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99 lines
2.0 KiB
Markdown
99 lines
2.0 KiB
Markdown
---
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id: 595608ff8bcd7a50bd490181
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title: Hailstone sequence
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challengeType: 1
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forumTopicId: 302279
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dashedName: hailstone-sequence
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---
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# --description--
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Hailstone 数字序列可以从一个起始正整数 `n` 生成：
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- If `n` is `1` then the sequence ends
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- If `n` is `even` then the next `n` of the sequence `= n/2`
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- If `n` is `odd` then the next `n` of the sequence `= (3 * n) + 1`
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The (unproven) Collatz conjecture is that the hailstone sequence for any starting number always terminates.
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The hailstone sequence is also known as hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as the Collatz sequence.
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# --instructions--
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1. Create a routine to generate the hailstone sequence for a number
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2. Your function should return an array with the number less than `limit` which has the longest hailstone sequence and that sequence's length. (But don't show the actual sequence!)
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# --hints--
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`hailstoneSequence` 应该是一个函数。
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```js
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assert(typeof hailstoneSequence === 'function');
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```
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`hailstoneSequence(30)` should return an array.
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```js
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assert(Array.isArray(hailstoneSequence(30)));
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```
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`hailstoneSequence(30)` should return `[27, 112]`.
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```js
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assert.deepEqual(hailstoneSequence(30), [27, 112]);
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```
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`hailstoneSequence(50000)` should return `[35655, 324]`.
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```js
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assert.deepEqual(hailstoneSequence(50000), [35655, 324]);
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```
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`hailstoneSequence(100000)` should return `[77031, 351]`.
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```js
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assert.deepEqual(hailstoneSequence(100000), [77031, 351]);
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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 hailstoneSequence(limit) {
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const res = [];
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return res;
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}
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```
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# --solutions--
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```js
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function hailstoneSequence (limit) {
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function hailstone(n) {
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const seq = [n];
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while (n > 1) {
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n = n % 2 ? 3 * n + 1 : n / 2;
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seq.push(n);
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}
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return seq;
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}
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let n = 0;
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let max = 0;
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for (let i = limit; --i;) {
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const seq = hailstone(i);
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const sLen = seq.length;
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if (sLen > max) {
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n = i;
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max = sLen;
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}
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}
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return [n, max];
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}
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```
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