From 33e714a9f72cb1d5be4d8fb9acd9e2cd3a6fb465 Mon Sep 17 00:00:00 2001
From: WillFlame <flameyanai@gmail.com>
Date: Sun, 24 Dec 2023 12:26:42 -0500
Subject: [PATCH] Add 2023 day 24

---
 2023/day24.clj | 60 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 60 insertions(+)
 create mode 100644 2023/day24.clj

diff --git a/2023/day24.clj b/2023/day24.clj
new file mode 100644
index 0000000..6bc48b6
--- /dev/null
+++ b/2023/day24.clj
@@ -0,0 +1,60 @@
+(ns clojure-aoc.core (:gen-class)
+    (:require [clojure.core.matrix :as matrix]
+              [clojure.core.matrix.linear :as linear]
+              clojure.string))
+
+(def input (-> (slurp "input.txt") (clojure.string/split #"\n")))
+
+(defn parse-hailstone [line]
+  (->> (re-matches #"(\d+), (\d+), (\d+) @ *(-?\d+), *(-?\d+), *(-?\d+)" line)
+                   next
+                   (map #(Long/parseLong %))))
+
+(defn intersect [[x1 y1 z1 vx1 vy1 vz1] [x2 y2 z2 vx2 vy2 vz2]]
+  (let [denom (- (/ (* vy2 vx1) vx2) vy1)]
+    (if (zero? denom)
+      nil
+      (let [t1 (/ (- y1 y2 (* (/ vy2 vx2) (- x1 x2))) (- (/ (* vy2 vx1) vx2) vy1))
+            x' (+ (* vx1 t1) x1)
+            y' (+ (* vy1 t1) y1)
+            t2 (/ (+ (* vx1 t1) x1 (- x2)) vx2)]
+        [t1 t2 x' y']))))
+
+(def part1
+  (let [hailstones (map parse-hailstone input)
+        min-test 200000000000000
+        max-test 400000000000000]
+    (->> (for [a hailstones b hailstones :while (not= a b)]
+           (intersect a b))
+         (filter (complement nil?))
+         (filter (fn [[t1 t2 x y]] (and (pos? t1) (pos? t2) (< min-test x max-test) (< min-test y max-test))))
+         count)))
+
+;; For part 2, note that we have n+6 unknowns and 3n equations. Thus, we only need n = 3 to solve.
+;; We can get vector equations p0 + t[i]*v0 == p[i] + t[i]*v[i] ==> (p0 - p[i]) == - t[i] * (v0 - v[i]) ==>
+;; (p0 - p[i]) x (v0 - v[i]) == 0, after right crossing both sides by (v0 - v[i]) since the vectors are parallel.
+;; This is still bilinear, but if we pick two i's then they have a common p0 x v0 term which can then be removed.
+;; We thus get p0 x (v[i] - v[j]) + v0 x (p[i] - p[j]) - (p[i] x v[i] - p[j] x v[j]) == 0 for hailstones i, j,
+;; and can pick two pairs to solve the system of 6 linear equations.
+
+(defn symbolic-cross [[p1 v1] [p2 v2]]
+  (let [[p12x p12y p12z] (matrix/sub p1 p2)
+        [v12x v12y v12z] (matrix/sub v1 v2)]
+  [[0        v12z     (- v12y) 0        p12z     (- p12y)]
+   [(- v12z) 0        v12x     (- p12z) 0        p12x]
+   [v12y     (- v12x) 0        p12y     (- p12x) 0]]))
+
+(defn augh [[p1 v1] [p2 v2] [p3 v3]]
+  (let [b1 (matrix/sub (matrix/cross p1 v1) (matrix/cross p2 v2))
+        b2 (matrix/sub (matrix/cross p1 v1) (matrix/cross p3 v3))
+        a (concat (symbolic-cross [p1 v1] [p2 v2]) (symbolic-cross [p1 v1] [p3 v3]))
+        b (concat b1 b2)]
+    (matrix/mmul (linear/solve a) b)))
+
+(def part2
+  (let [hailstones (map parse-hailstone input)
+      [x y z _ _ _] (apply augh (map #(partition 3 %) (take 3 hailstones)))]
+  (long (+ x y z))))
+
+(defn -main [& args]
+  (println part1 " " part2))