C++实现复数类和大整数类

用C++实现复数类以及大整数类，主要是练习C++的运算符重载等知识。

复数类：

主要实现构造，重载+-运算符。

#include<bits/stdc++.h>
using namespace std;

class Complex {
public:
    double real;
    double image;
    Complex(double r=2.0,double i=-2.0);
    Complex(const Complex& c);
    
    //一元运算符推荐不用友元 
    Complex& operator += (const Complex& c);
    Complex& operator -= (const Complex& c);
    
    //二元运算符推荐用友元 
    friend bool operator == (const Complex& c1,const Complex& c2);
    friend Complex operator + (const Complex& c1,const Complex& c2);
    friend ostream& operator << (ostream& o,const Complex& c);
};

Complex::Complex(double r,double i) : real(r),image(i) { }
Complex::Complex(const Complex& c) {
    this->real=c.real;
    this->image=c.image;
}

Complex& Complex::operator +=(const Complex& c) {
    this->real+=c.real;
    this->image+=c.image;
    return *this;
}

Complex& Complex::operator -=(const Complex& c) {
    this->real-=c.real;
    this->image-=c.image;
    return *this;
}

bool operator == (const Complex& c1,const Complex& c2) {
    return (c1.real==c2.real && c1.image==c2.image);
}

Complex operator + (const Complex& c1,const Complex &c2) {
    Complex ret(c1.real+c2.real,c1.image+c2.image);
    return ret;
}

ostream& operator << (ostream& o,const Complex& c) {
    o<<c.real<<" "<<c.image<<endl;
    return o; 
}

int main()
{
    Complex c1;
    Complex c2(3.0,-3.0);
    Complex c3=c1;
    cout<<"c1:"<<c1<<"c2:"<<c2<<"c3:"<<c3;
    cout<<"c1==c2 ? "<<(c1==c2)<<endl;
    cout<<"c1==c3 ? "<<(c1==c3)<<endl;
    cout<<"c1+c2 : "<<(c1+c2);
    
    c1+=c2;
    cout<<"c1:"<<c1;
    c1-=c3;
    cout<<"c1:"<<c1;
    return 0;
} 

大整数类：

#include<bits/stdc++.h>
using namespace std;

class BigInteger {
private:
    vector<char> digits;
    bool sign;
    void trim();
    
public:
    BigInteger();
    BigInteger(int b);
    BigInteger(const string& s);
    BigInteger(const BigInteger& b);
    
    friend int abscompare(const BigInteger& b1,const BigInteger& b2);
    friend bool operator == (const BigInteger& b1,const BigInteger& b2);
    friend bool operator < (const BigInteger& b1,const BigInteger& b2);
    friend bool operator > (const BigInteger& b1,const BigInteger& b2);
    
    BigInteger operator - ();    //负号 
    BigInteger& operator += (const BigInteger& b);
    BigInteger& operator -= (const BigInteger& b);
    BigInteger& operator *= (const BigInteger& b);
    BigInteger& operator /= (const BigInteger& b);
    
    friend void carry(BigInteger& b);
    friend BigInteger operator + (const BigInteger& b1,const BigInteger& b2);
    friend BigInteger operator - (const BigInteger& b1,const BigInteger& b2);
    friend BigInteger operator * (const BigInteger& b1,const BigInteger& b2);
    friend BigInteger operator / (const BigInteger& b1,const BigInteger& b2);
    
    void print();
};

BigInteger::BigInteger() {
    sign=true;
}
BigInteger::BigInteger(int b) {
    if (b<0) { sign=false; b=-b; }
    else sign=true;
    while (b) {
        digits.push_back(char('0'+b%10));
        b/=10;
    }
}
BigInteger::BigInteger(const string& s) {
    int start=0,len=s.length();
    if (s[0]=='-') { start=1; sign=false; }
    else { start=0; sign=true; }
    
    for (int i=len-1;i>=start;i--)
        digits.push_back(s[i]);
}
BigInteger::BigInteger(const BigInteger& b) {
    sign=b.sign;
    digits=b.digits;
}

void BigInteger::print() {
    if (!sign) cout<<"-";
    for (int i=digits.size()-1;i>=0;i--)
        cout<<digits[i];
    //cout<<endl;    
}

BigInteger BigInteger::operator - () {
    BigInteger tmp=*this;
    tmp.sign=1-tmp.sign;
    return tmp;
}

//比较b1和b2的绝对值大小，b1>b2返回1，b1==b2返回0，b1<b2返回-1 
int abscompare(const BigInteger& b1,const BigInteger& b2) {
    if (b1.digits.size()>b2.digits.size()) return 1;
    if (b1.digits.size()<b2.digits.size()) return -1;
    bool bigger=0,smaller=0;
    int len=b1.digits.size();
    for (int i=len-1;i>=0;i--) {
        if (b1.digits[i]>b2.digits[i]) { bigger=true; break; }
        if (b1.digits[i]<b2.digits[i]) { smaller=true; break; }
    }
    if (bigger) return 1;
    else if (smaller) return -1;
    else return 0;
}
bool operator == (const BigInteger& b1,const BigInteger& b2) {
    if (b1.sign!=b2.sign) return false;
    return (abscompare(b1,b2)==0);
}
bool operator < (const BigInteger& b1,const BigInteger& b2) {
    if (b1.sign==true && b2.sign==false) return false;
    if (b1.sign==false && b2.sign==true) return true;
    int cmp=abscompare(b1,b2);
    if (b1.sign==true)
        if (cmp>=0) return false;
        else return true;
    if (b1.sign==false)
        if (cmp<=0) return true;
        else return false;    
}
bool operator > (const BigInteger& b1,const BigInteger& b2) {
    if (b1.sign==true && b2.sign==false) return true;
    if (b1.sign==false && b2.sign==true) return false;
    int cmp=abscompare(b1,b2);
    if (b1.sign==true)
        if (cmp<=0) return false;
        else return true;
    if (b1.sign==false)
        if (cmp>=0) return true;
        else return false;    
}

void carry(BigInteger &b) {
    int len=b.digits.size();
    for (int i=0;i<len-1;i++) {
        b.digits[i+1]+=(b.digits[i]-'0')/10;
        b.digits[i]=(b.digits[i]-'0')%10+'0';
    }
    while (b.digits[b.digits.size()-1]>='0'+10) {
        int t=b.digits.size()-1;
        b.digits.push_back((b.digits[t]-'0')/10+'0');
        b.digits[t]=(b.digits[t]-'0')%10+'0';
    }
}
BigInteger operator + (const BigInteger& b1,const BigInteger& b2) {
    if (b1.sign!=b2.sign) {
        BigInteger newb1(b1),newb2(b2);
        if (b1.sign==true && b2.sign==false) return (newb1-(-newb2));
        else return newb2-(-newb1);
    }
    int maxlen=max(b1.digits.size(),b2.digits.size());
    BigInteger ret;
    for (int i=0;i<maxlen;i++)
        if (b1.digits.size()-1>=i && b2.digits.size()-1>=i) ret.digits.push_back(b1.digits[i]+b2.digits[i]-'0');
        else if (b1.digits.size()-1>=i) ret.digits.push_back(b1.digits[i]);
        else ret.digits.push_back(b2.digits[i]);
    carry(ret);
    ret.sign=b1.sign;
    return ret;
}
BigInteger operator - (const BigInteger& b1,const BigInteger& b2) {        //待完善 
    if (b1.sign!=b2.sign) {
        BigInteger newb1(b1),newb2(b2);
        return (newb1+(-newb2));
    }
    if (b1.sign==false && b2.sign==false) {
        BigInteger newb1(b1),newb2(b2);
        return (-newb2)-(-newb1);
    }
    if (b1<b2) {
        BigInteger newb1(b1),newb2(b2);
        return -(newb2-newb1);
    }
    
    BigInteger ret;
    int maxlen=max(b1.digits.size(),b2.digits.size());
    for (int i=0;i<maxlen;i++)
        if (b1.digits.size()-1>=i && b2.digits.size()-1>=i) ret.digits.push_back(b1.digits[i]-b2.digits[i]);
        else ret.digits.push_back(b1.digits[i]-'0');
    for (int i=0;i<maxlen;i++)
        if (ret.digits[i]<0) {
            ret.digits[i+1]--;
            ret.digits[i]+=10;
        } 
    while (ret.digits.size()>1 && ret.digits[ret.digits.size()-1]==0) ret.digits.pop_back();
    for (int i=0;i<ret.digits.size();i++) ret.digits[i]+='0';
    return ret;
}
BigInteger operator * (const BigInteger& b1,const BigInteger& b2) {
    BigInteger ret;
    ret.sign=(b1.sign==b2.sign);
    int len1=b1.digits.size(),len2=b2.digits.size();
    vector<int> tmp(len1+len2,0);
    for (int i=0;i<len1;i++)
        for (int j=0;j<len2;j++)
            tmp[i+j]+=(b1.digits[i]-'0')*(b2.digits[j]-'0');
    for (int i=0;i<(len1+len2-1);i++) {
        tmp[i+1]+=tmp[i]/10;
        tmp[i]%=10;
    }
    while (tmp[tmp.size()-1]>=10) {
        tmp.push_back(tmp[tmp.size()-1]/10);
        tmp[tmp.size()-2]%=10;
    }
    for (int i=0;i<tmp.size();i++)
        ret.digits.push_back(tmp[i]+'0');
    while (ret.digits.size()>1 && ret.digits[ret.digits.size()-1]=='0') ret.digits.pop_back();
    return ret;    
}

BigInteger& BigInteger::operator +=(const BigInteger& b) {
    *this=*this+b;
    return *this;
}
BigInteger& BigInteger::operator -=(const BigInteger& b) {
    *this=*this-b;
    return *this;
}
BigInteger& BigInteger::operator *=(const BigInteger& b) {
    *this=*this*b;
    return *this;
}

int main()
{
    BigInteger b1(81532);
    BigInteger b2(-156156131);
    BigInteger b3(string("-1561565")); 
    cout<<"b1: "; b1.print(); cout<<endl; 
    cout<<"b2: "; b2.print(); cout<<endl; 
    cout<<"b3: "; b3.print(); cout<<endl; 
    BigInteger b4(b2);
    cout<<"b4: "; b4.print(); cout<<endl; 
    
    BigInteger b5(81533);
    cout<<"-b5 : "; (-b5).print(); cout<<endl;
    cout<<"b2==b1 ? "<<(b2==b1)<<endl;
    cout<<"b2==b4 ? "<<(b2==b4)<<endl;
    cout<<"b1>b5 ? "<<(b1>b5)<<endl;
    cout<<"b1<b5 ? "<<(b1<b5)<<endl;
    cout<<"b5<-b5 ? "<<(-b5>b5)<<endl;
    
    //开始测试加减乘除
    BigInteger b6=b1+b5;
    cout<<"b1+b5 : "; b6.print(); cout<<endl;
    cout<<"b1-b5 : "; (b1-b5).print(); cout<<endl;
    cout<<"b4-b2 : "; (b4-b2).print(); cout<<endl;
    cout<<"b2-b1 : "; (b2-b1).print(); cout<<endl;
    cout<<"b2+b1 : "; (b2+b1).print(); cout<<endl;
    cout<<"b1*b5 : "; (b1*b5).print(); cout<<endl;
    cout<<"b1*b2 : "; (b1*b2).print(); cout<<endl; 

    //测试+=，-=，*=，/=；
    b5*=b1;  
    cout<<"b1*b5 : "; b5.print(); cout<<endl;
    b1*=b2;
    cout<<"b1*b2 : "; b1.print(); cout<<endl; 
    return 0;
}