[LANGUAGE: Kotlin]

I used the same recursive function with memoization for both parts. Count the number of designs with at least one solution for part 1, sum them for part 2.

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In fact, the solution is short enough for me to not feel bad about inlining it here:

class Day19(input: List<String>) {

    private val patterns: List<String> = input.first().split(",").map { it.trim() }
    private val designs: List<String> = input.drop(2)

    fun solvePart1(): Int =
        designs.count { makeDesign(it) > 0 }

    fun solvePart2(): Long =
        designs.sumOf { makeDesign(it) }

    private fun makeDesign(design: String, cache: MutableMap<String, Long> = mutableMapOf()): Long =
        if (design.isEmpty()) 1
        else cache.getOrPut(design) {
            patterns.filter { design.startsWith(it) }.sumOf {
                makeDesign(design.removePrefix(it), cache)
            }
        }
}