Day 19

Advent of Code: Worked Solutions

Setup

# Libraries
library(tidyverse)
library(unglue)
library(sets)

# Read input from file
input <- read_lines("../input/day19.txt", skip_empty_rows = FALSE)

Part 1

Separate the input into rules and parts:

parts <- input |> 
  keep(~ str_starts(.x, "\\{")) |> 
  unglue_data(
    "{x=[x],m=[m],a=[a],s=[s]}", 
    open = "[", 
    close = "]", 
    convert = TRUE
  ) |> 
  pmap(\(x, m, a, s) lst(x, m, a, s))

rules <- input |> 
  keep(~ str_starts(.x, "\\w")) |> 
  unglue_data("[name]{[rules]}", open = "[", close = "]") |> 
  mutate(rules = str_split(rules, ",")) |> 
  unnest_longer(rules, values_to = "condition", indices_to = "cond_num") |> 
  unglue_unnest(
    condition, 
    c("{var}{eq=[<>]}{val}:{goto}", "{goto}"), 
    convert = TRUE
  ) |> 
  mutate(value = pmap(
    lst(var, eq, val, goto), 
    ~ lst(var = ..1, eq = ..2, val = ..3, goto = ..4)
  )) |> 
  summarize(value = list(value), .by = name) |> 
  deframe()

Define a function that rates a part according to the rule list for each workflow:

rate <- function(part, workflow = "in") {
  if (workflow %in% c('A', 'R')) 
    return(workflow == 'A')
  
  workflow <- rules[[workflow]]
  
  for (rule in workflow) {
    if (is.na(rule$var))
      return(rate(part, rule$goto))
    if (get(rule$eq)(part[[rule$var]], rule$val))
      return(rate(part, rule$goto))
  }
}

Rate the list of parts, then for the accepted parts, add all ratings:

keep(parts, map_lgl(parts, rate)) |> 
  unlist() |> 
  sum()

Part 2

Define a function to cut the valid set of inputs into a set of intervals. Looping through our rules, trim down the intervals for x, m, a, and s until we have the final set of valid inputs:

keys  <- set_names(c("x", "m", "a", "s"))
empty <- map(keys, ~ interval(domain = 'Z'))
init  <- map(keys, ~ interval(l = 1, r = 4000, domain = 'Z'))

rate_range <- function(cur_range, workflow = "in") {
  
  if (workflow == 'A') 
    return(list(cur_range))
  if (workflow == 'R')
    return(list())
  
  workflow <- rules[[workflow]]
  accepted <- list()

  for (rule in workflow) {
    if (is.na(rule$var)) {
      accepted <- c(accepted, rate_range(cur_range, rule$goto))
      return(accepted)
    }

    rule_range <- sets::interval(
      l = case_match(rule$eq, '<' ~ 1,            '>' ~ rule$val + 1),
      r = case_match(rule$eq, '<' ~ rule$val - 1, '>' ~ 4000),
      domain = 'Z'
    )

    rule_pass <- cur_range |>
      modify_at(rule$var, ~ interval_intersection(.x, rule_range))
    rule_fail <- cur_range |>
      modify_at(rule$var, ~ interval_complement(rule_range, .x))

    accepted <- c(accepted, rate_range(rule_pass, rule$goto))
    cur_range <- rule_fail
  }
}

Run and compute the number of total valid combinations:

rate_range(init) |> 
  map(\(intrvl) map_dbl(intrvl, ~ length(as.set(.x)))) |> 
  map_dbl(prod) |>
  sum() |> 
  format(scientific = FALSE)