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committee, how would you state your objective What would you want the committee to do as a result of reading your report and listening to your presentation What did you decide How did you state your objective Here s what Brad wrote:

In C#, a method can call itself This process is called recursion, and a method that calls itself is said to be recursive In general, recursion is the process of defining something in terms of itself and is somewhat similar to a circular definition The key component of a recursive method is that it contains a statement that executes a call to itself Recursion is a powerful control mechanism The classic example of recursion is the computation of the factorial of a number The factorial of a number N is the product of all the whole numbers between 1 and N For example, 3 factorial is 1 2 3, or 6 The following program shows a recursive way to compute the factorial of a number For comparison purposes, a nonrecursive equivalent is also included

(c )

// A simple example of recursion using System; class Factorial {

8:

// This is a recursive method public int FactR(int n) { int result;

if(n==1) return 1; result = FactR(n-1) * n; return result; } // This is an iterative equivalent public int FactI(int n) { int t, result; result = 1; for(t=1; t <= n; t++) result *= t; return result; } } class Recursion { static void Main() { Factorial f = new Factorial(); ConsoleWriteLine("Factorials using recursive method"); ConsoleWriteLine("Factorial of 3 is " + fFactR(3)); ConsoleWriteLine("Factorial of 4 is " + fFactR(4)); ConsoleWriteLine("Factorial of 5 is " + fFactR(5)); ConsoleWriteLine(); ConsoleWriteLine("Factorials using iterative method"); ConsoleWriteLine("Factorial of 3 is " + fFactI(3)); ConsoleWriteLine("Factorial of 4 is " + fFactI(4)); ConsoleWriteLine("Factorial of 5 is " + fFactI(5)); } }

10 (a) Each person has one and only one mother This is a function (b) Some men have more than one sister, others have none This is not a function (c) Each real numbers has exactly one cube root This is a function (d) Each positive integer has just one square This is a function (e) Some cars have several passengers Some have none So this is not a function (f) Each toe is attached to one and only one foot This is a function (g) Each rational number has precisely one integer which just follows it This is a function (h) Each integer has one and only one predecessor This is a function (i) Each real number has a well-defined cube, and adding four is a welldefined operation This is a function

The output from this program is shown here:

Factorials using recursive method Factorial of 3 is 6 Factorial of 4 is 24 Factorial of 5 is 120 Factorials using iterative method Factorial of 3 is 6 Factorial of 4 is 24 Factorial of 5 is 120

The operation of the nonrecursive method FactI( ) should be clear It uses a loop starting at 1 and progressively multiplies each number by the moving product The operation of the recursive FactR( ) is a bit more complex When FactR( ) is called with an argument of 1, the method returns 1; otherwise, it returns the product of FactR(n 1)*n To evaluate this expression, FactR( ) is called with n 1 This process repeats until n equals 1 and the calls to the method begin returning For example, when the factorial of 2 is calculated, the

Note that Brad didn t focus on passive objectives such as being understood, thanked, or respected He went for action

12 (a) (b) (c) (d) (e) (f)

Part I:

Notice that the addition of GetPrevious( ) required a change to the implementations of the methods defined by ISeries However, since the interface to those methods stays the same, the change is seamless and does not break preexisting code This is one of the advantages of interfaces As explained, any number of classes can implement an interface For example, here is a class called Primes that generates a series of prime numbers Notice that its implementation of ISeries is fundamentally different than the one provided by ByTwos