C++ 有理数运算符重载

有理数运算重载

要求：有理数为最简有理数，若分子与分母整除输出整数。

思想总结：

简单代码思想： 1.有理数简化： 判断分子分母大小，取较小值作为辅助变量，用循环for( i=min; i>1; i-- )判断分子分母同时%i，判断余数，当余数为0表示有公因数，且最大公约数将是第一个被提取出。 2.有理数加减：判断操作数双方分母是否相同，用累加方式找最小公倍数，直到双方分母相同，在对分子进行相加减。 3.整数输出：判断分子是否能整除分母，若余数为0，则满足条件。 4.打印：调用行为print，依次对分子分母根据格式 （分子 “/” 分母 ）进行输出

代码优化： 1.有理数简化：采用欧立德算法，循环对除数进行求模，在将被除数作为除数，直到余数为0，即获得最大公约数，即当前除数为最大公因数。 2.有理数加减：不用找最小公倍数，直接用公式，这样操作只需一步，效率高。 例如：a/b + a1/b1 = (a * b1 + a1 * b) / b*b1 3.打印：将std类中的左移运算符<<重载，使它能够输出Ration格式的数据。

初版本

#include <iostream> #include <string> #include <stdlib.h> class Ration { public: Ration(); Ration(int d, int m); Ration operator+(Ration d); Ration operator-(Ration d); Ration operator*(Ration d); Ration operator/(Ration d); void print(); private: int molecule; int denominator; }; Ration::Ration() { denominator = 0; molecule = 0; } Ration::Ration(int d, int m) { denominator = d; molecule = m; } Ration Ration::operator+(Ration d) { Ration c; int mtmp = molecule, dtmp = denominator; int mtmp2 = d.molecule, dtmp2 = d.denominator; while( mtmp != mtmp2 ) { if(mtmp < mtmp2) { mtmp += molecule; dtmp += denominator; } else if( mtmp > mtmp2 ) { mtmp2 += d.molecule; dtmp2 += d.denominator; } } c.molecule = mtmp; c.denominator = dtmp + dtmp2; return c; } Ration Ration::operator-(Ration d) { Ration c; int mtmp = molecule, dtmp = denominator; int mtmp2 = d.molecule, dtmp2 = d.denominator; while( mtmp != mtmp2 ) { if(mtmp < mtmp2) { mtmp += molecule; dtmp += denominator; } else if( mtmp > mtmp2 ) { mtmp2 += d.molecule; dtmp2 += d.denominator; } } c.molecule = mtmp; c.denominator = dtmp - dtmp2; return c; } Ration Ration::operator*(Ration d) { Ration c; c.molecule = molecule * d.molecule; c.denominator = denominator * d.denominator; return c; } Ration Ration::operator/(Ration d) { Ration c; c.molecule = molecule * d.denominator; c.denominator = denominator * d.molecule; return c; } void Ration::print() { int i=0; if( abs(molecule) > abs(denominator) ) { for(i=abs(denominator); i>1; i--) { if( denominator % i == 0 && molecule % i == 0 ) { molecule /= i; denominator /= i; break; } } } else { for(i=abs(molecule); i>1; i--) { if( denominator % i == 0 && molecule % i == 0 ) { molecule /= i; denominator /= i; break; } } } if( denominator % molecule == 0 ) std::cout << "整数：" << denominator << std::endl; else std::cout << denominator << " / " << molecule << std::endl; } int main() { Ration r1(3,8),r2(13,8),r3; r3 = r1 + r2; r3.print(); r3 = r1 - r2; r3.print(); r3 = r2 * r1; r3.print(); r3 = r2 / r1; r3.print(); std::cin.get(); return 0; }

优化版本

#include <iostream> #include <string> #include <stdlib.h> class Ration { public: Ration(); Ration(int m, int d); Ration operator+(Ration d); Ration operator-(Ration d); Ration operator*(Ration d); Ration operator/(Ration d); private: void normalize();//简化 int molecule;//分子 int denominator;//分母 friend std::ostream& operator<<(std::ostream &os, Ration f); }; Ration::Ration() { molecule = 0; denominator = 0; } Ration::Ration(int m, int d) { molecule = m; denominator = d; normalize();//简化 } void Ration::normalize() { //分母不为负数，若为负数则将符号提到分子 if( denominator < 0 ) { denominator = -denominator; molecule = -molecule; } //欧几里德算法 int a = abs( molecule ); int b = abs( denominator ); //最大公约数 while( b > 0 ) { int t = a%b; a=b; b=t; } molecule /= a; denominator /= a; } Ration Ration::operator+(Ration d) { int a = molecule, a1 = denominator; int b = d.molecule, b1 = d.denominator; int c = a*b1 + a1*b; int f = a1 * b1; return Ration(c, f); } Ration Ration::operator-(Ration d) { int a = molecule, a1 = denominator; int b = d.molecule, b1 = d.denominator; int c = a*b1 - a1*b; int f = a1 * b1; return Ration(c, f); } Ration Ration::operator*(Ration d) { int a = molecule, a1 = denominator; int b = d.molecule, b1 = d.denominator; int c = a * b; int f = a1 * b1; return Ration(c, f); } Ration Ration::operator/(Ration d) { int a = molecule, a1 = denominator; int b = d.molecule, b1 = d.denominator; int c = a * b1; int f = a1 * b; return Ration(c, f); } void Ration::print() { if( molecule % denominator == 0 ) std::cout << "整数：" << molecule << std::endl; else std::cout << molecule << "/" << denominator << std::endl; } std::ostream &operator<<(std::ostream &os, Ration f); int main() { Ration r1(3,8),r2(13,8),r3; std::cout << r1 << "+" << r2 << "=" << (r1+r2) << std::endl; std::cout << r1 << "-" << r2 << "=" << (r1-r2) << std::endl; std::cout << r1 << "*" << r2 << "=" << (r1*r2) << std::endl; std::cout << r1 << "/" << r2 << "=" << (r1/r2) << std::endl; return 0; } std::ostream &operator<<(std::ostream &os, Ration f) { os << f.molecule << "/" << f.denominator; return os; }