99 lines
2.1 KiB
Markdown
99 lines
2.1 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ec5
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title: Josephus problem
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challengeType: 5
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forumTopicId: 302294
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dashedName: josephus-problem
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---
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# --description--
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[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 $n-1$.
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An executioner walks along the circle, starting from prisoner $0$, removing every $k$-th prisoner and killing him.
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As the process goes on, the circle becomes smaller and smaller, until only one prisoner remains, who is then freed.
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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.
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Given any $n, k > 0$, find out which prisoner will be the final survivor.
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In one such incident, there were 41 prisoners and every 3<sup>rd</sup> prisoner was being killed ($k=3$).
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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.
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Which number was he?
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# --instructions--
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Write a function that takes the initial number of prisoners and 'k' as parameter and returns the number of the prisoner that survives.
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# --hints--
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`josephus` should be a function.
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```js
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assert(typeof josephus == 'function');
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```
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`josephus(30,3)` should return a number.
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```js
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assert(typeof josephus(30, 3) == 'number');
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```
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`josephus(30,3)` should return `28`.
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```js
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assert.equal(josephus(30, 3), 28);
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```
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`josephus(30,5)` should return `2`.
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```js
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assert.equal(josephus(30, 5), 2);
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```
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`josephus(20,2)` should return `8`.
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```js
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assert.equal(josephus(20, 2), 8);
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```
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`josephus(17,6)` should return `1`.
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```js
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assert.equal(josephus(17, 6), 1);
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```
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`josephus(29,4)` should return `1`.
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```js
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assert.equal(josephus(29, 4), 1);
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```
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# --seed--
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## --seed-contents--
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```js
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function josephus(init, kill) {
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}
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```
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# --solutions--
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```js
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function josephus(init, kill) {
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const arr = Array.from(Array(init).keys());
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let curr = -1
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while (arr.length > 1) {
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curr = (curr + kill) % arr.length;
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arr.splice(curr, 1);
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curr--;
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}
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return arr[0];
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}
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```
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