freeCodeCamp/curriculum/challenges/espanol/10-coding-interview-prep/rosetta-code/longest-increasing-subsequence.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5e6dd139859c290b6ab80292	Longest increasing subsequence	5	385272	longest-increasing-subsequence

--description--

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:

For the following array:

\\{3, 10, 2, 1, 20\\}

Longest increasing sequence is:

\\{3, 10, 20\\}

For more information on this problem please see [Wikipedia](https://en.wikipedia.org/wiki/Longest increasing subsequence).

--instructions--

Write a function that takes an array of numbers as a parameter and returns the longest increasing subsequence.

It is guaranteed that every array will have a longest increasing subsequence.

--hints--

findSequence should be a function.

assert(typeof findSequence == 'function');

findSequence([3, 10, 2, 1, 20]) should return a array.

assert(Array.isArray(findSequence([3, 10, 2, 1, 20])));

findSequence([3, 10, 2, 1, 20]) should return [3, 10, 20].

assert.deepEqual(findSequence([3, 10, 2, 1, 20]), [3, 10, 20]);

findSequence([2, 7, 3, 5, 8]) should return [2, 3, 5, 8].

assert.deepEqual(findSequence([2, 7, 3, 5, 8]), [2, 3, 5, 8]);

findSequence([2, 6, 4, 5, 1]) should return [2, 4, 5].

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].

assert.deepEqual(findSequence([10, 22, 9, 33, 21, 50, 60, 80]), [
  10,
  22,
  33,
  50,
  60,
  80
]);

findSequence([0, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]) should return [0, 2, 6, 9, 11, 15.

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--

function findSequence(input) {

}

--solutions--

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;
}