2.1 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5a23c84252665b21eecc7ec5 | Josephus problem | 5 | 302294 | josephus-problem |
--description--
[Josephus problem](https://en.wikipedia.org/wiki/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 3rd 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];
}