solution.py

# 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.


def josephus_survivor(n, k):
    res = 0

    for i in range(1, n + 1):
        res = (res + k) % i

    return res + 1