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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?

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3 回答 3

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我认为问题是:

virtual Number *add(const Number *n) const {
   n->add(this);
}

如果将 Rational 与存储在 Number * 中的 Natural 相乘,它不能将 Number * 多态向上转换为 Natural *。我同意 w/g-makulik,因为引用/值在这里更有意义,因为您到处都在泄漏内存。删除对数字 + 数字的支持。另外,如果我将 Natural 和 Rational 加在一起,我会得到一个 Number *,但它是什么类型的数字?我认为架构需要更多的思考。我可能会完全摆脱基类的纯虚方法(toString 除外)。例如:

class Number
{
    public:
        virtual string toString() = 0;
};

class Rational : public Number
{
    string toString() {...}
    // forget 'add', use operators
    Rational operator+(const Rational & _rhs) const {Rational ret; ...; return ret;}
    Rational & operator+=(const Rational & _rhs) const {...; return *this;}
    ...
}

编辑 为了快速修复,我认为您只需要摆脱virtual Number *operator*(const Rational) const = 0;,并将其替换为每个子类的版本(例如,Rational * operator*(const Natural) const

或者,将枚举成员变量添加到 Number 以跟踪类型:

enum Type { NATURAL, RATIONAL, ...}

Type mType;

或使用 RTTI,这样您就可以在 Number::add 中选择性地选择正确的添加方法:

Number * add(Number * _rhs)
{
   if(_rhs->mType == RATIONAL)
      return this->add((Rational *)_rhs);
   ...
}

它看起来有点草率,但它会工作

于 2013-03-21T19:46:04.980 回答
0

这称为多分派。这里有一些链接可以查看

Multiple_dispatch

最佳多方法实现

于 2013-03-21T19:59:15.790 回答
0

看起来访客模式是我一直在寻找的。我想让函数在同一个类中接受和访问。我相信我的错误是给他们起相同的名字。

于 2013-03-28T16:22:18.343 回答