115 lines
2.8 KiB
Markdown
115 lines
2.8 KiB
Markdown
---
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title: Hailstone sequence
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id: 595608ff8bcd7a50bd490181
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challengeType: 5
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forumTopicId: 302279
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---
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## Description
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<section id='description'>
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The Hailstone sequence of numbers can be generated from a starting positive integer, <code>n</code> by:
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<ul>
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<li>If <code>n</code> is <code>1</code> then the sequence ends</li>
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<li>If <code>n</code> is <code>even</code> then the next <code>n</code> of the sequence <code>= n/2</code></li>
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<li>If <code>n</code> is <code>odd</code> then the next <code>n</code> of the sequence <code>= (3 * n) + 1</code></li>
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</ul>
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The (unproven) <a href="https://en.wikipedia.org/wiki/Collatz conjecture" title="wp: Collatz conjecture" target="_blank">Collatz conjecture</a> 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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</section>
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## Instructions
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<section id='instructions'>
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<ol>
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<li>Create a routine to generate the hailstone sequence for a number</li>
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<li>Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with <code>27, 82, 41, 124</code> and ending with <code>8, 4, 2, 1</code></li>
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<li>Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length. (But don't show the actual sequence!)</li>
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</ol>
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<strong>See also:</strong>
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<ul>
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<li><a href="https://xkcd.com/710" target="_blank">xkcd</a> (humourous).</li>
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</ul>
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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>hailstoneSequence</code> should be a function.
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testString: assert(typeof hailstoneSequence === 'function');
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- text: <code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</code>
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testString: assert.deepEqual(hailstoneSequence(), res);
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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 hailstoneSequence() {
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const res = [];
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return res;
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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const res = [[27, 82, 41, 124, 8, 4, 2, 1], [351, 77031]];
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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 hailstoneSequence () {
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const res = [];
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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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const h = hailstone(27);
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const hLen = h.length;
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res.push([...h.slice(0, 4), ...h.slice(hLen - 4, hLen)]);
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let n = 0;
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let max = 0;
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for (let i = 100000; --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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res.push([max, n]);
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return res;
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}
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```
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</section>
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