fraction

this assignment you are required to complete a class for fractions. It stores the numerator and the denominator, with the lowest terms. It is able to communicate with iostreams by the operator << and >>. For more details, read the header file. Sample Input 1 0 2 3 Sample Output NaN NaN NaN NaN NaN False True False False True True Hint: 如果分母为0，那么进行四则运算时返回一个0/0. ==操作符 相等的情况是 两个数分母都为0或者两个数本身相等。 <的操作就按正常的比较即可。

main函数

void print(const bool & f) { if (f) std::cout << "True" << std::endl; else std::cout << "False" << std::endl; } int main() { fraction f1, f2; std::cin >> f1 >> f2; std::cout << f1 + f2 << ' ' << f1 - f2 << ' ' << f1 * f2 << ' ' << f1 / f2 << std::endl; f1 += f2; f1 -= f2; f1 *= f2; f1 /= f2; std::cout << f1 << std::endl; print(f1 == f2); print(f1 != f2); print(f1 < f2); print(f1 > f2); print(f1 <= f2); print(f1 >= f2); return 0; }

.h文件

#include <iostream> class fraction { private: int _numerator, _denominator; int gcd(const int &, const int &) const; // If you don't need this method, just ignore it. void simp(); // To get the lowest terms. public: fraction(const int & = 0, const int & = 1); // The numerator and the denominator // fraction(5) = 5/1 = 5 :) fraction(const fraction &); // copy constructor void operator=(const fraction &); // You must know the meaning of +-*/, don't you ? fraction operator+(const fraction &) const; fraction operator-(const fraction &) const; fraction operator*(const fraction &) const; fraction operator/(const fraction &) const; void operator+=(const fraction &); void operator-=(const fraction &); void operator*=(const fraction &); void operator/=(const fraction &); // Comparison operators bool operator==(const fraction &) const; bool operator!=(const fraction &) const; bool operator<(const fraction &) const; bool operator>(const fraction &) const; bool operator<=(const fraction &) const; bool operator>=(const fraction &) const; friend std::istream & operator>>(std::istream &, fraction &); // Input Format: two integers with a space in it // "a b" is correct. Not "a/b" friend std::ostream & operator<<(std::ostream &, const fraction &); // Normally you should output "a/b" without any space and LF // Sometims you may output a single integer (Why? Guess XD) // If it is not a number (den = 0), output "NaN" };

解答

long long mgcd( long long a,long long b) { long long i; if (b==0) i=a; else i=mgcd(b,a%b); return i; } // If you don't need this method, just ignore it. void fraction::simp() { _numerator/=mgcd(_numerator,_denominator); _denominator/=mgcd(_numerator,_denominator); } // To get the lowest terms. fraction::fraction(const int&a,const int&b):_numerator(a),_denominator(b) { } // The numerator and the denominator // fraction(5) = 5/1 = 5 :) fraction::fraction(const fraction &a) { _numerator=a._numerator; _denominator=a._denominator; } // copy constructor void fraction::operator=(const fraction &a) { this->_denominator=a._denominator; this->_numerator=a._numerator; } // You must know the meaning of +-*/, don't you ? fraction fraction::operator+(const fraction &t)const { fraction temp; long long a=_denominator; long long c=_numerator; long long b=t._denominator; long long d=t._numerator; long long m=mgcd(a*b, b*c+a*d); temp._denominator=(int)(a*b/m); temp._numerator=(int)((b*c+a*d)/m); return temp; } fraction fraction::operator-(const fraction &t) const { fraction temp; long long a=_denominator; long long c=_numerator; long long b=t._denominator; long long d=t._numerator; long long m=mgcd(a*b, b*c-a*d); temp._denominator=(int)(a*b/m); temp._numerator=(int)((b*c-a*d)/m); return temp; } fraction fraction::operator*(const fraction &t) const { fraction temp; long long a=_denominator; long long c=_numerator; long long b=t._denominator; long long d=t._numerator; long long m=mgcd(a*b, c*d); temp._denominator=(int)(a*b/m); temp._numerator=(int)((c*d)/m); return temp; } fraction fraction::operator/(const fraction &t) const { fraction temp; long long a=_denominator; long long c=_numerator; long long b=t._denominator; long long d=t._numerator; long long m=mgcd(a*d, c*b); temp._denominator=(int)(a*d/m); temp._numerator=(int)((c*b)/m); return temp; } void fraction::operator+=(const fraction &a) { (*this)=(*this)+a; } void fraction::operator-=(const fraction &a) { (*this)=(*this)-a; } void fraction::operator*=(const fraction &a) { (*this)=(*this)*a; } void fraction::operator/=(const fraction &a) { (*this)=(*this)/a; } // Comparison operators bool fraction::operator==(const fraction &a) const { fraction temp1(*this),temp2(a); temp1.simp(); temp2.simp(); if((temp1._denominator==temp2._denominator&&temp1._numerator==temp2._numerator)||(temp1._denominator==0&&temp2._denominator==0)) return true; return false; } bool fraction::operator!=(const fraction &a) const { if((*this)==a) return false; return true; } bool fraction::operator<(const fraction &a) const { double m=a._numerator*1.0/a._denominator; double n=_numerator*1.0/_denominator; if(n<m) return true; return false; } bool fraction::operator>(const fraction &a) const { if((*this)<a||(*this)==a) return false; return true; } bool fraction::operator<=(const fraction &a) const { if((*this)<a||(*this)==a) return true; return false; } bool fraction::operator>=(const fraction &a) const { if((*this)>a||(*this)==a) return true; return false; } std:: istream &operator>>(std::istream &in, fraction &a) { in>>a._numerator>>a._denominator; return in; } // Input Format: two integers with a space in it // "a b" is correct. Not "a/b" std::ostream & operator<<(std::ostream &out, const fraction &a) { if((a._numerator<0&&a._denominator>0)||(a._numerator>0&&a._denominator<0)) out<<'-'<<abs(a._numerator)<<'/'<<abs(a._denominator); else out<<abs(a._numerator)<<'/'<<abs(a._denominator); return out;

心得： （1）

fraction fraction::operator+(const fraction &t)const { fraction temp; long long a=_denominator; long long c=_numerator; long long b=t._denominator; long long d=t._numerator; long long m=mgcd(a*b, b*c+a*d); temp._denominator=(int)(a*b/m); temp._numerator=(int)((b*c+a*d)/m); return temp; }

这样写的目的主要是为了避免溢出的情况。