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=;i<s.size();i++)
         if (s[i]!='')
             break;
     if (i==s.size()) s="";
     else {
         for (;i<s.size();i++)
             tmp+=s[i];
         s=tmp;
     }
 }
 class big_int
 {
     private :
         bool flag;
         string s;
     public :
         big_int (){ flag=; s=""; }
         big_int (int x);
         bool operator ==(const big_int& x)  {
             string tmp=x.s;
             change (s);
             change (tmp);
             if (x.s==""&&s=="") 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!="") cout<<"-";
             change (x.s);
             cout<<x.s;
             return out;
         }
         friend istream& operator>>(istream& in,big_int& x) {
             string  tmp;
             cin>>tmp;
             if (tmp[]=='-') {
                 x.flag=;
                 x.s=tmp.substr(,tmp.size()-);
             }
             else {
                 x.flag=;
                 x.s=tmp;
             }
             return in;
         }
 };
 big_int:: big_int (int x)  {
             if (x<) flag=;
             else     flag=;
             x=abs(x);

             s="";  string tmp="";
             if (x==) s+=tmp;
             while (x!=) {
                 tmp[]=''+x%;
                 s+=tmp;
                 x/=;
             }
             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=; int t1,t2;
     string ans="";  string tmp="";
     for (int i=;i<len;i++) {
         t1=t2=;
         if (i<s1.size())  t1=s1[i]-'';
         if (i<s2.size())  t2=s2[i]-'';
         int t=t1+t2+k;
         tmp[]=''+t%;  k=t/;
         ans+=tmp;
     }
     if (k!=) {
         tmp[]=''+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="";
     for (int i=;i<len;i++) {
         t1=s1[i]-''; t2=;
         if (i<s2.size())  t2=s2[i]-'';
         if (t1<t2) {
             for (int j=i+;j<len;j++)
                 if (s1[j]-''==) s1[j]='';
                 else {
                     s1[j]--;
                     break;
                 }
             t1+=;
         }
         tmp[]=t1-t2+'';
         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=;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="";
     for (int i=;i<=k;i++) ans+=tmp;
     k=;
     for (int i=;i<s.size();i++) {
         int t=s[i]-'';
         int p=t*x+k;
         tmp[]=''+p%; ans+=tmp;
         k=p/;
     }
     if (k)  {
         tmp[]=''+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="";
     for (int i=;i<s2.size();i++) {
         int x=s2[i]-'';
         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==) {
          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=;
     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=="")  {
         cout<<"error"<<endl;
         exit(-);
     }
     big_int c;
     big_int _a=a, _b=b;
     _a.flag=_b.flag=;
     if (m_cmp(_b.s,_a.s)) return c;

     stack <big_int> q;
     big_int k=;
     while () {
         big_int x=k*_b; q.push(k);
         if (m_cmp(x.s,_a.s))
             break;
         k=k*;
     }
     big_int tmp=_a;
     while (tmp.s!=""&&!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=;
     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=-;
     cout<<c<<endl;
     while (cin>>a>>b) {
         c=a+;
         cout<<c<<" ";
         c=a-b;
         cout<<c<<" ";
         c=a*b;
         cout<<c<<" ";
         c=a/b;
         cout<<c<<" ";
         c=a%b;
         cout<<c<<endl;
     }
     return ;
 }