JoeSurvivor.rb

=begin

In this kata you have to correctly return who is the "survivor", ie: the last
element of a Josephus permutation.

Basically you have to assume that n people are put into a circle and that they
are eliminated in steps of k elements, like this:

josephus_survivor(7,3) => means 7 people in a circle;
one every 3 is eliminated until one remains
[1,2,3,4,5,6,7] - initial sequence
[1,2,4,5,6,7] => 3 is counted out
[1,2,4,5,7] => 6 is counted out
[1,4,5,7] => 2 is counted out
[1,4,5] => 7 is counted out
[1,4] => 5 is counted out
[4] => 1 counted out, 4 is the last element - the survivor!
The above link about the "base" kata description will give you a more thorough
insight about the origin of this kind of permutation, but basically that's all
that there is to know to solve this kata.

Notes and tips: using the solution to the other kata to check your function may
be helpful, but as much larger numbers will be used, using an array/list to
compute the number of the survivor may be too slow; you may assume that both n
and k will always be >=1.

=end

# My Solution
def josephus_survivor(n,k)
  people = []
  0.upto(n-1) {|x| people << x+1}
  0.upto(n-2) do |x|
    people = people.rotate(k-1)
    people.shift
  end
  people[0]
end

# Better Solution
def josephus_survivor(n, k)
  n < 1 ? 1 : (josephus_survivor(n - 1, k) + k - 1) % n + 1;
end