freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/greatest-subsequential-sum.english.md

---
title: Greatest subsequential sum
id: 5a23c84252665b21eecc7e84
challengeType: 5
---

## Description
<section id='description'>
Given a sequence of integers, find a continuous subsequence which maximizes the sum of its elements, that is, the elements of no other single subsequence add up to a value larger than this one.
An empty subsequence is considered to have the sum of \( 0 \);  thus if all elements are negative, the result must be the empty sequence.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>maximumSubsequence</code> should be a function.
    testString: assert(typeof maximumSubsequence=='function','<code>maximumSubsequence</code> should be a function.');
  - text: <code>maximumSubsequence([1,2,-1,3,10,-10])</code> should return an array.
    testString: assert(Array.isArray(maximumSubsequence([1,2,-1,3,10,-10])),'<code>maximumSubsequence([1,2,-1,3,10,-10])</code> should return an array.');
  - text: <code>maximumSubsequence([1,2,-1,3,10,-10])</code> should return <code>[ 1, 2, -1, 3, 10 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([1,2,-1,3,10,-10]), [ 1, 2, -1, 3, 10 ],'<code>maximumSubsequence([1,2,-1,3,10,-10])</code> should return <code>[ 1, 2, -1, 3, 10 ]</code>.');
  - text: <code>maximumSubsequence([0, 8, 10, -2, -4, -1, -5, -3])</code> should return <code>[ 0, 8, 10 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([0, 8, 10, -2, -4, -1, -5, -3]), [ 0, 8, 10 ],'<code>maximumSubsequence([0, 8, 10, -2, -4, -1, -5, -3])</code> should return <code>[ 0, 8, 10 ]</code>.');
  - text: <code>maximumSubsequence([9, 9, -10, 1])</code> should return <code>[ 9, 9 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([9, 9, -10, 1]), [ 9, 9 ],'<code>maximumSubsequence([9, 9, -10, 1])</code> should return <code>[ 9, 9 ]</code>.');
  - text: <code>maximumSubsequence([7, 1, -5, -3, -8, 1]</code> should return <code>[ 7, 1 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([7, 1, -5, -3, -8, 1]), [ 7, 1 ],'<code>maximumSubsequence([7, 1, -5, -3, -8, 1]</code> should return <code>[ 7, 1 ]</code>.');
  - text: <code>maximumSubsequence([-3, 6, -1, 4, -4, -6])</code> should return <code>[ 6, -1, 4 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([-3, 6, -1, 4, -4, -6]), [ 6, -1, 4 ],'<code>maximumSubsequence([-3, 6, -1, 4, -4, -6])</code> should return <code>[ 6, -1, 4 ]</code>.');
  - text: <code>maximumSubsequence([-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1])</code> should return <code>[ 3, 5, 6, -2, -1, 4 ]</code>.
    testString: assert.deepEqual(maximumSubsequence([-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1]), [ 3, 5, 6, -2, -1, 4 ],'<code>maximumSubsequence([-1, -2, 3, 5, 6, -2, -1, 4, -4, 2, -1])</code> should return <code>[ 3, 5, 6, -2, -1, 4 ]</code>.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function maximumSubsequence (population) {
  // Good luck!
}
```

</div>

</section>

## Solution
<section id='solution'>


```js
function maximumSubsequence(population) {
  function sumValues(arr) {
      var result = 0;
      for (var i = 0, len = arr.length; i < len; i++) {
          result += arr[i];
      }
      return result;
  }
  var greatest;
  var maxValue = 0;
  var subsequence = [];

  for (var i = 0, len = population.length; i < len; i++) {
      for (var j = i; j <= len; j++) {
          var subsequence = population.slice(i, j);
          var value = sumValues(subsequence);
          if (value > maxValue) {
              maxValue = value;
              greatest = subsequence;
          };
      }
  }

  return greatest;
}



```

</section>