From dbe3f062ad66e1d8d05a3e7cb21a4a1b8165b181 Mon Sep 17 00:00:00 2001
From: Sanders Lin <45224617+SandersLin@users.noreply.github.com>
Date: Sun, 10 Feb 2019 02:00:05 +0800
Subject: [PATCH] Project Euler Problem 14 Solution 2 (#651)

---
 project_euler/problem_14/sol2.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)
 create mode 100644 project_euler/problem_14/sol2.py

diff --git a/project_euler/problem_14/sol2.py b/project_euler/problem_14/sol2.py
new file mode 100644
index 000000000000..b9de42be1108
--- /dev/null
+++ b/project_euler/problem_14/sol2.py
@@ -0,0 +1,16 @@
+def collatz_sequence(n):
+  """Collatz conjecture: start with any positive integer n.Next termis obtained from the previous term as follows:
+  if the previous term is even, the next term is one half the previous term.
+  If the previous term is odd, the next term is 3 times the previous term plus 1.
+  The conjecture states the sequence will always reach 1 regaardess of starting n."""
+  sequence = [n]
+  while n != 1:
+    if n % 2 == 0:# even
+      n //= 2
+    else:
+      n = 3*n +1
+    sequence.append(n)
+  return sequence
+
+answer = max([(len(collatz_sequence(i)), i)  for i in range(1,1000000)])
+print("Longest Collatz sequence under one million is %d with length %d" % (answer[1],answer[0]))
\ No newline at end of file