freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/rosetta-code/josephus-problem.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5a23c84252665b21eecc7ec5	Josephus problem	5	302294	josephus-problem

--description--

Josephus problem is a math puzzle with a grim description: n prisoners are standing on a circle, sequentially numbered from 0 to n-1.

An executioner walks along the circle, starting from prisoner 0, removing every $k$-th prisoner and killing him.

As the process goes on, the circle becomes smaller and smaller, until only one prisoner remains, who is then freed.

For example, if there are n=5 prisoners and k=2, the order the prisoners are killed in (let's call it the "killing sequence") will be 1, 3, 0, and 4, and the survivor will be #2.

Given any n, k > 0, find out which prisoner will be the final survivor.

In one such incident, there were 41 prisoners and every 3^rd prisoner was being killed (k=3).

Among them was a clever chap name Josephus who worked out the problem, stood at the surviving position, and lived on to tell the tale.

Which number was he?

--instructions--

Write a function that takes the initial number of prisoners and 'k' as parameter and returns the number of the prisoner that survives.

--hints--

josephus should be a function.

assert(typeof josephus == 'function');

josephus(30,3) should return a number.

assert(typeof josephus(30, 3) == 'number');

josephus(30,3) should return 28.

assert.equal(josephus(30, 3), 28);

josephus(30,5) should return 2.

assert.equal(josephus(30, 5), 2);

josephus(20,2) should return 8.

assert.equal(josephus(20, 2), 8);

josephus(17,6) should return 1.

assert.equal(josephus(17, 6), 1);

josephus(29,4) should return 1.

assert.equal(josephus(29, 4), 1);

--seed--

--seed-contents--

function josephus(init, kill) {

}

--solutions--

function josephus(init, kill) {
  const arr = Array.from(Array(init).keys());
  let curr = -1
  while (arr.length > 1) {
    curr = (curr + kill) % arr.length;
    arr.splice(curr, 1);
    curr--;
  }
  return arr[0];
}