A permutation of the letters in an alphabet can be described by a string that contains
each letter exactly once. For example, CABD describes the permutation of ABCD that maps
A to C, B to A, C to B, and D to D. If we repeatedly
apply that permutation, we will get the sequence ABCD,CABD,BCAD,ABCD,CABD,BCAD,ABCD,... This
permutation is cyclic with length 3.
We want to find the permutation of the first n letters of
ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
that has the longest cycle. Create
a class Permutation that contains the method best that takes the number of characters n
as input and returns the lexicographically first permutation that has the maximum
possible cycle length.
"Lexicographically first" means the String that would sort first among all the permutations of maximum cycle length, using the ASCII sequence (which sorts uppercase letters before lowercase letters).
