我正在努力添加代表适当数学对象的类 Natural、Rational、Complex 的操作。我需要它来计算 x 中的多项式。
所有类都继承抽象类 Number。将所有系数都放在一个数字数组中,我想计算多项式。为此,我需要乘以双倍(x 是双倍)的操作。x 被转化为有理数并相乘。这工作正常。我的问题是如何添加抽象类型 Number 的类?
我不能让它工作。我所得到的只是 Number::add(Number) 中的永无止境的递归(它调用自己而不是调用其他类型的 Natural、Rational、Complex 方法)。
#include #include #include #include #include #include #include using namespace std;
class Natural;class Rational;class Complex;
class Number {
public:
virtual string toString() const = 0;
virtual Number *operator*(const Rational) const = 0;
virtual Number *add(const Natural*) const = 0;
virtual Number *add(const Rational*) const = 0;
virtual Number *add(const Complex*) const = 0;
virtual Number *add(const Number *n) const {
n->add(this);
}
};
class Natural : public Number {
friend class Complex;
int n;
public:
Natural(const Natural &s) {
n = s.n;
}
Natural(int number) : n(number) {}
string toString() const {
stringstream ss;
ss << n;
return ss.str();
}
operator Rational() const;
operator Complex() const;
operator int() const {
return n;
}
Number *operator*(const Rational r) const;
Number *add(const Natural* number) const {
return new Natural(n + number->n);
}
Number *add(const Rational*) const;
Number *add(const Complex*) const;
};
class Rational : public Number {
friend class Natural;
int numerator, denominator;
void divideByGCD() {
int a = numerator, b = denominator;
//cout << a << ' ' << b << ' ';
if(a < b) {
int temp = a;
a = b;
b = temp;
}
while (b > 0) {
int r = a % b;
a = b; b = r;
//cout << r << endl;
}
numerator /= a;
denominator /= a;
//cout << a << endl;
}
public:
Rational() {}
Rational(const Rational &s) {
numerator = s.numerator;
denominator = s.denominator;
}
Rational(int n, int d) {
if(d == 0) throw new runtime_error("denominator equals 0");
if(d < 0) {
numerator = -n;
denominator = -d;
} else {
numerator = n;
denominator = d;
}
divideByGCD();
}
Rational(double d) {
int i = 0, mul = 1;
int r = d-floor(d);;
while(r!=0) {
i++; mul *= 10;
r = 10*r-floor(10*r);
}
numerator = (int)mul*d;
denominator = mul;
divideByGCD();
}
string toString() const {
stringstream ss;
ss << numerator;
if(denominator > 1) ss << '/' << denominator;
return ss.str();
}
operator const Complex() const;
operator const double() const {
return (double)numerator/denominator;
}
Number *operator*(const Rational r) const {
return new Rational(numerator*r.numerator, denominator*r.denominator);
}
Number *add(const Rational* r) const {
return new Rational(numerator*r->denominator+r->numerator*denominator, denominator*r->denominator);
}
Number *add(const Natural*) const;
Number *add(const Complex*) const;
};
class Complex : public Number {
friend class Rational;
double real, imaginary;
static const double radius = 10;
public:
Complex() {}
Complex(const Complex &s) {
real = s.real;
imaginary = s.imaginary;
}
Complex(const double r, const double im) : real(r), imaginary(im) {}
string toString() const {
stringstream ss;
ss << real;
if(imaginary != 0) ss << '+' << imaginary << 'i';
return ss.str();
}
Number *operator*(const Rational r) const;
Number *add(const Complex* c) const {
return new Complex(real + c->real, imaginary + c->imaginary);
}
Number *add(const Natural*) const;
Number *add(const Rational*) const;
};
Natural::operator Rational() const {
return Rational(n,1);
}
Natural::operator Complex() const {
return Complex(n, 0);
}
Rational::operator const Complex() const {
return Complex((double)numerator/denominator, 0);
}
Number *Natural::operator*(const Rational r) const {
return new Rational(n*r.numerator, r.denominator);
}
Number *Complex::operator*(const Rational r) const {
return new Complex(real*(double)r, imaginary*(double)r);
}
Number *Natural::add(const Rational *r) const {
if(r->denominator == 1) return new Natural(n+r->numerator);
else return new Rational(n*r->denominator,r->denominator);
}
Number *Natural::add(const Complex *c) const {
return c->add(this);
}
Number *Rational::add(const Natural *n) const {
return n->add(this);
}
Number *Rational::add(const Complex *c) const {
return new Complex(c->real+(double)*this, c->imaginary);
}
Number *Complex::add(const Natural *number) const {
return new Complex(real+number->n, imaginary);
}
Number *Complex::add(const Rational *r) const {
return r->add(this);
}
Number *poly(double x, Number *a[], unsigned int size) {
if(size == 1) return a[0];
else return a[0]->add((*poly(x, a+1, size-1))*Rational(x));
}
int main() {
cout << (Natural(5)*(Rational)2.0)->toString() << endl;
Number *coefs[] = {new Natural(5), new Natural(6)};
cout << poly(2, coefs, 2) << endl;
}
我应该如何修复 Number::add(Number) 以便在对 Number 程序本身类型的对象调用 add 时确定要选择哪个虚拟方法 add?