93 lines
3.1 KiB
Markdown
93 lines
3.1 KiB
Markdown
---
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id: 5e6dd139859c290b6ab80292
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title: Longest increasing subsequence
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challengeType: 5
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isHidden: false
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---
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## Description
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<section id='description'>
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The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. An example:
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For the following array:
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$\{3, 10, 2, 1, 20\}$
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Longest increasing sequence is:
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$\{3, 10, 20\}$
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For more information on this problem please see <a href="https://en.wikipedia.org/wiki/Longest increasing subsequence" target="_blank">Wikipedia</a>.
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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 takes an array of numbers as a parameter and returns the longest increasing subsequence.
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It is guaranteed that every array will have a longest increasing subsequence.
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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>findSequence</code> should be a function.
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testString: assert(typeof findSequence == 'function');
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- text: <code>findSequence([3, 10, 2, 1, 20])</code> should return a array.
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testString: assert(Array.isArray(findSequence([3, 10, 2, 1, 20])));
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- text: <code>findSequence([3, 10, 2, 1, 20])</code> should return <code>[3, 10, 20]</code>.
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testString: assert.deepEqual(findSequence([3, 10, 2, 1, 20]), [3, 10, 20]);
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- text: <code>findSequence([2, 7, 3, 5, 8])</code> should return <code>[2, 3, 5, 8]</code>.
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testString: assert.deepEqual(findSequence([2, 7, 3, 5, 8]), [2, 3, 5, 8]);
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- text: <code>findSequence([2, 6, 4, 5, 1])</code> should return <code>[2, 4, 5]</code>.
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testString: assert.deepEqual(findSequence([2, 6, 4, 5, 1]), [2, 4, 5]);
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- text: <code>findSequence([10, 22, 9, 33, 21, 50, 60, 80])</code> should return <code>[10, 22, 33, 50, 60, 80]</code>.
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testString: assert.deepEqual(findSequence([10, 22, 9, 33, 21, 50, 60, 80]), [10, 22, 33, 50, 60, 80]);
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- text: <code>findSequence([0, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15])</code> should return <code>[0, 2, 6, 9, 11, 15</code>.
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testString: assert.deepEqual(findSequence([0, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]), [0, 2, 6, 9, 11, 15]);
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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 findSequence(input) {
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}
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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 findSequence(input) {
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var len = input.length;
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var result = []
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for (var i = 0; i < len; i++) result.push(1)
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for (var i = 0; i < len; i++)
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for (var j = i - 1; j >= 0; j--)
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if (input[i] > input[j] && result[j] >= result[i])
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result[i] = result[j] + 1;
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var maxValue = Math.max.apply(null, result);
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var maxIndex = result.indexOf(Math.max.apply(Math, result));
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var output = [];
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output.push(input[maxIndex]);
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for (var i = maxIndex; i >= 0; i--) {
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if (maxValue == 0) break;
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if (input[maxIndex] > input[i] && result[i] == maxValue - 1) {
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output.push(input[i]);
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maxValue--;
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}
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}
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output.reverse();
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return output;
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}
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```
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</section>
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