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 29.

assert.equal(josephus(30, 3), 29);

josephus(30,5) should return 3.

assert.equal(josephus(30, 5), 3);

josephus(20,2) should return 9.

assert.equal(josephus(20, 2), 9);

josephus(17,6) should return 2.

assert.equal(josephus(17, 6), 2);

josephus(29,4) should return 2.

assert.equal(josephus(29, 4), 2);

--seed--

--seed-contents--

function josephus(init, kill) {

}

--solutions--

function josephus(init, kill) {
  var Josephus = {
    init: function(n) {
      this.head = {};
      var current = this.head;
      for (var i = 0; i < n - 1; i++) {
        current.label = i + 1;
        current.next = {
          prev: current
        };
        current = current.next;
      }
      current.label = n;
      current.next = this.head;
      this.head.prev = current;
      return this;
    },
    kill: function(spacing) {
      var current = this.head;
      while (current.next !== current) {
        for (var i = 0; i < spacing - 1; i++) {
          current = current.next;
        }
        current.prev.next = current.next;
        current.next.prev = current.prev;
        current = current.next;
      }
      return current.label;
    }
  }

  return Josephus.init(init).kill(kill)
}