From ffcf15c67e5729f723d26e05915d4b7c866e9d54 Mon Sep 17 00:00:00 2001
From: Alpha Chen <alpha@kejadlen.dev>
Date: Mon, 14 Dec 2020 08:03:54 -0800
Subject: [PATCH] [2020][ruby][13.x]

---
 2020/ruby/day_13.rb | 42 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 2020/ruby/day_13.rb

diff --git a/2020/ruby/day_13.rb b/2020/ruby/day_13.rb
new file mode 100644
index 0000000..d0bc482
--- /dev/null
+++ b/2020/ruby/day_13.rb
@@ -0,0 +1,42 @@
+input = ARGF.read.split("\n")
+depart_time = input.shift.to_i
+buses = input.shift.split(?,).map {|b| b != ?x ? b.to_i : nil }
+
+# p buses.compact.map {|bus|
+#   d = bus * ((depart_time / bus) + 1)
+#   [bus, d - depart_time]
+# }.min_by(&:last).inject {|a,b| a * b }
+
+# shamelessly copied from https://rosettacode.org/wiki/Chinese_remainder_theorem#Ruby
+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
+
+buses = buses.map.with_index.select {|b,_| b }
+# p 0.step(by: buses[0][0]).lazy.find {|depart_time|
+#   buses.all? {|b,i| (depart_time + i) % b == 0 }
+# }
+
+mods, remainders = buses.map {|b,i| [b, b-i] }.transpose
+p chinese_remainder(mods, remainders)