From 1ba4804977ec0356e0ac9f62c5d5d9253064c646 Mon Sep 17 00:00:00 2001
From: WillFlame <flameyanai@gmail.com>
Date: Thu, 21 Dec 2023 20:42:07 -0500
Subject: [PATCH] Add 2023 day 21

---
 2023/day21.clj | 73 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 73 insertions(+)
 create mode 100644 2023/day21.clj

diff --git a/2023/day21.clj b/2023/day21.clj
new file mode 100644
index 0000000..df085c7
--- /dev/null
+++ b/2023/day21.clj
@@ -0,0 +1,73 @@
+(ns clojure-aoc.core (:gen-class)
+  (:require [clojure-aoc.grids :as grids]
+    clojure.string))
+
+(def input (-> (slurp "input.txt") (clojure.string/split #"\n")))
+
+(def movements
+  (memoize
+    (fn [grid loc]
+      (->> (grids/neighbours grid loc)
+        (filter #(let [char (grids/at grid %)] (or (= char \.) (= char \S))))))))
+
+;; The number of steps can be calculated by keeping track of a frontier of nodes and the previous steps.
+;; The new number of steps can be calculated using (new frontier + number of steps from 2 iterations ago).
+(defn dests [grid start steps]
+  (loop [i 0 frontier #{start} last-frontier #{} last-sum 1 ll-sum 0]
+    (if (= i steps)
+      last-sum
+      (let [reducer (fn [new-frontier loc]
+                      (let [dests (movements grid loc)]
+                        (into new-frontier (filter #(not (contains? last-frontier %)) dests))))
+            new-frontier (reduce reducer #{} frontier)]
+        (recur (inc i) new-frontier frontier (+ ll-sum (count new-frontier)) last-sum)))))
+
+(def part1
+  (let [grid (map seq input)
+        start (grids/find-pred grid #(= \S (grids/at grid %)))]
+    (dests grid start 64)))
+
+;; Not needed as part of the answer, but helpful to prove that 131 steps (from the centre) will cover the entire grid.
+;; Thus, being able to reach the corner of a cell is sufficient to prove that the cell will be filled.
+(defn steps-to-fill [grid start]
+  (loop [i 0 frontier #{start} last-frontier #{}]
+    (if (empty? frontier)
+      i
+      (let [reducer (fn [new-frontier loc]
+                      (let [dests (movements grid loc)]
+                        (into new-frontier (filter #(not (contains? last-frontier %)) dests))))
+            new-frontier (reduce reducer #{} frontier)]
+        (recur (inc i) new-frontier frontier)))))
+
+(defn get-corners [dim]
+  [[0 0] [0 (dec dim)] [(dec dim) 0] [(dec dim) (dec dim)]])
+
+(defn get-middles [dim]
+  (let [mid (quot dim 2)]
+    [[0 mid] [mid 0] [(dec dim) mid] [mid (dec dim)]]))
+
+;; Because S is in the middle of a 131x131 grid and there's an unobstructed path along that row+column, along with the edges,
+;; it is always optimal to start a cell at either one of the middle points or one of the corners.
+;; Then, the number of tiles you can reach in cell (4, 3) is the same number of tiles as (3, 4), since both start in the bottom left corner.
+;; After that, it's just math based on a checkerboard pattern and making sure you count the frontier of the diamond properly.
+(def part2
+  (let [grid (map seq input)
+        dim (count grid)
+        mid (quot dim 2)
+        radius (dec (quot 26501365 dim))
+        start (grids/find-pred grid #(= \S (grids/at grid %)))
+        odd-steps (dests grid start dim)
+        even-steps (dests grid start (inc dim))
+        outers (map #(dests grid % (dec mid)) (get-corners dim))
+        inners (map #(dests grid % (+ mid dim -1)) (get-corners dim))
+        middles (map #(dests grid % (dec dim)) (get-middles dim))]
+    (->> [(* (Math/pow radius 2) odd-steps)
+          (* (Math/pow (inc radius) 2) even-steps)
+          (map #(* (inc radius) %) outers)
+          (map #(* radius %) inners)
+          middles]
+      flatten
+      (apply +))))
+
+(defn -main [& args]
+  (println (str part1 " " part2)))