5kyu_JosephusSurvivor.js

// 5kyu - Josephus Survivor

// 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.

function josephusSurvivor(n, k) {
    return n <= 1 ? 1 : (josephusSurvivor(n - 1, k) + k - 1) % n + 1;
}