ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
104 lines
2.5 KiB
Markdown
104 lines
2.5 KiB
Markdown
---
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id: 5a23c84252665b21eecc7ec5
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title: 约瑟夫斯问题
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challengeType: 5
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videoUrl: ''
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dashedName: josephus-problem
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---
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# --description--
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[约瑟夫斯问题](<https://en.wikipedia.org/wiki/Josephus problem>)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 $，囚犯被杀的命令（我们称之为“杀戮序列”）将是1,3,0和4，幸存者将是＃2。鉴于任何$ n，k> 0 $ ，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（$ K = 3 $）。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。
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# --hints--
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`josephus`应该是一个功能。
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```js
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assert(typeof josephus == 'function');
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```
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`josephus(30,3)`应该返回一个数字。
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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)`应该回`29` 。
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```js
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assert.equal(josephus(30, 3), 29);
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```
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`josephus(30,5)`应该返回`3` 。
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```js
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assert.equal(josephus(30, 5), 3);
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```
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`josephus(20,2)`应该返回`9` 。
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```js
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assert.equal(josephus(20, 2), 9);
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```
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`josephus(17,6)`应该回归`2` 。
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```js
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assert.equal(josephus(17, 6), 2);
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```
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`josephus(29,4)`应该返回`2` 。
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```js
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assert.equal(josephus(29, 4), 2);
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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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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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