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always The print ( ) function defined in the base class is not virtual. So the call p->print ( ) :print ( ) because p has type Person*. The pointer invokes that same base class function Person : p is statically bound to that base class function at compile time. Now change the base class function Person : :print ( ) into a virtual function, and run the same program:

Fig. 8-22

class Person { public: Person(char*

char[strlen(s+l)];

Fig. 8-23

strcpy(name, s);

Tangents PA and PB are drawn to a circle from external point P. m APB nearest tenth the radius of the circle.

In some applications, it is more natural to use arrays whose subscripts begin at 1 rather than 0. Thus, a one-dimensional, n-element array will range from 1 to n rather than 0 to n a more natural selection for many

virtual void print0 protected: char* name;

A square unit is the surface enclosed by a square whose side is 1 unit (Fig. 9-1). The area of a closed plane figure, such as a polygon, is the number of square units contained in its surface. Since a rectangle 5 units long and 4 units wide can be divided into 20 unit squares, its area is 20 square units (Fig. 9-2). The area of a rectangle equals the product of the length of its base and the length of its altitude (Fig. 9-3). Thus if b 8 in and h 3 in, then A 24 in2. The area of a square equals the square of the length of a side (Fig. 9-4). Thus if s 6, then A s2 36. It follows that the area of a square also equals one-half the square of the length of a diagonal. Since A s2 and s d / !2, A 1 d 2. 2 Note that we sometimes use the letter A for both a vertex of a figure and its area. You should have no trouble determining which is meant. The reader should feel free to use a calculator for the work in this chapter.

{ tout << 'My name is ' << name << '.\n"; }

Fig. 9-1

Now the pointer p is dynamically bound to the print ( ) function of whatever object it points to. So invokes the base class function Person : : print ( ) , the second call the first call p->print() invokes the derived class function student : : print ( ) , and the third call invokes the derived class is polymorphic because its function Professor: :print (>. We say that the call p->print() meaning changes according to circumstance.

Fig. 9-2

In general, a member function should be declared as virtual whenever it is anticipated that at least some of its subclasses will define their own local version of the function.

Virtual functions are overridden by functions that have the same signature and are defined in subclasses. Since the names of constructors and destructors involve the names of their different classes, it would seem that constructors and destructors could not be declared virtual. That is indeed true for constructors. However, an exception is made for destructors. Every class has a unique destructor, either defined explicitly within the class definition or implicitly by the compiler. An explicit destructor may be defined to be virtual. The following example illustrates the value in defining a virtual destructor:

Fig. 9-3

EXAMPLE 11.12 Memory Leak This program is similar to Example 11.6:

Fig. 9-4

programmers. The Option Base statement allows the lower limit for all arrays within a module to be changed to 1. This statement is written simply as

class X { public:

9.1 Area of a rectangle (a) Find the area of a rectangle if the base has length 15 and the perimeter is 50. (b) Find the area of a rectangle if the altitude has length 10 and the diagonal has length 26. (c) Find the lengths of the base and altitude of a rectangle if its area is 70 and its perimeter is 34.

x0 1 p = new int[2];

See Fig. 9-5. (a) Here p 50 and b 15. Since p Hence, A bh 15(10) 150. 2b 2h, we have 50 b2 2(15) b2 2h so h 102 or b 10. 24.

-X() { delete [] p; private: int* p; >;

CHAP. 1 l]

(b) Here d 26 and h 10. In right ^ACD, d2 Hence, A bh 24(10) 240.