Add "Maximum subarray sum" kata

Author: juan-antonio-ledesma

5-kyu/maximum-subarray-sum.md

@@ -0,0 +1,39 @@
+<h1>Maximum subarray sum <sup><sup>5 Kyu</sup></sup></h1>
+
+<sup>
+  <a href="https://www.codewars.com/kata/54521e9ec8e60bc4de000d6c">
+    <strong>LINK TO THE KATA</strong>
+  </a> - <code>ALGORITHMS</code> <code>LISTS</code> <code>DYNAMIC PROGRAMMING</code> <code>FUNDAMENTALS</code> <code>PERFORMANCE</code>
+</sup>
+
+## Description
+
+The maximum sum subarray problem consists in finding the maximum sum of a contiguous subsequence in an array or list of integers:
+
+```javascript
+maxSequence([-2, 1, -3, 4, -1, 2, 1, -5, 4])
+// should be 6: [4, -1, 2, 1]
+```
+
+Easy case is when the list is made up of only positive numbers and the maximum sum is the sum of the whole array. If the list is made up of only negative numbers, return 0 instead.
+
+Empty list is considered to have zero greatest sum. Note that the empty list or array is also a valid sublist/subarray.
+
+## Solution
+
+```javascript
+const maxSequence = arr => {
+  let maxSoFar = 0
+  let maxEndingHere = 0
+
+  for (let i = 0; i < arr.length; i++) {
+    maxEndingHere += arr[i]
+
+    if (maxEndingHere < 0) maxEndingHere = 0
+
+    if (maxSoFar < maxEndingHere) maxSoFar = maxEndingHere
+  }
+
+  return maxSoFar
+}
+```

README.md

@@ -41,6 +41,7 @@ JavaScript katas on Codewars are programming challenges that help you improve yo
 - **[Greed is Good](./5-kyu/greed-is-good.md)**<br><sup>`ALGORITHMS`</sup>
 - **[Human Readable Time](./5-kyu/human-readable-time.md)**<br><sup>`DATE TIME` `MATHEMATICS` `ALGORITHMS`</sup>
 - **[Josephus Survivor](./5-kyu/josephus-survivor.md)**<br><sup>`MATHEMATICS` `COMBINATORICS` `ALGORITHMS` `LISTS` `ARRAYS`</sup>
+- **[Maximum subarray sum](./5-kyu/maximum-subarray-sum.md)**<br><sup>`ALGORITHMS` `LISTS` `DYNAMIC PROGRAMMING` `FUNDAMENTALS` `PERFORMANCE`</sup>
 - **[Mean Square Error](./5-kyu/mean-square-error.md)**<br><sup>`ARRAYS` `MATHEMATICS` `ALGORITHMS`</sup>
 - **[Moving Zeros To The End](./5-kyu/moving-zeros-to-the-end.md)**<br><sup>`ARRAYS` `SORTING` `ALGORITHMS`</sup>
 - **[Not very secure](./5-kyu/not-very-secure.md)**<br><sup>`REGULAR EXPRESSIONS` `STRINGS`</sup>