133 lines
3.7 KiB
Markdown
133 lines
3.7 KiB
Markdown
---
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title: Taxicab numbers
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id: 594ecc0d9a8cf816e3340187
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challengeType: 5
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forumTopicId: 302337
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---
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## Description
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<section id='description'>
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A <a href="https://en.wikipedia.org/wiki/Hardy–Ramanujan number" title="wp: Hardy–Ramanujan number" target="_blank">taxicab number</a> (the definition that is being used here) is a positive integer that can be expressed as the sum of two positive cubes in more than one way.
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The first taxicab number is <code>1729</code>, which is:
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<span style="margin-left: 2em;">1<sup>3</sup> + 12<sup>3</sup> and</span>
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<span style="margin-left: 2em;">9<sup>3</sup> + 10<sup>3</sup>.</span>
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Taxicab numbers are also known as:
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<ul>
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<li>taxi numbers</li>
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<li>taxi-cab numbers</li>
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<li>taxi cab numbers</li>
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<li>Hardy-Ramanujan numbers</li>
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</ul>
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</section>
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## Instructions
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<section id='instructions'>
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Write a function that returns the lowest <code>n</code> taxicab numbers. For each of the taxicab numbers, show the number as well as its constituent cubes.
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<strong>See also:</strong>
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<ul>
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<li><a href="https://oeis.org/A001235" target="_blank">A001235 taxicab numbers</a> on The On-Line Encyclopedia of Integer Sequences.</li>
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<li><a href="https://en.wikipedia.org/wiki/Taxicab_number" target="_blank">taxicab number</a> on Wikipedia.</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>taxicabNumbers</code> is a function.
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testString: assert(typeof taxicabNumbers === 'function');
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- text: <code>taxicabNumbers</code> should return an array.
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testString: assert(typeof taxicabNumbers(2) === 'object');
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- text: <code>taxicabNumbers</code> should return an array of numbers.
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testString: assert(typeof taxicabNumbers(100)[0] === 'number');
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- text: <code>taxicabNumbers(4)</code> must return [1729, 4104, 13832, 20683].
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testString: assert.deepEqual(taxicabNumbers(4), res4);
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- text: <code>taxicabNumbers(25)</code> should return [1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597]
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testString: assert.deepEqual(taxicabNumbers(25), res25);
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- text: <code>taxicabNumbers(39)</code> resulting numbers from 20 - 29 should be [314496,320264,327763,373464,402597,439101,443889,513000,513856].
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testString: assert.deepEqual(taxicabNumbers(39).slice(20, 29), res39From20To29);
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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 taxicabNumbers(n) {
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// Good luck!
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return true;
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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 res4 = [1729, 4104, 13832, 20683];
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const res25 = [
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1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656,
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110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763,
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373464, 402597
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];
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const res39From20To29 = [314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856];
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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 taxicabNumbers(nNumbers) {
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const cubeN = [];
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const s3s = {};
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const e = 100;
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for (let n = 1; n < e; n += 1) {
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cubeN[n] = n * n * n;
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}
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for (let a = 1; a < e - 1; a += 1) {
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const a3 = cubeN[a];
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for (let b = a; b < e; b += 1) {
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const b3 = cubeN[b];
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const s3 = a3 + b3;
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let abs = s3s[s3];
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if (!abs) {
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s3s[s3] = abs = [];
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}
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abs.push([a, b]);
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}
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}
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let i = 0;
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const res = [];
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Object.keys(s3s).forEach(s3 => {
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const abs = s3s[s3];
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if (abs.length >= 2) { // No two cube pairs found
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i += 1;
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if (i <= nNumbers) {
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res.push(s3);
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}
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}
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});
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return res.map(item => parseInt(item, 10));
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}
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```
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</section>
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