6cfd0fc503
* fix: improve Project Euler descriptions and test case Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54 * feat: add typeof tests and gave functions proper names for first 100 challenges * fix: continue fixing test descriptions and adding "before test" sections * fix: address review comments * fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays * fix: implement bug fixes and improvements from review * fix: remove console.log statements from seed and solution
113 lines
2.8 KiB
Markdown
113 lines
2.8 KiB
Markdown
---
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id: 5900f37a1000cf542c50fe8d
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challengeType: 5
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title: 'Problem 14: Longest Collatz sequence'
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forumTopicId: 301768
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---
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## Description
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<section id='description'>
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The following iterative sequence is defined for the set of positive integers:
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<div style='padding-left: 4em;'><var>n</var> → <var>n</var>/2 (<var>n</var> is even)</div>
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<div style='padding-left: 4em;'><var>n</var> → 3<var>n</var> + 1 (<var>n</var> is odd)</div>
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Using the rule above and starting with 13, we generate the following sequence:
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<div style='text-align: center;'>13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1</div>
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It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
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Which starting number, under the given `limit`, produces the longest chain?
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**Note:** Once the chain starts the terms are allowed to go above one million.
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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>longestCollatzSequence(14)</code> should return a number.
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testString: assert(typeof longestCollatzSequence(14) === 'number');
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- text: <code>longestCollatzSequence(14)</code> should return 9.
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testString: assert.strictEqual(longestCollatzSequence(14), 9);
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- text: <code>longestCollatzSequence(5847)</code> should return 3711.
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testString: assert.strictEqual(longestCollatzSequence(5847), 3711);
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- text: <code>longestCollatzSequence(46500)</code> should return 35655.
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testString: assert.strictEqual(longestCollatzSequence(46500), 35655);
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- text: <code>longestCollatzSequence(54512)</code> should return 52527.
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testString: assert.strictEqual(longestCollatzSequence(54512), 52527);
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- text: <code>longestCollatzSequence(100000)</code> should return 77031.
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testString: assert.strictEqual(longestCollatzSequence(100000), 77031);
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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 longestCollatzSequence(limit) {
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// Good luck!
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return true;
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}
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longestCollatzSequence(14);
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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 longestCollatzSequence(limit) {
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let longestSequenceLength = 0;
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let startingNum = 0;
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function sequenceLength(num) {
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let length = 1;
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while (num >= 1) {
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if (num === 1) { break;
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} else if (num % 2 === 0) {
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num = num / 2;
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length++;
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} else {
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num = num * 3 + 1;
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length++;
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}
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}
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return length;
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}
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for (let i = 2; i < limit; i++) {
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let currSequenceLength = sequenceLength(i);
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if (currSequenceLength > longestSequenceLength) {
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longestSequenceLength = currSequenceLength;
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startingNum = i;
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}
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}
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return startingNum;
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}
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```
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</section>
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