Egyptian Multiplication and SDLList class

The ancient Egyptians knew how to work with fractions but saw beauty in

representing fractions as a sum of distinct unit fractions (fractions

whose numerator equals 1). For example, the ancient Egyptians would

represent the fraction ľ as

1/4 + 1/5 + 1/6 + 1/20 + 1/21 + 1/30 + 1/420

This can be accomplished by starting with an SDLList<BigInteger>

consisting of three fours [4, 4, 4] which represents Ľ + Ľ + Ľ. Note that

it is necessary to store only the denominators. The idea is to remove a

duplicate integer x from the SDLList and replace it by adding the integers

x+1 and x(x+1). [Word of warning: you will have to use the methods add()

and multiply() from BigInteger]. Why does this process work? The reason is

1/x = 1/(x+1) + 1/[x(x+1)].

Let’s complete this example. By showing the contents of the SDLList after

each duplicate is removed.

[4, 4, 4] remove 4 add 5 and 20

[4, 4, 5, 20] remove 4 add 5 and 20

[4, 5, 5, 20, 20] remove 5 add 6 and 30

[4, 5, 6, 20, 20, 30] remove 20 add 21 and 420

[4, 5, 6, 20, 21, 30, 420] each entry is distinct

The EgyptianFraction class should have instance variables

private SDLList<BigInteger> representation;

private BigInteger numerator;

private BigInteger denominator;

You will need methods to

1) detect duplicate items in the


2) remove a duplicate from the SDLList

3) print the representation of an

Egyptian Fraction,

as well as, a constructor that initializes the SDLList based on the

inputted fraction.

Skills: Java

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