| The Cantor Set is an important mathematical construction devised by the
19th century mathematician Georg Cantor. It is defined as follows:
Start with the set of real numbers from 0.0 to 1.0 inclusive, which is denoted by [0.0, 1.0]. Then -
At step 1, remove the open middle third of [0.0, 1.0] ("open" means not including
its endpoints).
-
At step 2, remove the open middle thirds of the 2 remaining intervals.
- ...
-
At step k, remove the open middle thirds of the 2^(k-1) remaining intervals.
- ...
The Cantor Set is the part of [0.0, 1.0] that is not removed by this process.
We want software to help determine if a given number is in the Cantor Set. Create
a class CantorSet that contains a method removed that is given a String value that
represents a real number in [0.0, 1.0] and returns the step at which value is
removed in the above construction. If it is not removed before step 1,000,000
return 0 indicating that it is highly likely that it is in the Cantor Set.
|