From 8c33b12b21f30724c6a6e3cc357facb7b0cc1b85 Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <marcin.j.chrzanowski@gmail.com>
Date: Fri, 25 Dec 2020 15:29:50 +0100
Subject: Add day 13

---
 13/a.rb      | 19 +++++++++++++++++++
 13/b.rb      | 35 +++++++++++++++++++++++++++++++++++
 13/input.txt |  2 ++
 3 files changed, 56 insertions(+)
 create mode 100644 13/a.rb
 create mode 100644 13/b.rb
 create mode 100644 13/input.txt

diff --git a/13/a.rb b/13/a.rb
new file mode 100644
index 0000000..ebadaf0
--- /dev/null
+++ b/13/a.rb
@@ -0,0 +1,19 @@
+earliest, notes = File.readlines('input.txt')
+earliest = earliest.to_i
+ids = notes.split(',').filter_map do |id|
+  if id != 'x'
+    id.to_i
+  end
+end
+
+best_wait = ids.max + 1
+best_id = 0
+ids.each do |id|
+  wait = id - (earliest % id)
+  if  wait < best_wait
+    best_wait = wait
+    best_id = id
+  end
+end
+
+puts best_wait * best_id
diff --git a/13/b.rb b/13/b.rb
new file mode 100644
index 0000000..71b6a6f
--- /dev/null
+++ b/13/b.rb
@@ -0,0 +1,35 @@
+def extended_gcd(a, b)
+  last_remainder, remainder = a.abs, b.abs
+  x, last_x, y, last_y = 0, 1, 1, 0
+  while remainder != 0
+    last_remainder, (quotient, remainder) = remainder, last_remainder.divmod(remainder)
+    x, last_x = last_x - quotient*x, x
+    y, last_y = last_y - quotient*y, y
+  end
+  return last_remainder, last_x * (a < 0 ? -1 : 1)
+end
+ 
+def invmod(e, et)
+  g, x = extended_gcd(e, et)
+  if g != 1
+    raise 'Multiplicative inverse modulo does not exist!'
+  end
+  x % et
+end
+ 
+def chinese_remainder(mods, remainders)
+  max = mods.inject( :* )  # product of all moduli
+  series = remainders.zip(mods).map{ |r,m| (r * max * invmod(max/m, m) / m) }
+  series.inject( :+ ) % max 
+end
+
+notes = File.readlines('input.txt')[1]
+ids = notes.split(',').each_with_index.filter_map do |id, i|
+  if id != 'x'
+    [id.to_i, -i % id.to_i]
+  end
+end
+
+moduli = ids.map {|m| m[0]}
+remainders = ids.map {|m| m[1]}
+puts chinese_remainder(moduli, remainders)
diff --git a/13/input.txt b/13/input.txt
new file mode 100644
index 0000000..096e2cc
--- /dev/null
+++ b/13/input.txt
@@ -0,0 +1,2 @@
+1002618
+19,x,x,x,x,x,x,x,x,41,x,x,x,37,x,x,x,x,x,367,x,x,x,x,x,x,x,x,x,x,x,x,13,x,x,x,17,x,x,x,x,x,x,x,x,x,x,x,29,x,373,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,x,23
-- 
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