Add 2024 day 19 article (#819)

* Add day 19 article.

* Fix inconsistent capital letters.

* Update Solver.scala.

* Update solutions submodule.

---------

Co-authored-by: Seth Tisue <[email protected]>

Author: AvaPL

docs/2024/puzzles/day19.md

@@ -2,10 +2,197 @@ import Solver from "../../../../../website/src/components/Solver.js"
 
 # Day 19: Linen Layout
 
+by [Paweł Cembaluk](https://github.com/AvaPL)
+
 ## Puzzle description
 
 https://adventofcode.com/2024/day/19
 
+## Solution summary
+
+The puzzle involves arranging towels to match specified patterns. Each towel has a predefined stripe sequence, and the
+task is to determine:
+
+- **Part 1**: How many patterns can be formed using the available towels?
+- **Part 2**: For each pattern, how many unique ways exist to form it using the towels?
+
+The solution leverages regular expressions to validate patterns in Part 1 and employs recursion with memoization for
+efficient counting in Part 2.
+
+## Part 1
+
+### Parsing the input
+
+The input consists of two sections:
+
+- **Towels**: A comma-separated list of towels (e.g., `r, wr, b, g`).
+- **Desired Patterns**: A list of patterns to match, each on a new line.
+
+To parse the input, we split it into two parts: towels and desired patterns. Towels are extracted as a comma-separated
+list, while patterns are read line by line after a blank line. We also introduce type aliases `Towel` and `Pattern` for
+clarity in representing these inputs.
+
+Here’s the code for parsing:
+
+```scala 3
+type Towel = String
+type Pattern = String
+
+def parse(input: String): (List[Towel], List[Pattern]) =
+  val Array(towelsString, patternsString) = input.split("\n\n")
+  val towels = towelsString.split(", ").toList
+  val patterns = patternsString.split("\n").toList
+  (towels, patterns)
+```
+
+### Solution
+
+To determine if a pattern can be formed, we use a regular expression. While this could be done manually by checking
+combinations, the tools in the standard library make it exceptionally easy. The regex matches sequences formed by
+repeating any combination of the available towels:
+
+```scala 3
+def isPossible(towels: List[Towel])(pattern: Pattern): Boolean =
+  val regex = towels.mkString("^(", "|", ")*$").r
+  regex.matches(pattern)
+```
+
+`towels.mkString("^(", "|", ")*$")` builds a regex like `^(r|wr|b|g)*$`. Here’s how it works:
+
+- `^`: Ensures the match starts at the beginning of the string.
+- `(` and `)`: Groups the towel patterns so they can be alternated.
+- `|`: Acts as a logical OR between different towels.
+- `*`: Matches zero or more repetitions of the group.
+- `$`: Ensures the match ends at the string’s end.
+
+This approach is simplified because we know the towels contain only letters. If the input could be any string, we would
+need to use `Regex.quote` to handle special characters properly.
+
+Finally, using the `isPossible` function, we filter and count the patterns that can be formed:
+
+```scala 3
+def part1(input: String): Int =
+  val (towels, patterns) = parse(input)
+  patterns.count(isPossible(towels))
+```
+
+## Part 2
+
+To count all unique ways to form a pattern, we start with a base algorithm that recursively matches towels from the
+start of the pattern. For each match, we remove the matched part and solve for the remaining pattern. This ensures we
+explore all possible combinations of towels. Since the numbers involved can grow significantly, we use `Long` to handle
+the large values resulting from these calculations.
+
+Here’s the code for the base algorithm:
+
+```scala 3
+def countOptions(towels: List[Towel], pattern: Pattern): Long =
+  towels
+    .collect {
+      case towel if pattern.startsWith(towel) => // Match the towel at the beginning of the pattern
+        pattern.drop(towel.length) // Remove the matched towel
+    }
+    .map { remainingPattern =>
+      if (remainingPattern.isEmpty) 1 // The pattern is fully matched
+      else countOptions(towels, remainingPattern) // Recursively solve the remaining pattern
+    }
+    .sum // Sum the results for all possible towels
+```
+
+That's not enough though. The above algorithm will repeatedly solve the same sub-patterns quite often, making it
+inefficient. To optimize it, we introduce memoization. Memoization stores results for previously solved sub-patterns,
+eliminating redundant computations. We also pass all the patterns to the function to fully utilize the memoization
+cache.
+
+Here's the code with additional cache for already calculated sub-patterns:
+
+```scala 3
+def countOptions(towels: List[Towel], patterns: List[Pattern]): Long =
+  val cache = mutable.Map.empty[Pattern, Long]
+
+  def loop(pattern: Pattern): Long =
+    cache.getOrElseUpdate( // Get the result from the cache
+      pattern,
+      // Calculate the result if it's not in the cache
+      towels
+        .collect {
+          case towel if pattern.startsWith(towel) => // Match the towel at the beginning of the pattern
+            pattern.drop(towel.length) // Remove the matched towel
+        }
+        .map { remainingPattern =>
+          if (remainingPattern.isEmpty) 1 // The pattern is fully matched
+          else loop(remainingPattern) // Recursively solve the remaining pattern
+        }
+        .sum // Sum the results for all possible towels
+    )
+
+  patterns.map(loop).sum // Sum the results for all patterns
+```
+
+Now, we just have to pass the input to the `countOptions` function to get the final result:
+
+```scala 3
+def part2(input: String): Long =
+  val (towels, patterns) = parse(input)
+  countOptions(towels, patterns)
+```
+
+## Final code
+
+```scala 3
+type Towel = String
+type Pattern = String
+
+def parse(input: String): (List[Towel], List[Pattern]) =
+  val Array(towelsString, patternsString) = input.split("\n\n")
+  val towels = towelsString.split(", ").toList
+  val patterns = patternsString.split("\n").toList
+  (towels, patterns)
+
+def part1(input: String): Int =
+  val (towels, patterns) = parse(input)
+  val possiblePatterns = patterns.filter(isPossible(towels))
+  possiblePatterns.size
+
+def isPossible(towels: List[Towel])(pattern: Pattern): Boolean =
+  val regex = towels.mkString("^(", "|", ")*$").r
+  regex.matches(pattern)
+
+def part2(input: String): Long =
+  val (towels, patterns) = parse(input)
+  countOptions(towels, patterns)
+
+def countOptions(towels: List[Towel], patterns: List[Pattern]): Long =
+  val cache = mutable.Map.empty[Pattern, Long]
+
+  def loop(pattern: Pattern): Long =
+    cache.getOrElseUpdate(
+      pattern,
+      towels
+        .collect {
+          case towel if pattern.startsWith(towel) =>
+            pattern.drop(towel.length)
+        }
+        .map { remainingPattern =>
+          if (remainingPattern.isEmpty) 1
+          else loop(remainingPattern)
+        }
+        .sum
+    )
+
+  patterns.map(loop).sum
+```
+
+## Run it in the browser
+
+### Part 1
+
+<Solver puzzle="day19-part1" year="2024"/>
+
+### Part 2
+
+<Solver puzzle="day19-part2" year="2024"/>
+
 ## Solutions from the community
 
 - [Solution](https://github.com/nikiforo/aoc24/blob/main/src/main/scala/io/github/nikiforo/aoc24/D19T2.scala) by [Artem Nikiforov](https://github.com/nikiforo)

solutions

@@ -11,6 +11,8 @@ object Solver:
     Map(
       "day13-part1" -> day13.part1,
       "day13-part2" -> day13.part2,
+      "day19-part1" -> day19.part1,
+      "day19-part2" -> day19.part2,
       "day14-part1" -> day14.part1,
       "day14-part2" -> day14.part2,
       "day21-part1" -> day21.part1,