/********************************************************************
 CS177/477 C++ Programming
 Fall 1999

 An abstract data type for large integers

 Your task is to write a class for very large integers, i.e. ones that
 do not have a size limitation, and can be any number of digits long.
 Your program will consist of a single class, and a main function that
 tests its capabilities.

 The assignment will be split into two parts. This is part 1, in which
 your program will create large integers, read them from the keyboard
 and display them on the screen.

 Your program must:
  1. be capable of representing integers of any length
  2. have constructors to initialize numbers with standard integers
     (type long int), and from a string of digits (e.g. "1234567890")
  3. be capable of reading and displaying objects of the type

  You can use this skeleton for the class itself and for the global functions:

  class Bignum {
  private:
    // insert here your representation of a very large integer using a vector
  public:
    Bignum(); // default constructor
    Bignum(long n); // constructor for "small" integers
    Bignum(string n); // constructor for very large integers
  protected:
    // insert here any accessor functions you may require
    void Extract(istream& sin); // the method for input
    void Insert(ostream& sout); // the method for output
  };
  
  // define overloaded operators with global functions
  ostream& operator<<(ostream& str, const Bignum& b) { ... }
  istream& operator>>(istream& sin, Bignum& b) { ... }

  Hints and notes
  o Use a vector of unsigned char to hold the digits of the number--use
    push_back to add digits--store them in reverse order, e.g. the number
    12345 is stored as digits 5, 4, 3, 2, 1
  o Use #include's for <vector> and <string> to use these facilities
  o Use const reference parameters in the implementations of the operators
    to avoid copying of the vector inside each object
  o Return a reference to the stream at the end of the insertion (<<)
    operator and the extraction (>>) operator
  o Use for loops, either forward or backward to process elements of the
    vectors
  o Implement member functions to do the work of the operations, and then
    global overloaded operators that call them. You will also need accessor
    functions for the private variable(s) in the class.

  Testing
  Your program should be able to succesfully compile and execute the
  following main function (assuming the name of the class is Bignum):
//////////////////////////////////////////////////////////////////////
  int main() {
  Bignum t1, t2(1234567890), t3("11223344556677889900"); // three different
                                                  // constructors
  cout << "t1 is " << t1 << endl; // print the initial values
  cout << "t2 is " << t2 << endl;
  cout << "t3 is " << t3 << endl;

  Bignum t0; // for input
  cin >> t0;
  cout << "t0 is " << t0 << endl;

  return 0;
}
///////////////////////////////////////////////////////////////////////

  Include this main function in your file and compile it with your
  class declaration and its methods.

///////////////////////////////////////////////////////////////////////
 DUE DATE: MONDAY NOVEMBER 1st. IN CLASS.
//////////////////////////////////////////////////////////////////////