From bfcf986c6076501a3053f7c83b5026ee980576a6 Mon Sep 17 00:00:00 2001
From: Waddah <waddah.ja@gmail.com>
Date: Sat, 17 Oct 2020 23:33:32 +0300
Subject: [PATCH] add solution for Project Euler 014

---
 Project-Euler/Problem014.js | 47 +++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 Project-Euler/Problem014.js

diff --git a/Project-Euler/Problem014.js b/Project-Euler/Problem014.js
new file mode 100644
index 000000000..62a2974ec
--- /dev/null
+++ b/Project-Euler/Problem014.js
@@ -0,0 +1,47 @@
+/*
+Longest Collatz sequence
+
+The following iterative sequence is defined for the set of positive integers:
+
+n → n/2 (n is even)
+n → 3n + 1 (n is odd)
+
+Using the rule above and starting with 13, we generate the following sequence:
+
+13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
+It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
+
+Which starting number, under one million, produces the longest chain?
+
+NOTE: Once the chain starts the terms are allowed to go above one million.
+*/
+
+const getCollatzSequenceLength = (num, seqLength) => {
+  if (num === 1) {
+    return seqLength
+  } else {
+    let newElement
+    if (num % 2 === 0) {
+      newElement = num / 2
+    } else {
+      newElement = (3 * num) + 1
+    }
+    seqLength++
+    return getCollatzSequenceLength(newElement, seqLength)
+  }
+}
+
+const findLongestCollatzSequence = () => {
+  let startingPointForLargestSequence = 1
+  let largestSequnceLength = 1
+  for (let i = 2; i < 1000000; i++) {
+    const currentSequenceLength = getCollatzSequenceLength(i, 1)
+    if (currentSequenceLength > largestSequnceLength) {
+      startingPointForLargestSequence = i
+      largestSequnceLength = currentSequenceLength
+    }
+  }
+  return startingPointForLargestSequence
+}
+
+console.log(findLongestCollatzSequence())