From 64338f7ae089954bffd14f30c3dd01c575d590cb Mon Sep 17 00:00:00 2001
From: Matteo Landi <matteo@matteolandi.net>
Date: Thu, 1 Feb 2024 23:08:37 +0100
Subject: [PATCH] Refactor 2023/24

- Use DEFINE-SOLUTION, DEFINE-TEST
- Extract some functions to better explain what's going on -- for part
  2 in particular
---
 src/2023/day24.lisp | 77 +++++++++++++++++++++++++++------------------
 1 file changed, 47 insertions(+), 30 deletions(-)

diff --git a/src/2023/day24.lisp b/src/2023/day24.lisp
index 35bf8a4..a7e6d1d 100644
--- a/src/2023/day24.lisp
+++ b/src/2023/day24.lisp
@@ -3,9 +3,8 @@
 
 
 (defun hailstone (s) (extract-integers s))
-#+#:excluded (hailstone "248315803897794, 386127890875011, 326651351825022 @ -89, -119, 32")
 
-(defun parse-input (&optional (strings (uiop:read-file-lines #P"src/2023/day24.txt")))
+(defun parse-input (&optional (strings (aoc::read-problem-input 2023 24)))
   (mapcar #'hailstone strings))
 
 
@@ -21,13 +20,19 @@
       (list (/ xnum den) (/ ynum den)))))
 
 
+(defun ignore-axis (n h)
+  (destructuring-bind (x y z vx vy vz) h
+    (ecase n
+      (0 (list y z vy vz))
+      (1 (list x z vx vz))
+      (2 (list x y vx vy)))))
+
 (defun in-the-future? (x1 y1 x2 y2 x3 y3)
   (bnd* ((dx21 (- x2 x1)) (dx31 (- x3 x1))
          (dy21 (- y2 y1)) (dy31 (- y3 y1)))
     (and (>= (* dx21 dx31) 0)
          (>= (* dy21 dy31) 0))))
 
-
 (defun all-intersections (&optional (hh (parse-input)))
   (looping
     (dosublists (((x1 y1 vx1 vy1) . rest) hh)
@@ -40,42 +45,54 @@
                            (in-the-future? x3 y3 x4 y4 x y))
                   (collect! (list x y)))))))))))
 
-(defun ignore-axis (n h)
-  (destructuring-bind (x y z vx vy vz) h
-    (ecase n
-      (0 (list y z vy vz))
-      (1 (list x z vx vz))
-      (2 (list x y vx vy)))))
 
-#+#:excluded (length (all-intersections))
 (defun part1 (&optional (hh (parse-input)))
   (looping
     (doseq ((x y) (all-intersections (mapcar [ignore-axis 2 _] hh)))
       (count! (and (<= 200000000000000 x 400000000000000)
                    (<= 200000000000000 y 400000000000000))))))
-#+#:excluded (part1 7 27)
-#+#:excluded (part1  )
-; 24999 nope
-; 16779 !!!
 
+
+;; We know a position <x, y, z> exists such that, if we throw a hail rock with
+;; velocity <vx, vy, vz>, eventually it will collide with all the other rocks.
+;; This means that if we subtract <vx, vy, vz> from each rock in our input,
+;; eventually the rocks will all collide in <x, y, z>.
+;;
+;; So the idea is to take a few rocks from our input, brute-force a bunch of
+;; velocities along each axis, adjust rocks velocities, and see where the rocks
+;; collide.
+;;
+;; Re-using the logic from part1, we can find first where the rocks collide
+;; along x and y first, and then along x and z.
+;;
+;; Kudos to: https://www.youtube.com/watch?v=nP2ahZs40U8
 (defun adjust-velocity (dvx dvy h)
   (destructuring-bind (x y vx vy) h
     (list x y (+ vx dvx) (+ vy dvy))))
-#+#:excluded (untrace adjust-velocity)
+
+(defun find-single-intersection (hh)
+  (dorangei (vx -250 250)
+    (dorangei (vy -250 250)
+      (bnd1 (points (all-intersections (mapcar [adjust-velocity vx vy _]
+                                               hh)))
+        (when (and (> (length points) 1)
+                   (= (length (remove-duplicates points :test #'equal)) 1))
+          (return-from find-single-intersection (first points)))))))
 
 (defun part2 (&optional (hh (parse-input)))
-  (flet ((magic (axis &aux )
-           (bnd1 (hh (mapcar [ignore-axis axis _] (subseq hh 0 3)))
-             (dorangei (vx -300 300)
-               (dorangei (vy -300 300)
-                 (bnd1 (points (all-intersections (mapcar [adjust-velocity vx vy _]
-                                                          hh)))
-                   (when (and (> (length points) 1)
-                              (= (length (remove-duplicates points :test #'equal)) 1))
-                     (return-from magic (first points)))))))))
-    (destructuring-bind (px1 py) (magic 2)
-      (destructuring-bind (px2 pz) (magic 1)
-        (assert (= px1 px2))
-        (+ px1 py pz)))))
-#+#:excluded (time (part2))
-; 871983857253169
+  (recursively ((hh (copy-seq hh)))
+    (setf hh (shuffle hh))
+    (bnd1 (sample (subseq hh 0 3))
+      (awhen (find-single-intersection (mapcar [ignore-axis 2 _] sample))
+        (destructuring-bind (px1 py) it
+          (awhen (find-single-intersection (mapcar [ignore-axis 1 _] sample))
+            (destructuring-bind (px2 pz) it
+              (assert (= px1 px2))
+              (return-from recur (+ px1 py pz)))))))
+    (recur hh)))
+
+
+(define-solution (2023 24) (hh parse-input)
+  (values (part1 hh) (part2 hh)))
+
+(define-test (2023 24) (16779 871983857253169))