Utilize Arrow memoization (#285)

It's not strictly faster than my own cache; but I hadn't used it before,
so wanted to give it a try. It's quite simple!

src/main/kotlin/me/peckb/aoc/_2024/calendar/day21/Day21.kt

@@ -1,8 +1,9 @@
 package me.peckb.aoc._2024.calendar.day21
 
-import javax.inject.Inject
+import arrow.core.memoize
 import me.peckb.aoc.generators.InputGenerator.InputGeneratorFactory
 import java.util.LinkedList
+import javax.inject.Inject
 import kotlin.math.sign
 
 class Day21 @Inject constructor(
@@ -18,76 +19,72 @@ class Day21 @Inject constructor(
 
   private fun solve(input: Sequence<String>, indirections: Int) : Long {
     return input.sumOf { code ->
-      val length = getLength(NUMERIC_PAD, code, indirections)
+      val length = memoizedGetLength(NUMERIC_PAD, code, indirections)
       val size = code.take(3).toLong()
 
       length * size
     }
   }
 
-  private fun getLength(keyPad: Map<Char, Pair<Int, Int>>, code: String, indirections: Int): Long {
-    val lengthKey = LengthKey(keyPad.size, code, indirections)
+  private val memoizedGetLength = ::getLength.memoize()
 
-    if (LENGTH_CACHE.containsKey(lengthKey)) {
-      return LENGTH_CACHE[lengthKey]!!
-    }
+  private val memoizedPaths = ::paths.memoize()
 
+  private fun getLength(keyPad: Map<Char, Pair<Int, Int>>, code: String, indirections: Int): Long {
     if (indirections == 0) {
-      return code.length.toLong().also { LENGTH_CACHE[lengthKey] = it }
+      return code.length.toLong()
     }
 
     val minLength = "A${code}".toList()
       .windowed(2)
       .sumOf { (s, e) ->
-        paths(keyPad, s, e).minOf { getLength(DIRECTION_PAD, "${it}A", indirections - 1) }
+        memoizedPaths(keyPad, s, e).minOf { memoizedGetLength(DIRECTION_PAD, "${it}A", indirections - 1) }
       }
 
-    return minLength.also { LENGTH_CACHE[lengthKey] = it }
+    return minLength
   }
 
   private fun paths(keyPad: Map<Char, Pair<Int, Int>>, start: Char, end: Char): List<String> {
-    val pathKey = PathKey(keyPad.size, start, end)
-
-    if (PATHS_CACHE.containsKey(pathKey)) {
-      return PATHS_CACHE[pathKey]!!
-    }
-
     val paths = mutableListOf<String>()
+
     val partialPaths = LinkedList<Pair<Pair<Int, Int>, String>>().apply {
       add(keyPad[start]!! to "")
     }
 
     pathGeneration@ while(partialPaths.isNotEmpty()) {
       val (position, path) = partialPaths.poll()
-
       val target = keyPad[end]!!
+
       if (position == target) {
         paths.add(path)
         continue@pathGeneration
       }
 
-      val yDelta = target.second - position.second
-      if (yDelta != 0) {
-        val newPoint = position.first to position.second + yDelta.sign
+      val (yDelta, xDelta) = target - position
+
+      if (xDelta != 0) {
+        val newPoint = position.first to position.second + xDelta.sign
         if (newPoint in keyPad.values) {
-          val dir = if (yDelta > 0) { ">" } else { "<" }
+          val dir = if (xDelta > 0) { ">" } else { "<" }
           partialPaths.add(newPoint to "$path$dir")
         }
       }
 
-      val xDelta = target.first - position.first
-      if (xDelta != 0) {
-        val newPoint = position.first + xDelta.sign to position.second
+      if (yDelta != 0) {
+        val newPoint = position.first + yDelta.sign to position.second
         if (newPoint in keyPad.values) {
-          val dir = if (xDelta > 0) { "v" } else { "^" }
+          val dir = if (yDelta > 0) { "v" } else { "^" }
           partialPaths.add(newPoint to "$path$dir")
         }
       }
     }
 
-    return paths.also { PATHS_CACHE[pathKey] = it }
+    return paths
   }
 
+  private operator fun Pair<Int, Int>.minus(other: Pair<Int, Int>) =
+    this.first - other.first to this.second - other.second
+
   companion object {
     val NUMERIC_PAD = mapOf(
       '7' to (0 to 0), '8' to (0 to 1), '9' to (0 to 2),
@@ -100,13 +97,5 @@ class Day21 @Inject constructor(
                        '^' to (0 to 1), 'A' to (0 to 2),
       '<' to (1 to 0), 'v' to (1 to 1), '>' to (1 to 2)
     )
-
-    val LENGTH_CACHE = mutableMapOf<LengthKey, Long>()
-
-    val PATHS_CACHE = mutableMapOf<PathKey, List<String>>()
   }
 }
-
-data class LengthKey(val padIndicator: Int, val pattern: String, val robots: Int)
-
-data class PathKey(val padIndicator: Int, val start: Char, val end: Char)