From 3c06b19032a0184c0b3ad1ea352becb5d60c9e6a Mon Sep 17 00:00:00 2001
From: Charles Cabergs <me@cacharle.xyz>
Date: Tue, 22 Jun 2021 20:54:23 +0200
Subject: problem 13 14 in julia

---
 julia/014-longest_collatz_sequence.jl | 24 ++++++++++++++++++++++++
 1 file changed, 24 insertions(+)
 create mode 100644 julia/014-longest_collatz_sequence.jl

(limited to 'julia/014-longest_collatz_sequence.jl')

diff --git a/julia/014-longest_collatz_sequence.jl b/julia/014-longest_collatz_sequence.jl
new file mode 100644
index 0000000..1edaf98
--- /dev/null
+++ b/julia/014-longest_collatz_sequence.jl
@@ -0,0 +1,24 @@
+###
+# Longest Collatz sequence
+# Problem 14
+#
+# 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.
+###
+
+function collatz_length(n)
+    n == 1 && return 1
+    n % 2 == 0 && return 1 + collatz_length(n ÷ 2)
+    return 1 + collatz_length(3n + 1)
+end
+
+result = argmax([collatz_length(x) for x in 1:(1_000_000 - 1)])
+
+println(result)
-- 
cgit