CPSC 170 Program 3: Big Integers
Due Mon, April 10 2005

Overview

Your assignment is to write two classes:

• LinkedBigInt -- implements the the BigIntADT below; represents and manipulates arbitrarily large non-negative integers.

• EvalBigInts -- takes a postfix expression at the command line using only the operations +, *, e (exponent) and ! (factorial), and evaluates it using a stack and representing the numbers as LinkedBigInts.

The BigInt ADT and Implementation

public interface BigIntADT
{
    // Gives the number of digits in the BigInt
    public int length();

    // Returns a BigInt representing the sum of the
    // current BigInt and int2
    public BigIntADT add(BigIntADT int2);

    // Returns a BigInt representing the product of the
    // current BigInt and int2
    public BigIntADT mult(BigIntADT int2);

    // Returns a BigInt representing the the current BigInt
    // raised to the int2 power
    public BigIntADT power(BigIntADT int2);

    // Returns a BigInt representing the factorial of int
    public BigIntADT  factorial(BigIntADT int)

    // Returns true if the current BigInt is the same as
    // int2, false otherwise
    public boolean equals(BigIntADT int2);

    // Returns a string representation of the current BigInt
    public String toString();

    // Returns an iterator that provides the digits of the current 
    // BigInt, one at a time.
    public Iterator iterator();
}		    

• If you store the digits backwards in the list it will be easier to manipulate your BigInts (e.g., add them). Think about what you do in computing 437 + 28:
  • 8+7=15; put down the 5, carry the 1
  • 1 (carry) + 3 + 2 = 6
  • 4 + 0 = 4
  So the answer is 461. Note that it is computed from right to left, and that it may be necessary to deal with a carry at any point (think about 937 + 75). If each integer is stored backwards in a linked list (that is, with the rightmost digit first), in the first example you would have 8-2 and 7-3-4. Although this looks odd, it gives immediate access to just the digits that you need first: 8 and 7.

• Once you have figured out addition, multiplication should be easy. Just remember that x * y is just x + x + ... + x (y xs). That is, you can think of multiplication as repeated addition. Start with 0 and add x to it y times, and voila! You've computed x * y.

• Once you have figured out multiplication, exponentiation should be easy. Just remember that x^y is just x * x * ... * x (y xs). That is, you can think of exponentiation as repeated multiplication. Start with 1 and multiply by x y times, and voila! You've computed x^y.
  
  
• Factorial is the same idea yet again - start at 1 and work your way up to x (1 * 2 *.... * x)
  
  
• The equals method can just compare the corresponding digits of the two bigints. This does assume that there is just one representation for each integer -- in particular, that there are no leading 0s. So 0 should just be 0, never 00 or 000, and 16 should never be 016. Be sure that your initial representations are in this form and that your BigInts stay in this form as you manipulate them.

• You'll want to provide 3 constructors for generating BigInts.  
  
• The first should be null - this should create a BigInt initialized to 0.
  
• The second should take an int - allowing us to seemlessly translate between ints and BigInt. 
  
• The third should take a String value - this can be used to initialize a BigInt that is already too big  to be represented as an int.    You need to take care to ensure that the string contains only numbers.   If the constructor is called with a bad string, it should throw an  exception.
  
  

The EvalBigInts Class

  java EvalBigInts 2 3 e 5 6 "*" +

There is code for a stack evaluator in the text; yours will be similar, but your use of bigints will require some modifications.