C++求解形如“a/b x + d/c = f/e”的一元一次分式方程

思路比较清晰

1.从命令行读入方程

2.解析字符串，解析出几个参数a/b,d/c,f/e

3.Rational类定义了分数的运算，代入运算即可

这个小程序的结构

\---main.cpp       程序的入口

|---rational.h      分数类的声明

|---Rational.cpp分数类的实现

|---myException.h定义几个异常类

|---test.cpp单独使用，测试Rational类

代码如下

main.cpp

#include "rational.h"
#include "Rational.cpp"

using namespace std;

int main(){
while(1){
    cout << "输入方程：形如a/b x + d/c = f/e"<<endl;
    char Arr[50];
    cin.getline(Arr, 50);
    string equation(Arr);
   // cout << equation <<endl;
//   a/b x + d/c = f/e
    int pos_x = equation.find('x',0);
    int pos_p = equation.find('+',0);
    int pos_e = equation.find('=',0);

    Rational coe( equation.substr(0,pos_x) );// a/b
    Rational b( equation.substr(pos_p+1,pos_e - pos_p) );// d/c
    Rational c( equation.substr(pos_e+1,equation.length()-pos_e) );// f/e

 //   cout<<"coe = "<<coe<<endl;
 //   cout<<"b = "<<b<<endl;
 //   cout<<"c = "<<c<<endl;
    if(coe.getNumer() == 0 && b.isEqual(c)) cout<<"x ∈ Q"<<endl;
    else if(coe.getNumer() == 0 && !b.isEqual(c)) cout<<"无解"<<endl;
    else  cout<<"解得 x = "<<(c-b)/coe<<endl<<endl;

    system("pause");
    system("cls");
}
}

rational.h

#ifndef Rational_
#define Rational_
#include "myException.h"
#include<iostream>
using namespace std;

class Rational{
public:
    Rational(int x, int y);//传入分子分母构造分数
    Rational(string s);//从字符串构造分数
    Rational nega();//相反数
    Rational reci();//倒数
    bool isEqual(Rational that);
    Rational add(Rational that);//加法
    Rational sub(Rational that);//减法
    Rational mul(Rational that);//乘法
    Rational div(Rational that);//除法
    void Output(ostream &out)const;//输出方法
    int getNumer(){return numer;}
    int getDenom(){return denom;}
private:
    int numer;//分子
    int denom;//分母
    int gcd(int a, int b) const { return (b==0) ? a : gcd(b, a % b); }//最大公约数
};
#endif // Rational_define

Rational.cpp

#include "rational.h"
#include "myException.h"
#include<cstdlib>

using namespace std;

Rational::Rational(int x, int y){//传入分子分母构造分数
    if(y==0) throw new illegalDenominatorValue();
    numer = x;
    denom = y;
}
//从字符串构造分数
Rational::Rational(string s){
    int pos = s.find('/',0);
    if(pos <= 0 || pos >= s.length()-1) throw new illegalInputExpression();
    numer = atoi( s.substr(0,pos).c_str() );
    denom = atoi( s.substr(pos+1,s.length()-pos-1).c_str() );
    if(denom == 0 ) throw new illegalDenominatorValue();
}
//相反数
Rational Rational::nega(){
    return Rational(-numer, denom);
}
//倒数
Rational Rational::reci(){
    if(numer == 0) throw new NoReciprocal();
    return Rational(denom,numer);
}
//相等
 bool Rational::isEqual(Rational that){
    return numer * that.denom == denom * that.numer;
 }
//加法
Rational Rational::add(Rational that){
    return Rational(numer * that.denom + denom * that.numer,denom * that.denom);
}
//减法
Rational Rational::sub(Rational that){
    return add(that.nega());
}
//乘法
Rational Rational::mul(Rational that){
    return Rational(numer  *  that.numer, denom * that.denom);
}
//除法
Rational Rational::div(Rational that){
    return mul(that.reci());
}
//输出
 void Rational::Output(ostream &out)const{
        int c = gcd(numer,denom);
       // int c = 1;
        out<<numer/c<<"/"<<denom/c;
 }
 //输出操作符重载
ostream& operator<<(ostream& out, const Rational& r){
    r.Output(out);
    return out;
}
//操作符重载
Rational operator +(Rational a, Rational b){
    return a.add(b);
}
Rational operator -(Rational a, Rational b){
    return a.sub(b);
}
Rational operator *(Rational a, Rational b){
    return a.mul(b);
}
Rational operator /(Rational a, Rational b){
    return a.div(b);
}

myException.h

// exception classes for various error types

#ifndef myExceptions_
#define myExceptions_
#include <string>
#include<iostream>
using namespace std;

// illegal Denominator value
class illegalDenominatorValue
{
   public:
      illegalDenominatorValue(string theMessage = "Denominator must be nonezero!"){
          message = theMessage;
      }
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};

// illegal input Expression
class illegalInputExpression
{
   public:
      illegalInputExpression(string theMessage = "Illegal  input Expression"){
          message = theMessage;
      }
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};
//倒数
class NoReciprocal
{
   public:
      NoReciprocal(string theMessage = "No Reciprocal with numerator=0"){
          message = theMessage;
      }
      void outputMessage() {cout << message << endl;}
   private:
      string message;
};
#endif

test.cpp

#include "rational.h"
#include "Rational.cpp"
using namespace std;
int main(){
    Rational a(1,2);
    Rational b("1/4");
    //Rational c("1/0");
    //Rational c("1/");
    cout<<"a =  \t"<<   a       <<endl;
    cout<<"b =  \t"<<   b       <<endl;
    cout<<"-a = \t"<<   a.nega()<<endl;
    cout<<"1/b =\t"<<   b.reci()<<endl;

    cout<<"a.add(b) =\t"<<   a.add(b)<<endl;
    cout<<"a.sub(b) =\t"<<   a.sub(b)<<endl;
    cout<<"a.mul(b) =\t"<<   a.mul(b)<<endl;
    cout<<"a.div(b) =\t"<<   a.div(b)<<endl;

    cout<<"a+b =\t"<<   a+b<<endl;
    cout<<"a-b =\t"<<   a-b<<endl;
    cout<<"a*b =\t"<<   a*b<<endl;
    cout<<"a/c =\t"<<   a/b<<endl;

    return 0;
}

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