C++实现分数四则运算
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#include <iostream>
using namespace std;
// 辗转相除法求最大公约数（12和18的最大公约数：6）
int gcd (int a, int b)
a = (a < 0) ? (a = -a) : (a = a);
b = (b < 0) ? (b = -b) : (b = b);
while (b != 0)
int rem = a % b;
a = b;
b = rem;
return a;
// 求最小公倍数（12和18的最小公倍数：36）
int lcm (int a, int b)
return a * b / gcd(a, b);
class Fraction
public:
int molecule; // 分子
int denominar; // 分母
// 构造函数，参数：分子，分母（默认为1）
Fraction (int mo, int de = 1)
if (mo > 0 && de < 0) // 若负号在分母上，则移至分子上
mo = -mo;
de = -de;
else if (mo < 0 && de < 0) // 分子与分母均为负，结果得正
mo = -mo;
de = -de;
else
mo = mo;
de = de;
int g = gcd(mo, de); // 求分子与分母的最大公约数
if (g != 0) // 在约分前，先判断最大公约数是否为0
this->molecule = mo / g;
this->denominar = de / g;
// 拷贝构造函数
Fraction (const Fraction &F)
int mo = F.molecule;
int de = F.denominar;
if (mo > 0 && de < 0) // 若负号在分母上，则移至分子上
mo = -mo;
de = -de;
else if (mo < 0 && de < 0) // 分子与分母均为负，结果得正
mo = -mo;
de = -de;
else
mo = mo;
de = de;
int g = gcd(mo, de); // 求分子与分母的最大公约数
if (g != 0) // 在约分前，先判断最大公约数是否为0
this->molecule = mo / g;
this->denominar = de / g;
// 析构函数
~Fraction ()
// 什么也不做
// 重载运算符：+
Fraction operator + (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0)) // 判断分母是否为0
int de = lcm(this->denominar, other.denominar);
int mo = (this->molecule * de / this->denominar) + (other.molecule * de / other.denominar);
return Fraction(mo, de);
else
return Fraction(1, 0);
// 重载运算符：-
Fraction operator - (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0)) // 判断分母是否为0
int de = lcm(this->denominar, other.denominar);
int mo = (this->molecule * de / this->denominar) - (other.molecule * de / other.denominar);
return Fraction(mo, de);
else
return Fraction(1, 0);
// 重载运算符：*
Fraction operator * (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0)) // 判断分母是否为0
int de = this->denominar * other.denominar;
int mo = this->molecule * other.molecule;
return Fraction(mo, de);
else
return Fraction(1, 0);
// 重载运算符：/
Fraction operator / (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0)) // 判断分母是否为0
int de = this->denominar * other.molecule;
int mo = this->molecule * other.denominar;
return Fraction(mo, de);
else
return Fraction(1, 0);
// 重载运算符：<
bool operator < (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 < l2;
else
return false;
// 重载运算符：>
bool operator > (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 > l2;
else
return false;
// 重载运算符：<=
bool operator <= (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 <= l2;
else
return false;
// 重载运算符：>=
bool operator >= (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 >= l2;
else
return false;
// 重载运算符：==
bool operator == (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 == l2;
else
return false;
// 重载运算符：!=
bool operator != (const Fraction &other)
if ((this->denominar != 0) && (other.denominar != 0))
int l = lcm(this->denominar, other.denominar);
int l1 = this->molecule * l / this->denominar;
int l2 = other.molecule * l / other.denominar;
return l1 != l2;
else
return false;
// 重载赋值运算符：=
void operator = (const Fraction &F)
int mo = F.molecule;
int de = F.denominar;
if (mo > 0 && de < 0) // 若负号在分母上，则移至分子上
mo = -mo;
de = -de;
else if (mo < 0 && de < 0) // 分子与分母均为负，结果得正
mo = -mo;
de = -de;
else
mo = mo;
de = de;
int g = gcd(mo, de); // 求分子与分母的最大公约数
if (g != 0) // 在约分前，先判断最大公约数是否为0
this->molecule = mo / g;
this->denominar = de / g;
// 重载输入流：>>
friend std::istream &operator >> (std::istream &input, Fraction &F)
input >> F.molecule >> F.denominar;
int mo = F.molecule;
int de = F.denominar;
if (mo > 0 && de < 0) // 若负号在分母上，则移至分子上
mo = -mo;
de = -de;
else if (mo < 0 && de < 0) // 分子与分母均为负，结果得正
mo = -mo;
de = -de;
else
mo = mo;
de = de;
int g = gcd(mo, de); // 求分子与分母的最大公约数
if (g != 0) // 在约分前，先判断最大公约数是否为0
F.molecule = mo / g;
F.denominar = de / g;
return input;
// 重载输出流：<<
friend std::ostream &operator << (std::ostream &output, Fraction &F)
if (F.denominar == 1 && F.molecule >= 0) // 分子大于等于0，分母为1
output << F.molecule;
else if (F.denominar == 1 && F.molecule < 0)// 分子小于0，分母为1
output << "(" << F.molecule << ")";
else if (F.denominar == 0) // 分母为0
output << "NaN";
else
output << "(" << F.molecule << "/" << F.denominar << ")";
return output;
;
int main()
int a, b;
cout << "请输入第一个分数的分子与分母：";
Fraction num1(1);
cin >> num1;
cout << num1 << endl;
cout << "请输入第二个分数的分子与分母：";
Fraction num2(1);
cin >> num2;
cout << num2 << endl;
cout << "请输入第三个分数的分子与分母：";
Fraction num7(1);
cin >> num7;
cout << num7 << endl;
cout << endl << "测试所有功能：" << endl;
Fraction num3 = num1 + num2;
Fraction num4 = num1 - num2;
Fraction num5 = num1 * num2;
Fraction num6 = num1 / num2;
cout << num1 << " + " << num2 << " = " << num3 << endl;
cout << num1 << " - " << num2 << " = " << num4 << endl;
cout << num1 << " * " << num2 << " = " << num5 << endl;
cout << num1 << " / " << num2 << " = " << num6 << endl;
cout << num1 << " < " << num2 << " ? " << (num1 < num2) << endl;
cout << num1 << " > " << num2 << " ? " << (num1 > num2) << endl;
cout << num1 << " <= " << num2 << " ? " << (num1 <= num2) << endl;
cout << num1 << " >= " << num2 << " ? " << (num1 >= num2) << endl;
cout << num1 << " == " << num2 << " ? " << (num1 == num2) << endl;
cout << num1 << " != " << num2 << " ? " << (num1 != num2) << endl;
cout << endl << "测试赋值功能：" << endl;
num2 = num7;
num3 = num1 + num2;
num4 = num1 - num2;
num5 = num1 * num2;
num6 = num1 / num2;
cout << num1 << " + " << num2 << " = " << num3 << endl;
cout << num1 << " - " << num2 << " = " << num4 << endl;
cout << num1 << " * " << num2 << " = " << num5 << endl;
cout << num1 << " / " << num2 << " = " << num6 << endl;
cout << num1 << " < " << num2 << " ? " << (num1 < num2) << endl;
cout << num1 << " > " << num2 << " ? " << (num1 > num2) << endl;
cout << num1 << " <= " << num2 << " ? " << (num1 <= num2) << endl;
cout << num1 << " >= " << num2 << " ? " << (num1 >= num2) << endl;
cout << num1 << " == " << num2 << " ? " << (num1 == num2) << endl;
cout << num1 << " != " << num2 << " ? " << (num1 != num2) << endl;
return 0;
输入与输出样例 1：
请输入第一个分数的分子与分母：70 90
(7/9)
请输入第二个分数的分子与分母：45 60
(3/4)
请输入第三个分数的分子与分母：13 44
(13/44)
测试所有功能：
(7/9) + (3/4) = (55/36)
(7/9) - (3/4) = (1/36)
(7/9) * (3/4) = (7/12)
(7/9) / (3/4) = (28/27)
(7/9) < (3/4) ? 0
(7/9) > (3/4) ? 1
(7/9) <= (3/4) ? 0
(7/9) >= (3/4) ? 1
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