Code.cpp

struct Bigint {
 // representations and structures

    string a; // to store the digits
    int sign; // sign = -1 for negative numbers, sign = 1 otherwise

 // constructors

    Bigint() {} // default constructor
    Bigint( string b ) { (*this) = b; } // constructor for string

 // some helpful methods

    int size() { // returns number of digits
        return a.size();
    }

    Bigint inverseSign() { // changes the sign
        sign *= -1;
        return (*this);
    }

    Bigint normalize( int newSign ) { // removes leading 0, fixes sign
        for( int i = a.size() - 1; i > 0 && a[i] == '0'; i-- )
        a.erase(a.begin() + i);
       sign = ( a.size() == 1 && a[0] == '0' ) ? 1 : newSign;
       return (*this);
    }

 // assignment operator

    void operator = ( string b ) { // assigns a string to Bigint
        a = b[0] == '-' ? b.substr(1) : b;
        reverse( a.begin(), a.end() );
        this->normalize( b[0] == '-' ? -1 : 1 );
    }

 // conditional operators

    bool operator < ( const Bigint &b ) const { // less than operator
        if( sign != b.sign ) return sign < b.sign;
        if( a.size() != b.a.size() )
        return sign == 1 ? a.size() < b.a.size() : a.size() > b.a.size();
        for( int i = a.size() - 1; i >= 0; i-- ) if( a[i] != b.a[i] )
        return sign == 1 ? a[i] < b.a[i] : a[i] > b.a[i];
        return false;
    }

    bool operator == ( const Bigint &b ) const { // operator for equality
        return a == b.a && sign == b.sign;
    }

    Bigint operator + ( Bigint b ) { // addition operator overloading
        if( sign != b.sign ) return (*this) - b.inverseSign();
        Bigint c;
        for(int i = 0, carry = 0; i<a.size() || i<b.size() || carry; i++ ) {
            carry+=(i<a.size() ? a[i]-48 : 0)+(i<b.a.size() ? b.a[i]-48 : 0);
            c.a += (carry % 10 + 48);
            carry /= 10;
        }
        return c.normalize(sign);
     }

     Bigint operator - ( Bigint b ) { // subtraction operator overloading
         if( sign != b.sign ) return (*this) + b.inverseSign();
         int s = sign; sign = b.sign = 1;
         if( (*this) < b ) return ((b - (*this)).inverseSign()).normalize(-s);
         Bigint c;
         for( int i = 0, borrow = 0; i < a.size(); i++ ) {
            borrow = a[i] - borrow - (i < b.size() ? b.a[i] : 48);
            c.a += borrow >= 0 ? borrow + 48 : borrow + 58;
            borrow = borrow >= 0 ? 0 : 1;
        }
        return c.normalize(s);
      }

      Bigint operator * ( Bigint b ) { // multiplication operator overloading
          Bigint c("0");
          for( int i = 0, k = a[i] - 48; i < a.size(); i++, k = a[i] - 48 ) {
              while(k--) c = c + b; // ith digit is k, so, we add k times
              b.a.insert(b.a.begin(), '0'); // multiplied by 10
           }
          return c.normalize(sign * b.sign);
       }
       Bigint operator / ( Bigint b ) { // division operator overloading
           if( b.size() == 1 && b.a[0] == '0' ) b.a[0] /= ( b.a[0] - 48 );
           Bigint c("0"), d;
           for( int j = 0; j < a.size(); j++ ) d.a += "0";
           int dSign = sign * b.sign; b.sign = 1;
           for( int i = a.size() - 1; i >= 0; i-- ) {
               c.a.insert( c.a.begin(), '0');
               c = c + a.substr( i, 1 );
               while( !( c < b ) ) c = c - b, d.a[i]++;
           }
           return d.normalize(dSign);
        }
     Bigint operator % ( Bigint b ) { // modulo operator overloading
         if( b.size() == 1 && b.a[0] == '0' ) b.a[0] /= ( b.a[0] - 48 );
         Bigint c("0");
         b.sign = 1;
         for( int i = a.size() - 1; i >= 0; i-- ) {
            c.a.insert( c.a.begin(), '0');
            c = c + a.substr( i, 1 );
            while( !( c < b ) ) c = c - b;
         }
         return c.normalize(sign);
    }
  // output method
    void print() {
        if( sign == -1 ) putchar('-');
        for( int i = a.size() - 1; i >= 0; i-- ) cout << a[i] ;
    }
};