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8.51 Implement the following additional member functions for the Rat ional class: int isEqualTo(Rationa1); int isGreaterThan(Rationa1); int isLessThan(Rationa1);
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So, for example, the call X. isGreaterThan (y) would return 1 or 0 according to whether the Rational object x is greater than the Rational object y. Note that this simulates the operator > for the Rat ional class.
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8.52 Implement the following additional constructor for the Rat ional class: Rational(Float);
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So, for example, the declaration Rational x ( 3 .14 ) x that represents the fraction 157/50.
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would construct the Rational object
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8.53 Implement a Complex class for complex numbers. Each object of this class will represent a
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complex number x -t y i, storing the real part x and the imaginary part y as real numbers of type double. Include a default constructor, a copy constructor, access functions, a norm ( > function that returns the norm (magnitude) of the complex number, an i sEqualTo ( complex) function,andarithmeticfunctions plus(Complex), minus(Complex), times(Complex), and dividedBy(Complex).
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8.54 Implement the following additional constructor for the Complex class (Problem 8.25): Complex(Rationa1);
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So, for example, the declarations
Rational Complex x(22,7); z(x);
would construct the Rat ional object x that represents the fraction 22/7 and the Complex object z that represents the real number 3.14159. 8.55 Implement the following additional functions for the Point class (Problem 8.17):
float Point dot(Point); cross(Point);
The dot ( > function returns the dot product (scalar product), and the cros s ( > returns the cross product (vector product).
function
8.56 Modify the String class (Problem 8.21) by adding a constructor that allows an object to be
initialized with a single character, constructing a string of length 1 containing that character.
8.57 Modify the String class (Problem 8.21) by adding the function String substr(short start, short length);
This function returns the String object that contains the substring of the owner indexed from startto start + length - 1. For example, if s represents the string I ABCDEFGHI JK I , then s . subs tr (2,s ) would return the object that represents the string YDEFG II, and s . subs tr ( 8 ,7 ) would return the object that represents the string I I JK I . Note that the value of start is the length of the omitted prefix.
8.58 Modify the Matrix class (Problem 8.23) so that it represents 3-by-3 matrices.
CHAP. 81
CLASSES
8.59 Implement a Quaternion class for hypercomplex numbers (also called hamiltonians ). Each object of this class will represent a hypercomplex number t + x i + y j + z k, where each of the components t, X, y, and z has type double. Include a default constructor, a copy constructor, access functions, a norm ( > function that returns the norm (magnitude) of the hypercomplex number, an isEqualTo (Quaternion) function, and arithmetic functions plus (Quaternion), minus(Quaternion) ,and times(Quaternion) ,where multiplication is defined
bythefollowingrules:i2=j2=k2=-1,ij=k=-ji,jk=i=-kj,andki=j=-ik.
Write a program like the one in Example 8.2, except insert the new nodes at the end of the list so that the data values can be input in the same order as they are output.
Answers to Review Questions
8 .1 8.2 8.3 8.4 A pub1 i c member is accessible from outside the class; a private member is not. The class interface consists of the member data and the member function prototypes (i.e. just the function declarations). The class implementation contains the definitions of the member functions. A class member function is part of the class, so it has access to the class s private parts. An applicaparts. tion function is declared outside the class, and so it does not have access to the class s private A constructor is a class member function that executes automatically whenever an object of that class is instantiated (i.e., constructed). A destructor is a class member function that executes automatically whenever the scope of that object terminates (i.e., is destructed). The default constructor is the unique constructor that has no parameters (or the one whose parameters all have default values). A class s copy constructor executes whenever an object of that class is copied by any mechanism except direct assignment. This includes initialization, passing a parameter by value, and returning by value. An access function is a pub1 i c class member function that returns the value of one of the class s data members. A utility function is a private class member function that is used only within the class to perform technical tasks. A c las s a n d a s t rut t in C++ are essentially the same. The only significant difference is that the default access level for a class of private, while that for a struct is pub1 ic. Every class constructor must h a v e the same name as the class itself.
8.5 8.6 8.7
8.8 8.9
8.10 Every class destructor must have the same name as the class itself, prefixed with a tilde (-). 8.11 There is no limit to the number of constructors that a class may have. But since multiple constructors are function overloads, they all must be distinguishable by their parameter lists. 8.12 A class can only one destructor. 8.13 The scope resolution operator : : used in general to resolve external references. It is used in a class definition whenever the definition of a member function is given outside the scope of the class definition. 8.14 There are four class member functions that are created automatically by the compiler if they are not included (by the programmer) in the class definition: the default constructor, the copy constructor, the destructor, and the overloaded assignment operator.
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