it again before exiting the method. The next time method MethodB is called, the instance variable begins with its modified value, 10. After the calls to MethodA and MethodB, the program again displays the local variable x in method showOutputButton_Click to show that none of the method calls modified this specific variable x, as the methods all referred to variables in other scopes. 6.14 Recursion The programs we have discussed generally are structured as methods that call one another in a hierarchical manner. For some problems, it is useful to have a method actually call itself. A recursive method is a method that calls itself either directly or indirectly through another method. Recursion is an important topic discussed at length in upper-level computer science courses. In this section and the next, we present two simple examples of recursion. We consider recursion conceptually first, then examine several programs containing recursive methods. Recursive problem-solving approaches have a number of elements in common. A recursive method is called to solve a problem. The method actually knows how to solve
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214 Methods Chapter 6 16 17 // Visual Studio .NET generated code 18 19 public void MethodA() 20 { 21 int x = 25; // initialized each time a is called 22 23 outputLabel.Text = outputLabel.Text + 24 “nnlocal x in MethodA is ” + x + 25 ” after entering MethodA”; 26 27 ++x; // increment local variable x 28 29 outputLabel.Text = outputLabel.Text + 30 “nlocal x in MethodA is ” + x + 31 ” before exiting MethodA”; 32 } 33 34 public void MethodB() 35 { 36 outputLabel.Text = outputLabel.Text + 37 “nninstance variable x is ” + x + 38 ” on entering MethodB”; 39 40 x *= 10; 41 42 outputLabel.Text = outputLabel.Text + 43 “ninstance varable x is ” + x + 44 ” on exiting MethodB”; 45 } 46 47 private void showOutputButton_Click( object sender, 48 System.EventArgs e ) 49 { 50 int x = 5; // local x in method showOutputButton_Click 51 52 outputLabel.Text = 53 “local x in method showOutputButton_Click is ” + x; 54 55 MethodA(); // MethodA has automatic local x; 56 MethodB(); // MethodB uses instance variable x 57 MethodA(); // MethodA creates new automatic local x 58 MethodB(); // instance variable x retains its value 59 60 outputLabel.Text = outputLabel.Text + “nn” + 61 “local x in method showOutputButton_Click is ” + x; 62 63 } // end method showOutputButton_Click 64 65 // main entry point for the application 66 [STAThread] 67 static void Main() 68 { Fig. 6.13 Scoping. (Part 2 of 3.)
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Chapter 6 Methods 213 able or reference declared in a block can be used only in that block or in blocks nested within that block. The possible scopes for an identifier are class scope and block scope. Members of a class have class scope and are visible in what is known as the declaration space of a class. Class scope begins at the opening left brace ({) of the class definition and terminates at the closing right brace (}). Class scope enables methods of a class to access all members defined in that class. In Chapter 8, Object-Based Programming, we see that static members are an exception to this rule. In a sense, all instance variables and methods of a class are global to the methods of the class in which they are defined (i.e., the methods can modify the instance variables directly and invoke other methods of the class). Identifiers declared inside a block have block scope (local-variable declaration space). Block scope begins at the identifier s declaration and ends at the block s terminating right brace (}). Local variables of a method have block scope, as do method parameters, which are local variables of the method. Any block may contain variable declarations. When blocks are nested in a method s body, and an identifier declared in an outer block has the same name as an identifier declared in an inner block, an error is generated. On the other hand, if a local variable in a method has the same name as an instance variable, the value in the calling method (main program) is hidden until the method terminates execution. In Chapter 8, Object-Based Programming, we discuss how to access such hidden instance variables. The reader should note that block scope also applies to methods and for structures. With for structures, any variable declared in the initialization portion of the for header will be in scope only within that for structure. Good Programming Practice 6.4 Avoid local-variable names that hide instance-variable names. The program in Fig. 6.13 demonstrates scoping issues with instance variables and local variables. Instance variable x (line 15) is initialized to 1. This instance variable is hidden in any block (or method) that declares a local variable named x. The showOutputButton_ Click event handler (lines 47 63) declares a local variable x and initializes it to 5 (line 50). Lines 52 53 display the value of this local variable to show that instance variable x (with value 1) is hidden in method showOutputButton_Click. 1 // Fig. 6.13: Scoping.cs 2 // Demonstrating scope of local and instance variables. 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 Scoping : System.Windows.Forms.Form 11 { 12 private System.Windows.Forms.Label outputLabel; 13 private System.Windows.Forms.Button showOutputButton; 14 15 public int x = 1; // instance variable Fig. 6.13 Scoping. (Part 1 of 3.)
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