Advent of code 2023 day 19 part2 improved

def day19_part2(s):
  s_rules, _ = s.split('\n\n')
  rules = {}
  for line in s_rules.splitlines():
    name, s_rules = line[:-1].split('{')
    rules[name] = s_rules.split(',')

  def compute(name, intervals):
    if name == 'R' or any(start >= stop for start, stop in intervals.values()):
      return 0
    if name == 'A':
      return math.prod(stop - start for start, stop in intervals.values())

    total = 0
    for rule in rules[name]:
      if rule.isalpha():
        return total + compute(rule, intervals)

      category, op, s_num, label = re.match(r'^(\w)([<>])(\d+):(\w+)$', rule).groups()
      num = int(s_num)
      start, stop = intervals[category]
      if op == '<':
        total += compute(label, intervals | {category: (start, min(stop, num))})
        intervals[category] = max(start, num), stop
      else:
        total += compute(label, intervals | {category: (max(start, num + 1), stop)})
        intervals[category] = start, min(stop, num + 1)

  return compute('in', {category: (1, 4001) for category in 'xmas'})