From b1a9c5dbb3b302e7457dd6c2178412a26b634b31 Mon Sep 17 00:00:00 2001
From: Jeremy Kaplan <jdkaplan@metagram.net>
Date: Thu, 7 Dec 2023 21:51:32 -0800
Subject: [PATCH] 2023 Day 8 Part 2

---
 2023/day08.nim | 64 +++++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 58 insertions(+), 6 deletions(-)

diff --git a/2023/day08.nim b/2023/day08.nim
index cf62849..75e7963 100644
--- a/2023/day08.nim
+++ b/2023/day08.nim
@@ -40,19 +40,71 @@ proc parseMap(text: string): Map =
   for node in parts[1].strip.splitLines.map(parseNode):
     result.nodes[node.id] = node
 
+func step(map: Map, loc: string, n: int): string =
+  case map.moves[n mod len(map.moves)]:
+    of L: map.nodes[loc].left
+    of R: map.nodes[loc].right
+
 proc dbg[T](v: T): T = (echo(v); v)
 
 proc part1(): int =
   let text = readFile("input/day08.txt")
   var map = parseMap(text)
 
-  var mv = 0
   var loc = "AAA"
   while loc != "ZZZ":
-    case map.moves[mv mod len(map.moves)]:
-      of L: loc = map.nodes[loc].left
-      of R: loc = map.nodes[loc].right
-    mv = mv + 1
-  return mv
+    loc = map.step(loc, result)
+    inc result
+
+func isDone(loc: string): bool =
+  loc.endsWith('Z')
+
+func walk(map: Map, start: string): seq[int] =
+  var loc = start
+  var mv = 0
+  while true:
+    if loc.isDone:
+      result.add mv
+      if result.len > 2:
+        if result[^1] - result[^2] == result[^2] - result[^3]:
+          return
+    loc = map.step(loc, mv)
+    inc mv
+
+func gcd(a: int, b: int): int =
+  var a = a
+  var b = b
+  while b != 0:
+    let t = b
+    b = a mod b
+    a = t
+  return a
+
+func gcd(nums: seq[int]): int =
+  result = gcd(nums[0], nums[1])
+  for n in nums[2..^1]:
+    result = gcd(result, n)
+
+proc part2(): int =
+  let text = readFile("input/day08.txt")
+  var map = parseMap(text)
+
+  var starts: seq[string]
+  for loc in map.nodes.keys:
+    if loc.endsWith('A'):
+      starts.add loc
+
+  var periods: seq[int]
+  for start in starts:
+    let times = map.walk(start)
+    assert(3 * times[0] == times[2])
+    periods.add times[0]
+
+  let gcd = gcd(periods)
+
+  result = periods[0]
+  for p in periods[1..^1]:
+    result *= int(p / gcd)
 
 echo part1()
+echo part2()