大整数四则运算------（c++ 实现 乘法没有用傅里叶变换）

/* 优点：
    1 支持负整数的运算
    2 良好的输出形式 没有前导零
    3 支持cin直接输入 支持cout直接输出
    4 支持整数的直接赋值  big_int x=100;
  缺点： 
    1 封装不好 基本都是友元函数操作
    2 速度慢  乘法没有使用FFT 除法采用二分法
              使用STL string储存数据也造成速度不是很快
    3 待解决的问题  不能直接输出 cout<<a-b
*/

#include <iostream>
#include <algorithm>
#include <stack>
using namespace std;
void change (string &s) {
    string tmp="";
    int i;
    for (i=0;i<s.size();i++)
        if (s[i]!='0')
            break;
    if (i==s.size()) s="0";
    else {
        for (;i<s.size();i++)
            tmp+=s[i];
        s=tmp;
    }
}
class big_int
{
    private :
        bool flag;
        string s;
    public :
        big_int (){ flag=1; s="0"; }
        big_int (int x);
        bool operator ==(const big_int& x)  {
            string tmp=x.s;
            change (s);
            change (tmp);
            if (x.s=="0"&&s=="0") return true;
            return x.flag==flag&&s==tmp;
        }
        friend big_int operator+(const big_int& a, const big_int& b );
        friend big_int operator-(const big_int& a, const big_int& b );
        friend big_int operator*(const big_int& a, const big_int& b);
        friend big_int operator/(const big_int& a, const big_int& b);
        friend big_int operator%(const big_int& a, const big_int& b);
        friend ostream& operator<<(ostream& out,big_int& x) {
            if (!x.flag&&x.s!="0") cout<<"-";
            change (x.s);
            cout<<x.s;
            return out;
        }
        friend istream& operator>>(istream& in,big_int& x) {
            string  tmp;
            cin>>tmp;
            if (tmp[0]=='-') {
                x.flag=0;
                x.s=tmp.substr(1,tmp.size()-1);
            }
            else {
                x.flag=1;
                x.s=tmp;
            }
            return in;
        }
};
big_int:: big_int (int x)  {
            if (x<0) flag=0;
            else     flag=1;
            x=abs(x);
 
            s="";  string tmp="0";
            if (x==0) s+=tmp;
            while (x!=0) {
                tmp[0]='0'+x%10;
                s+=tmp;
                x/=10;
            }
            reverse(s.begin(),s.end());
}
string  add(string s1,string s2) {
    reverse(s1.begin(),s1.end());
    reverse(s2.begin(),s2.end());
    int len =max (s1.size(),s2.size());
    int k=0; int t1,t2;
    string ans="";  string tmp="0";
    for (int i=0;i<len;i++) {
        t1=t2=0;
        if (i<s1.size())  t1=s1[i]-'0';
        if (i<s2.size())  t2=s2[i]-'0';
        int t=t1+t2+k;
        tmp[0]='0'+t%10;  k=t/10;
        ans+=tmp;
    }
    if (k!=0) {
        tmp[0]='0'+k;
        ans+=tmp;
    }
    reverse(ans.begin(),ans.end());
    return ans;
}
string sub (string s1,string s2) {
    reverse(s1.begin(),s1.end());
    reverse(s2.begin(),s2.end());
    int len =s1.size();
    int t1,t2;
    string ans="";  string tmp="0";
    for (int i=0;i<len;i++) {
        t1=s1[i]-'0'; t2=0;
        if (i<s2.size())  t2=s2[i]-'0';
        if (t1<t2) {
            for (int j=i+1;j<len;j++)
                if (s1[j]-'0'==0) s1[j]='9';
                else {
                    s1[j]--;
                    break;
                }
            t1+=10;
        }
        tmp[0]=t1-t2+'0';
        ans+=tmp;
    }
    reverse(ans.begin(),ans.end());
    change(ans);
    return ans;
}
bool m_cmp (string s1, string s2) {
    change (s1);
    change (s2);
    if (s1.size()==s2.size()) {
        for (int i=0;i<s1.size();i++)
            if (s1[i]!=s2[i])
                return s1[i]>s2[i];
    }
    return s1.size()>s2.size();
}
string s_mul (string s,int x,int k) {
    string ans=""; string tmp="0";
    for (int i=1;i<=k;i++) ans+=tmp;
    k=0;
    for (int i=0;i<s.size();i++) {
        int t=s[i]-'0';
        int p=t*x+k;
        tmp[0]='0'+p%10; ans+=tmp;
        k=p/10;
    }
    if (k)  {
        tmp[0]='0'+k;
        ans+=tmp;
    }
    reverse(ans.begin(),ans.end());
    change(ans);
    return ans;
}
string mul (string s1,string s2) {
    reverse(s1.begin(),s1.end());
    reverse(s2.begin(),s2.end());
    string ans="0";
    for (int i=0;i<s2.size();i++) {
        int x=s2[i]-'0';
        string tmp=s_mul (s1,x,i);
        ans=add(ans,tmp);
        //cout<<ans<<endl;
    }
    return ans;
}
big_int operator+(const big_int& a, const big_int& b ) {
     big_int c;
     int t=a.flag^b.flag;
     if (t==0) {
         c.s=add (a.s,b.s);
         c.flag=a.flag;
     }
     else {
        if (m_cmp(a.s,b.s))  {
            c.flag=a.flag;
            c.s=sub (a.s,b.s);
        }
        else {
            c.flag=b.flag;
            c.s=sub (b.s,a.s);
        }
     }
     return c;
}
big_int operator-(const big_int& a, const big_int& b ) {
    big_int c=b;
    c.flag=!b.flag;
    return a+c;
}
big_int operator*(const big_int& a, const big_int& b) {
    big_int c;
    int t=a.flag^b.flag;
    if (t)  c.flag=0;
    if (m_cmp(a.s,b.s)) c.s=mul (a.s,b.s);
    else            c.s=mul (b.s,a.s);
    return c;
}
big_int operator/(const big_int& a, const big_int& b) {
    if (b.s=="0")  {
        cout<<"error"<<endl;
        exit(-1);
    }
    big_int c;
    big_int _a=a, _b=b;
    _a.flag=_b.flag=1;
    if (m_cmp(_b.s,_a.s)) return c;
 
    stack <big_int> q;
    big_int k=1;
    while (1) {
        big_int x=k*_b; q.push(k);
        if (m_cmp(x.s,_a.s))
            break;
        k=k*2;
    }
    big_int tmp=_a;
    while (tmp.s!="0"&&!q.empty()) {
        k=q.top(); q.pop();
        big_int x=k*_b;
        if ( !m_cmp(x.s,tmp.s)) {
            tmp=tmp-x;
            c=c+k;
        }
    }
    if (a.flag^b.flag)  c.flag=0;
    return c;
}
big_int operator%(const big_int& a, const big_int& b) {
      big_int c=a/b;
      c=c*b;
      c=a-c;
      return c;
}
int main ()
{
    big_int a,b;
    big_int c=-100;  
    cout<<c<<endl;
    while (cin>>a>>b) {
        c=a+12;
        cout<<c<<" ";
        c=a-b;
        cout<<c<<" ";
        c=a*b;
        cout<<c<<" ";
        c=a/b;
        cout<<c<<" ";
        c=a%b;
        cout<<c<<endl;
    }
    return 0;
}