79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
110 lines
2.7 KiB
Markdown
110 lines
2.7 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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---
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## Description
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<section id='description'>
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<p>The Hailstone sequence of numbers can be generated from a starting positive integer, n by:</p>
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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 <code> = n/2 </code>
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If n is odd then the next n of the sequence <code> = (3 * n) + 1 </code><p>The (unproven) <a href="https://en.wikipedia.org/wiki/Collatz conjecture" title="wp: Collatz conjecture">Collatz conjecture</a> is that the hailstone sequence for any starting number always terminates.</p>
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<p>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.</p>
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Task:
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Create a routine to generate the hailstone sequence for a number.
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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>
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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!)See also:
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<a href="http://xkcd.com/710" title="link: http://xkcd.com/710">xkcd</a> (humourous).
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</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>hailstoneSequence</code> is a function.
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testString: assert(typeof hailstoneSequence === 'function', '<code>hailstoneSequence</code> is a 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, '<code>hailstoneSequence()</code> should return <code>[[27,82,41,124,8,4,2,1], [351, 77031]]</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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// noprotect
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function hailstoneSequence () {
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const res = [];
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// Good luck!
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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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// noprotect
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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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