大数处理复数——C++实现

 

大数处理复数——C++实现

 　　继博主处理大数加法、大数减法、大数乘法（大数除法暂未实现，不了解博主大数实现点这里： http://www.cnblogs.com/hugeNumber/articles/5376906.html）之后的另一篇有关大数处理复数的博文。同样风格，首先了解大数处理机理。　　

一、解题思路

核心思想

由于大数实现，需要大量分配动态内存，而且实现机理比较复杂，运算量巨大。本文 复数处理同样提供复数常规处理（即double类），预处理命令#define DOUBLE

方便了常规复数处理与复数的大数处理间切换。

 　　//复数类：

class complex{
private:
    numbertype real;//实部
    numbertype imag;//虚部

public:

    complex(){}

    complex(numbertype r, numbertype i):real(r),imag(i)//构造函数
    {}
    complex(complex &obj)//拷贝构造函数
    {
        this->real = obj.real;    //实部
        this->imag = obj.imag;    //虚部
    }
    complex (numbertype real)
    {
        this->real = real;
        imag = 0;
    }
#ifndef DOUBLE
    complex (char * nptr)
    {
        numbertype tmp(nptr);
        this->real = tmp;
        imag = 0;
    }
#endif
    //函数实现加减乘除，不提倡使用
    friend complex add(complex &a, complex &b);//加
    friend complex sub(complex &a, complex &b);//减
    friend complex mul(complex &a, complex &b);//乘
    friend complex div(complex &a, complex &b);//除
    //运算符重载
    friend complex operator+(complex &a, complex &b);
    friend complex operator-(complex &a, complex &b);
    friend complex operator*(complex &a, complex &b);
    friend complex operator/(complex &a, complex &b);
    friend ostream & operator<<(ostream &out, complex &obj);
};

二、具体实现
1 复数类成员函数实现

#include <string>
#include <cctype>
#include <algorithm>
#include <iostream>
using namespace std;
//复数常规处理与大数处理切换
typedef hugeNumber numbertype;

//typedef double numbertype;
//#define DOUBLE

class complex{
    numbertype real;//实部
    numbertype imag;//虚部
public:
    complex(){}
    complex(numbertype r, numbertype i):real(r),imag(i)
    {}
    complex(complex &obj)
    {
        this->real = obj.real;    //实部
        this->imag = obj.imag;    //虚部
    }
    complex (numbertype real)
    {
        this->real = real;
        imag = 0;
    }
#ifndef DOUBLE
    complex (char * nptr)
    {
        numbertype tmp(nptr);
        this->real = tmp;
        imag = 0;
    }
#endif
    
    friend complex add(complex &a, complex &b);//加
    friend complex sub(complex &a, complex &b);//减
    friend complex mul(complex &a, complex &b);//乘
    friend complex div(complex &a, complex &b);//除
    //运算符重载
    friend complex operator+(complex &a, complex &b);
    friend complex operator-(complex &a, complex &b);
    friend complex operator*(complex &a, complex &b);
    friend complex operator/(complex &a, complex &b);
    friend ostream & operator<<(ostream &out, complex &obj);
};
//加
complex add(complex &a, complex &b)
{
    return complex(a.real + b.real, a.imag + b.imag);
}
complex operator+(complex &a, complex &b)
{
    return complex(a.real + b.real, a.imag + b.imag);
}
//减
complex sub(complex &a, complex &b)
{
    return complex(a.real - b.real, a.imag - b.imag);
}
complex operator-(complex &a, complex &b)
{
    return complex(a.real - b.real, a.imag - b.imag);
}
//乘
complex mul(complex &a, complex &b)
{
    return complex(a.real * b.real - a.imag * b.imag , a.imag * b.real + a.real * b.imag);
}
complex operator*(complex &a, complex &b)
{
    return complex(a.real * b.real - a.imag * b.imag , a.imag * b.real + a.real * b.imag);
}

//除
#ifdef DOUBLE
complex div(complex &a, complex &b)
{
    numbertype tmreal, tmimage, tmp;
    tmp = b.real * b.real + b.imag * b.imag;
    //tmreal = (a.real * b.real + a.imag * b.imag)/(b.real * b.real + b.imag * b.imag);
    //tmimage = (a.imag * b.real - a.real * b.imag)/(b.real * b.real + b.imag * b.imag);
    tmreal = (a.real * b.real + a.imag * b.imag)/tmp;
    tmimage = (a.imag * b.real - a.real * b.imag)/tmp;
    return complex(tmreal, tmimage);
}
complex operator/(complex &a, complex &b)
{
    numbertype tmreal, tmimage, tmp;
    tmp = b.real * b.real + b.imag * b.imag;
    //tmreal = (a.real * b.real + a.imag * b.imag)/(b.real * b.real + b.imag * b.imag);
    //tmimage = (a.imag * b.real - a.real * b.imag)/(b.real * b.real + b.imag * b.imag);
    tmreal = (a.real * b.real + a.imag * b.imag)/tmp;
    tmimage = (a.imag * b.real - a.real * b.imag)/tmp;
    return complex(tmreal, tmimage);
}
ostream & operator<<(ostream &out, complex &obj)
{
    out<<obj.real;
    if(obj.imag > 0)out<<"+";
    out<<obj.imag<<" i";
    return out;
}
#endif
#ifndef DOUBLE
ostream & operator<<(ostream &out, complex &obj)
{
    out<<obj.real;
    if(obj.imag.getsign() == 1)
        out<<"+";
    out<<obj.imag<<" i";
    return out;
}
#endif
//friend complex add(complex &a, complex &b);//加
//friend complex sub(complex &a, complex &b);//减
//friend complex mul(complex &a, complex &b);//乘
//friend complex div(complex &a, complex &b);//除
////运算符重载
//friend complex operator+(complex &a, complex &b);
//friend complex operator-(complex &a, complex &b);
//friend complex operator*(complex &a, complex &b);
//friend complex operator/(complex &a, complex &b);
//friend ostream & operator<<(ostream &out, complex &obj);
//friend istream & operator>>(istream &in, complex &obj);

//int __wdiv(int divisor, int dividend)//除数与被除数
//{
//    int quotient;//商
//    unsigned char counter, sign;
//    sign = 0;
//    if(divisor < 0)
//    {
//        divisor = - divisor;
//        sign = 1;
//    }
//    if(dividend < 0)
//    {
//        dividend = - dividend;
//        sign = 1;
//    }
//
//    quotient = 0;
//    if(divisor != 0)
//    {
//        counter = 1;
//        while((divisor & 0x8000U == 0))
//        {
//            divisor <<= 1;
//            counter++;
//        }
//        do{
//            quotient <<= 1;
//            if((unsigned int)divisor <=(unsigned int)dividend)
//            {
//                dividend -= divisor;
//                quotient |= 1;
//            }
//            *(unsigned int *)&divisor >>= 1;        
//        }while(--counter != 0);
//    }
//    if(sign)
//        quotient = - quotient;
//    return quotient;
//}
//
//int __wmul(int multiplier, int multiplicand)
//{
//        int product = 0;
//        do{
//            if(multiplier & 1)
//                product += multiplicand;
//            multiplicand <<= 1;
//            multiplier >>= 1;
//        }while(multiplier != 0);
//        return product;
//}

void Input(hugeNumber &x, hugeNumber &y)
{
    char str[512];

    do{
        cout<<"请输入一个实数(退出请输入esc):"<<endl;
        cin.clear(); //cin.fail()返回0；
        cin.sync();  //清空流
        cin.getline(str,sizeof(str));
        string s(str);//char * To string
        transform(s.begin(),s.end(),s.begin(), ::tolower);//大写转小写
        const char *str1 = s.c_str();//string To char *
        if(strcmp(str1,"esc") == 0)exit(0);
    }while(!isNumber(str) );   
    x = hugeNumber(str);

    do{
        cout<<"请输入一个虚数(退出请输入esc):"<<endl;
        cin.clear(); //cin.fail()返回0；
        cin.sync();  //清空流
        cin.getline(str,sizeof(str));
        string s(str);//char * To string
        transform(s.begin(),s.end(),s.begin(), ::tolower);//大写转小写
        const char *str1 = s.c_str();//string To char *
        if(strcmp(str1,"esc") == 0)exit(0);
    }while(!isNumber(str) );

    y = hugeNumber(str);
}
void Input(double &x, double &y)
{
    char str[512];

    do{
        cout<<"请输入一个实数(esc:退出):"<<endl;
        cin>>str;   
        string s(str);//char * To string
        transform(s.begin(),s.end(),s.begin(), ::tolower);//大写转小写
        const char *str1 = s.c_str();//string To char *
        if(strcmp(str1,"esc") == 0)exit(0);
    }while( !Valid_Check_Double(str, &x));  

    do{
        cout<<"请输入一个虚数(esc:退出):"<<endl;
        cin>>str;   
        string s(str);//char * To string
        transform(s.begin(),s.end(),s.begin(), ::tolower);//大写转小写
        const char *str1 = s.c_str();//string To char *
        if(strcmp(str1,"esc") == 0)exit(0);
    }while( !Valid_Check_Double(str, &y));  

}

 

2 main测试函数：

int main()
{
    //测试用
    //numbertype x ("11111111.222222e32");
    //numbertype y ("444444444.5555e37");

    //numbertype x1("333333333333.4444e23");
    //numbertype y1("6666666.777777e28");
    
    numbertype x, y, x1, y1;
    cout<<"【请输入第一个复数：】"<<endl;
    Input(x, y);
    cout<<"【请输入第二个复数：】"<<endl;
    Input(x1, y1);

    complex a(x, y),b(x1, y1);

    cout<<"【您输入的两个复数分别为：】"<<endl;
    cout<<"a = "<<a<<endl<<"b = "<<b<<endl<<endl;

    cout<<endl<<"================================================================================"<<endl;

    //cout<<x-x1<<endl;
    //cout<<y-y1<<endl;
    ////测试一
    //cout<<"a+b="<<add(a,b)<<endl;
    //cout<<"a-b="<<sub(a,b)<<endl;
    //cout<<"a*b="<<mul(a,b)<<endl;

    ////测试二
    cout<<"a+b="<<a+b<<endl<<endl;
    cout<<"a+b+b="<<a+b+b<<endl<<endl;
    cout<<"a-b="<<a-b<<endl<<endl;
    cout<<"a*b="<<a*b<<endl;
#ifdef DOUBLE
    cout<<"a/b="<<a/b<<endl;
    cout<<"a/b="<<div(a,b)<<endl;
#endif

    /*hugeNumber a;
    cin>>a;
    cout<<"请输出结果:"<<endl<<a<<endl;*/
    return 0;
}

 

3 实验结果：

 

博文为作者原创，版权归云南师范大学信息学院所有，引用请注明出处！