65 lines
2.7 KiB
Markdown
65 lines
2.7 KiB
Markdown
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---
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title: Josephus problem
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id: 5a23c84252665b21eecc7ec5
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challengeType: 5
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videoUrl: ''
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localeTitle: 约瑟夫斯问题
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---
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## Description
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<section id="description"> <a href="https://en.wikipedia.org/wiki/Josephus problem">约瑟夫斯问题</a>是一个严峻描述的数学难题:$ n $囚犯站在一个圆圈上,顺序编号从$ 0 $到$ n-1 $。一名刽子手沿着圈子走,从囚犯$ 0 $开始,移走每个$ k $囚犯并杀死他。随着过程的继续,圆圈变得越来越小,直到只剩下一个囚犯,然后被释放。例如,如果$ n = 5 $囚犯和$ k = 2 $,囚犯被杀的命令(我们称之为“杀戮序列”)将是1,3,0和4,幸存者将是#2。鉴于任何<big>$ n,k> 0 $</big> ,找出哪个囚犯将成为最后的幸存者。在一个这样的事件中,有41个囚犯和每3 <sup>次</sup>囚犯被杀死<big>($ K = 3 $)。</big>其中有一个聪明的名字约瑟夫斯,他解决了这个问题,站在幸存的位置,并继续讲述这个故事。他是哪个号码?写一个函数,以囚犯的初始数量和'k'作为参数,并返回幸存的囚犯的数量。 </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>应该是一个功能。
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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>应该返回一个数字。'
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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>应该回<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>应该返回<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>应该返回<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>应该回归<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>应该返回<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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// solution required
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```
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</section>
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