From 38927a7889957b600fdadd3b3ee79b6413a6e74d Mon Sep 17 00:00:00 2001
From: Christian <me@ctsk.xyz>
Date: Sat, 14 Dec 2024 21:18:16 +0100
Subject: [PATCH] Day 14 Mathy solution

---
 aoc/src/dev/ctsk/aoc/Utils.scala      |  5 ++++
 aoc/src/dev/ctsk/aoc/days/Day14.scala | 34 ++++++++++-----------------
 2 files changed, 18 insertions(+), 21 deletions(-)

diff --git a/aoc/src/dev/ctsk/aoc/Utils.scala b/aoc/src/dev/ctsk/aoc/Utils.scala
index a56503f..bf0ff68 100644
--- a/aoc/src/dev/ctsk/aoc/Utils.scala
+++ b/aoc/src/dev/ctsk/aoc/Utils.scala
@@ -6,3 +6,8 @@ def gcd(a: Int, b: Int): Int =
 extension [A](xs: Seq[A])
   def pairs: Iterator[(A, A)] =
     xs.combinations(2).map(xs => (xs(0), xs(1)))
+
+def eea(a: Int, b: Int): (Int, Int, Int) =
+  if b == 0 then return (a, 1, 0)
+  val (d, x, y) = eea(b, a % b)
+  (d, y, x - y * (a / b))
diff --git a/aoc/src/dev/ctsk/aoc/days/Day14.scala b/aoc/src/dev/ctsk/aoc/days/Day14.scala
index 2ed03fd..445624d 100644
--- a/aoc/src/dev/ctsk/aoc/days/Day14.scala
+++ b/aoc/src/dev/ctsk/aoc/days/Day14.scala
@@ -1,9 +1,10 @@
 package dev.ctsk.aoc.days
 
-import dev.ctsk.aoc.*
+import dev.ctsk.aoc._
 import os.ReadablePath
-import scala.util.boundary
-import scala.util.boundary.break
+
+def mu(arr: Seq[Int]) = arr.sum * 1.0 / arr.length
+def va(arr: Seq[Int]) = { val m = mu(arr); arr.map(v => (v - m) * (v - m)).sum }
 
 object Day14 extends Solver(14):
   private val Y = 101
@@ -22,27 +23,18 @@ object Day14 extends Solver(14):
     ul * ur * dl * dr
 
   def part2(robots: Array[(Point, Point)]): Int =
-    val hist = Array.fill(X, Y)(0)
-    def isTree(t: Int): Boolean =
-      boundary:
-        for i <- robots.indices
-        do
-          val dst = go(robots(i), t)
-          if hist(dst.x)(dst.y) == t then break(false)
-          hist(dst.x)(dst.y) = t
-        break(true)
-
-    (1 to X * Y).find(isTree).get
+    val xo = (0 to 103).minBy(t => va(robots.map(go(_, t).x).take(50)))
+    val yo = (0 to 103).minBy(t => va(robots.map(go(_, t).y).take(50)))
+    val (_, iX, iY) = eea(X, Y)
+    (xo * iY * Y + yo * iX * X) % (X * Y)
 
   override def run(input: ReadablePath): (Timings, Solution) =
-    val (pre_time, robots) = timed {
-      os.read
-        .lines(input)
-        .map(longs)
-        .map { case Vector(y, x, dy, dx) => (Point.of(x, y), Point.of(dx, dy)) }
-        .toArray
-    }
+    def parse(line: String): (Point, Point) =
+      longs(line) match {
+        case Vector(y, x, dy, dx) => (Point.of(x, y), Point.of(dx, dy))
+      }
 
+    val (pre_time, robots) = timed { os.read.lines(input).map(parse).toArray }
     val (p1_time, p1) = timed { part1(robots) }
     val (p2_time, p2) = timed { part2(robots) }