79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
109 lines
3.5 KiB
Markdown
109 lines
3.5 KiB
Markdown
---
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title: Josephus problem
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id: 5a23c84252665b21eecc7ec5
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challengeType: 5
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---
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## Description
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<section id='description'>
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<a href="https://en.wikipedia.org/wiki/Josephus problem">Josephus problem</a> 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 <big>$n, k > 0$</big>, 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 (<big>$k=3$</big>).
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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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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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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>josephus</code> should be a function.
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testString: assert(typeof josephus=='function','<code>josephus</code> should be a function.');
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- text: <code>josephus(30,3)</code> should return a number.
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testString: assert(typeof josephus(30,3)=='number','<code>josephus(30,3)</code> should return a number.');
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- text: <code>josephus(30,3)</code> should return <code>29</code>.
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testString: assert.equal(josephus(30,3),29,'<code>josephus(30,3)</code> should return <code>29</code>.');
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- text: <code>josephus(30,5)</code> should return <code>3</code>.
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testString: assert.equal(josephus(30,5),3,'<code>josephus(30,5)</code> should return <code>3</code>.');
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- text: <code>josephus(20,2)</code> should return <code>9</code>.
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testString: assert.equal(josephus(20,2),9,'<code>josephus(20,2)</code> should return <code>9</code>.');
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- text: <code>josephus(17,6)</code> should return <code>2</code>.
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testString: assert.equal(josephus(17,6),2,'<code>josephus(17,6)</code> should return <code>2</code>.');
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- text: <code>josephus(29,4)</code> should return <code>2</code>.
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testString: assert.equal(josephus(29,4),2,'<code>josephus(29,4)</code> should return <code>2</code>.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function josephus (init, kill) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function josephus (init, kill) {
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var Josephus = {
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init: function(n) {
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this.head = {};
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var current = this.head;
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for (var i = 0; i < n - 1; i++) {
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current.label = i + 1;
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current.next = {
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prev: current
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};
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current = current.next;
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}
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current.label = n;
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current.next = this.head;
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this.head.prev = current;
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return this;
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},
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kill: function(spacing) {
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var current = this.head;
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while (current.next !== current) {
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for (var i = 0; i < spacing - 1; i++) {
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current = current.next;
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}
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current.prev.next = current.next;
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current.next.prev = current.prev;
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current = current.next;
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}
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return current.label;
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}
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}
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return Josephus.init(init).kill(kill)
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}
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```
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</section>
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