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---
id: 5e6dd139859c290b6ab80292
title: Longest increasing subsequence
challengeType: 5
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forumTopicId: 385272
2021-01-13 02:31:00 +00:00
dashedName: longest-increasing-subsequence
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---
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# --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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$\\{3, 10, 20\\}$
For more information on this problem please see [Wikipedia ](<https://en.wikipedia.org/wiki/Longest increasing subsequence> ).
# --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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# --hints--
`findSequence` should be a function.
```js
assert(typeof findSequence == 'function');
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```
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`findSequence([3, 10, 2, 1, 20])` should return a array.
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```js
assert(Array.isArray(findSequence([3, 10, 2, 1, 20])));
```
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`findSequence([3, 10, 2, 1, 20])` should return `[3, 10, 20]` .
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```js
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assert.deepEqual(findSequence([3, 10, 2, 1, 20]), [3, 10, 20]);
```
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`findSequence([2, 7, 3, 5, 8])` should return `[2, 3, 5, 8]` .
```js
assert.deepEqual(findSequence([2, 7, 3, 5, 8]), [2, 3, 5, 8]);
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```
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`findSequence([2, 6, 4, 5, 1])` should return `[2, 4, 5]` .
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```js
assert.deepEqual(findSequence([2, 6, 4, 5, 1]), [2, 4, 5]);
```
`findSequence([10, 22, 9, 33, 21, 50, 60, 80])` should return `[10, 22, 33, 50, 60, 80]` .
```js
assert.deepEqual(findSequence([10, 22, 9, 33, 21, 50, 60, 80]), [
10,
22,
33,
50,
60,
80
]);
```
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`findSequence([0, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15])` should return `[0, 2, 6, 9, 11, 15` .
```js
assert.deepEqual(
findSequence([0, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]),
[0, 2, 6, 9, 11, 15]
);
```
# --seed--
## --seed-contents--
```js
function findSequence(input) {
}
```
# --solutions--
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```js
function findSequence(input) {
var len = input.length;
var result = []
for (var i = 0; i < len ; i + + ) result . push ( 1 )
for (var i = 0; i < len ; i + + )
for (var j = i - 1; j >= 0; j--)
if (input[i] > input[j] & & result[j] >= result[i])
result[i] = result[j] + 1;
var maxValue = Math.max.apply(null, result);
var maxIndex = result.indexOf(Math.max.apply(Math, result));
var output = [];
output.push(input[maxIndex]);
for (var i = maxIndex; i >= 0; i--) {
if (maxValue == 0) break;
if (input[maxIndex] > input[i] & & result[i] == maxValue - 1) {
output.push(input[i]);
maxValue--;
}
}
output.reverse();
return output;
}
```