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A virtual method is a method that is declared as virtual in a base class The defining characteristic of a virtual method is that it can be redefined in one or more derived classes Thus, each derived class can have its own version of a virtual method Virtual methods are interesting because of what happens when one is called through a base class reference In this situation, C# determines which version of the method to call based upon the type of the object referred to by the reference and this determination is made at runtime Thus, when different objects are referred to, different versions of the virtual method are executed In other words, it is the type of the object being referred to (not the type of the reference) that determines which version of the virtual method will be executed Therefore, if a base class contains a virtual method and classes are derived from that base class, then when different types of objects are referred to through a base class reference, different versions of the virtual method can be executed You declare a method as virtual inside a base class by preceding its declaration with the keyword virtual When a virtual method is redefined by a derived class, the override modifier is used Thus, the process of redefining a virtual method inside a derived class is called method overriding When overriding a method, the name, return type, and signature of the overriding method must be the same as the virtual method that is being overridden Also, a virtual method cannot be specified as static or abstract (discussed later in this chapter) Method overriding forms the basis for one of C# s most powerful concepts: dynamic method dispatch Dynamic method dispatch is the mechanism by which a call to an overridden method is resolved at runtime, rather than compile time Dynamic method dispatch is important because this is how C# implements runtime polymorphism Here is an example that illustrates virtual methods and overriding:.

When I divided it, I got two sentences, one forty-two words long, the other twenty-eight words long Still too long The original second sentence was thirty words long But it s not a compound sentence 2 In complicated sentences, consider how many separate thoughts and ideas are being expressed Can any be eliminated Are any redundant Can separate thoughts be written as separate sentences I decided to separate all thoughts in the entire paragraph as a tool to help me make the introduction more concise Here are the thoughts I want to express

// Demonstrate a virtual method using System; class Base { // Create virtual method in the base class public virtual void Who() { ConsoleWriteLine("Who() in Base"); } } class Derived1 : Base { // Override Who() in a derived class public override void Who() { ConsoleWriteLine("Who() in Derived1"); } }

11:

The choice of u and v in the integration by parts technique is significant We selected u to be x because then du will be 1 dx, thereby simplifying the integral If we had instead selected u = cos x and dv = x dx then we would have found that v = x 2 /2 and du = sin x dx and the new integral v du = is more complicated

Part II:

ConsoleWriteLine("Number of elements: " + alCount); // Use foreach loop to display the list ConsoleWrite("Contents: "); foreach(char c in al) ConsoleWrite(c + " "); ConsoleWriteLine("\n"); ConsoleWriteLine("Adding 20 more elements"); // Add enough elements to force al to grow for(int i=0; i < 20; i++) alAdd((char)('a' + i)); ConsoleWriteLine("Current capacity: " + alCapacity); ConsoleWriteLine("Number of elements after adding 20: " + alCount); ConsoleWrite("Contents: "); foreach(char c in al) ConsoleWrite(c + " "); ConsoleWriteLine("\n"); // Change contents using array indexing ConsoleWriteLine("Change first three elements"); al[0] = 'X'; al[1] = 'Y'; al[2] = 'Z'; ConsoleWrite("Contents: "); foreach(char c in al) ConsoleWrite(c + " "); ConsoleWriteLine(); } }

The output from this program is shown here:

Keeping in mind that we want to choose u and v so as to simplify the integral, we take u = x 2 and dv = ex dx Then u( x) = x 2 v( x) = ex du = u ( x) dx = 2x dx dv = v ( x) dx = ex dx

Initial number of elements: 0 Adding 6 elements Number of elements: 6 Current contents: C A E B D F Removing 2 elements Number of elements: 4 Contents: C E B D Adding 20 more elements Current capacity: 32 Number of elements after adding 20: 24 Contents: C E B D a b c d e f g h i j k l m n o p q r s t Change first three elements Contents: X Y Z D a b c d e f g h i j k l m n o p q r s t

25:

Sorting and Searching an ArrayList An ArrayList can be sorted by Sort( ) Once sorted, it can be efficiently searched by BinarySearch( ) The following program demonstrates these methods: