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(ns clojure-aoc.core (:gen-class) | ||
(:require [clojure.core.matrix :as matrix] | ||
[clojure.core.matrix.linear :as linear] | ||
clojure.string)) | ||
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(def input (-> (slurp "input.txt") (clojure.string/split #"\n"))) | ||
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(defn parse-hailstone [line] | ||
(->> (re-matches #"(\d+), (\d+), (\d+) @ *(-?\d+), *(-?\d+), *(-?\d+)" line) | ||
next | ||
(map #(Long/parseLong %)))) | ||
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(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'])))) | ||
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(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))) | ||
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;; 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. | ||
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(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]])) | ||
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(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))) | ||
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(def part2 | ||
(let [hailstones (map parse-hailstone input) | ||
[x y z _ _ _] (apply augh (map #(partition 3 %) (take 3 hailstones)))] | ||
(long (+ x y z)))) | ||
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(defn -main [& args] | ||
(println part1 " " part2)) |