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11.1 All three of these operators are implemented as friend functions to give them access to the num and den data members of their owner objects: class Ratio { friend Ratio operator-(const Ratio&, const Ratio&); friend Ratio operator-(const Ratio&); friend bool operator<(const Ratio&, const Ratio&); public: Ratio(int =0, int =1); Ratio(const Ratio&); Ratio& operator=(const Ratio&); // other declarations go here private: int num, den; int gcd(int, int) int reduce(); }; The binary subtraction operator simply constructs and returns a Ratio object z that represents the difference x - y: Ratio operator-(const Ratio& x, const Ratio& y) { Ratio z(x.num*y.den - y.num*x.den, x.den*y.den);
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z.reduce(); return z; } Algebraically, the subtraction a/b - c/d is performed using the common denominator bd:
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So the numerator of x - y should be x.num*y.den - y.num*x.den and the denominator should be x.den*y.den. The function constructs the Ratio object z with that numerator and denominator. This algebraic formula can produce a fraction that is not in reduced form, even if x and y are. For example, 1/2 1/6 = (1 6 2 1)/(2 6) = 4/12. So we call the reduce() utility function before returning the resulting object z. The unary negation operator overloads the symbol - . It is distinguished from the binary subtraction operator by its parameter list; it has only one parameter: Ratio Ratio::operator-(const Ratio& x) { Ratio y(-x.num, x.den); return y; } To negate a fraction a/b we simply negate its numerator: (-a)/b. So the newly constructed Ratio object y has the same denominator as x but its numerator is -x.num. The less-than operator is easier to do if we first modify our default constructor to ensure that every object s den value is positive. Then we can use the standard equivalence for the less-than operator:
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bool operator<(const Ratio& x, const Ratio& y) { return (x.num*y.den < y.num*x.den); } Ratio::Ratio(int n, int d) : num(n), den(d) { if (d == 0) n = 0; else if (d < 0) { n *= -1; d *= -1; } reduce(); } The modification ensuring that den > 0 could instead be done in the reduce() function, since that utility should be called by every member function that allows den to be changed. However, none of our other member functions allows the sign of den to change, so by requiring it to be positive when the object is constructed we don t need to check the condition again. Here is the class declaration: class Vector { friend bool operator==(const Vector&, const Vector&); friend ostream& operator<<(ostream&, const Vector&); friend istream& operator>>(istream&, Vector&); public: Vector(int =1, double =0.0); // default constructor Vector(const Vector&); // copy constructor ~Vector(); // destructor const Vector& operator=(const Vector&); // assignment operator double& operator[](int) const; // subscript operator private: int size; double* data; }; Here is the implementation of the overloaded equality operator:
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bool operator==(const Vector& v, const Vector& w) { if (v.size != w.size) return 0; for (int i = 0; i < v.size; i++) if (v.data[i] != w.data[i]) return 0; return 1; } It is a nonmember function which returns 1 or 0 according to whether the two vectors v and w are equal. If their sizes are not equal, then it returns 0 immediately. Otherwise it checks the corresponding elements of the two vectors, one at a time. If there is any mismatch, then again it returns 0 immediately. Only if the entire loop finishes without finding any mismatches can we conclude that the two vectors are equal and return 1. Here is the implementation of the overloaded stream insertion operator: ostream& operator<<(ostream& ostr, const Vector& v) { ostr << '('; for (int i = 0; i < v.size-1; i++) { ostr << v[i] << ", "; if ((i+1)%8 == 0) cout << "\n "; } return ostr << v[i] << ")\n"; } This prints the vector like this: (1.11111, 2.22222, 3.33333, 4.44444, 5.55556). The conditional inside the loop allows the output to wrap around several lines neatly if the vector has more than 8 elements. The output is sent to ostr which is just a local name for the output stream that is passed to the function. That would be cout if the function is called like this: cout << v;. In the last line of the function, the expression ostr << v[i] << ")\n" makes two calls to the (standard) stream extraction operator. Those two calls return ostr as the value of this expression, and so that object ostr is then returned by this function. Here is the overloaded stream extraction operator: istream& operator>>(istream& istr, Vector& v) { for (int i = 0; i < v.size; i++) { cout << i << ": "; istr >> v[i]; } return istr; } This implementation prompts the user for each element of the vector v. It could also be implemented without user prompts, simply reading the elements one at a time. Notice that the elements are read from the input stream istr, which is the first parameter passed in to the function. When the function is called like this: cin >> v; the standard input stream cin will be passed to the parameter istr, so the vector elements are actually read from cin. The argument istr is simply a local name for the actual input stream which probably will be cin. Notice that this argument is also returned, allowing a cascade of calls like this: cin >> u >> v >> w;. Here is the implementation of the default constructor: Vector::Vector(int sz, double t) : size(sz) { data = new double[size]; for (int i = 0; i < size; i++) data[i] = t; }
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