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>
96 lines
1.9 KiB
Markdown
96 lines
1.9 KiB
Markdown
---
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id: 5900f37a1000cf542c50fe8d
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title: 问题14：最长的Collatz序列
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challengeType: 5
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videoUrl: ''
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dashedName: problem-14-longest-collatz-sequence
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---
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# --description--
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为正整数集定义以下迭代序列：
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`n` → `n` / 2（ `n`是偶数）
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`n` →3 `n` + 1（ `n`为奇数）
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使用上面的规则并从13开始，我们生成以下序列：
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13→40→20→10→5→16→8→4→2→1
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可以看出，该序列（从13开始并在1结束）包含10个项。虽然尚未证实（Collatz问题），但是认为所有起始数字都在1处结束。在给定`limit`下，哪个起始数产生最长链？注意：一旦链条启动，条款允许超过一百万。
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# --hints--
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`longestCollatzSequence(14)`应该返回9。
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```js
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assert.strictEqual(longestCollatzSequence(14), 9);
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```
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`longestCollatzSequence(5847)`应返回3711。
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```js
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assert.strictEqual(longestCollatzSequence(5847), 3711);
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```
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`longestCollatzSequence(46500)`应返回35655。
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```js
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assert.strictEqual(longestCollatzSequence(46500), 35655);
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```
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`longestCollatzSequence(54512)`应返回52527。
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```js
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assert.strictEqual(longestCollatzSequence(54512), 52527);
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```
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`longestCollatzSequence(1000000)`应返回837799。
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```js
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assert.strictEqual(longestCollatzSequence(100000), 77031);
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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 longestCollatzSequence(limit) {
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return true;
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}
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longestCollatzSequence(14);
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```
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# --solutions--
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```js
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function longestCollatzSequence(limit) {
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let longest = 1;
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let maxLength = 1;
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for (let i = Math.floor(limit / 2); i < limit; i++) {
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let len = colLen(i);
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if (len > maxLength) {
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longest = i;
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maxLength = len;
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}
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}
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return longest;
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}
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const knownSequence = { '1': 1 };
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function colLen(n) {
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if (knownSequence[n]) {
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return knownSequence[n];
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} else {
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const len = n % 2 === 0 ? colLen(n / 2) + 1 : colLen((3 * n + 1) / 2) + 2;
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knownSequence[n] = len;
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return len;
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}
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}
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```
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