From db081bed303bc2d55e184ceaab47f8c56ea0eb64 Mon Sep 17 00:00:00 2001
From: Jeremy Kaplan <code@jdkaplan.dev>
Date: Sat, 8 Aug 2026 14:08:51 -0400
Subject: [PATCH] 2017 Day 13 Part 2

---
 2017/day13.py | 72 ++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 71 insertions(+), 1 deletion(-)

diff --git a/2017/day13.py b/2017/day13.py
index de669c9..4a88f1d 100644
--- a/2017/day13.py
+++ b/2017/day13.py
@@ -1,7 +1,10 @@
+from math import lcm
+from dataclasses import dataclass
+
 with open("input/day13.txt") as f:
     input = f.read()
 
-scanners = {}
+scanners: dict[int, int] = {}
 
 for line in input.splitlines():
     parts = line.split(": ")
@@ -26,4 +29,71 @@ def part1(scanners):
     return severity
 
 
+def is_safe(scanners, delay):
+    for depth in range(max(scanners.keys()) + 1):
+        r = scanners.get(depth)
+        if r is None:
+            continue
+
+        assert r > 1, r
+        cycle = (r - 1) * 2
+        pos = (delay + depth) % cycle
+        if pos == 0:
+            return False
+    return True
+
+
+@dataclass
+class Scanner:
+    depth: int
+    cycle: int
+
+
+@dataclass(order=True)
+class Candidate:
+    delay: int
+    increment: int
+
+    def __init__(self, delay: int, increment: int):
+        self.delay = delay % increment
+        self.increment = increment
+
+    def __hash__(self):
+        return hash((self.delay % self.increment, self.increment))
+
+    def scale(self, scalar: int) -> set["Candidate"]:
+        res = set()
+        increment = self.increment * scalar
+        for i in range(scalar + 1):
+            res.add(Candidate(self.delay + i * self.increment, increment))
+        return res
+
+    def __str__(self):
+        return f"{self.delay} + k * {self.increment}"
+
+
+def part2(scanner_map: dict[int, int]):
+    scanners: list[Scanner] = []
+    for depth in range(max(scanner_map.keys()) + 1):
+        r = scanner_map.get(depth)
+        if r is None:
+            continue
+        cycle = (r - 1) * 2
+        scanners.append(Scanner(depth, cycle))
+
+    candidates = {Candidate(0, 1)}
+    for s in scanners:
+        next: set[Candidate] = set()
+        for c in candidates:
+            scalar = lcm(c.increment, s.cycle) // c.increment
+            for n in c.scale(scalar):
+                if (n.delay + s.depth) % s.cycle:
+                    next.add(n)
+
+        candidates = next
+
+    return min(c.delay for c in candidates)
+
+
 print(part1(scanners))
+print(part2(scanners))