Solution to problem 19 part 2 in Python

src/Year_2020/P19.py

@@ -89,7 +89,9 @@ with open("files/P19.txt", "r") as f:
     rules, messages = [f.split("\n") for f in f.read().strip().split("\n\n")]
 
 
-def dfs(tree, node, depth):
+def dfs(tree: dict[int, int], node: str, depth: int) -> str:
+    if depth > 15:
+        return ""
     rule = ""
     for next in tree[node].split():
         if next == "|":
@@ -101,7 +103,7 @@ def dfs(tree, node, depth):
     return "(" + rule + ")"
 
 
-def part_1():
+def part_1() -> None:
     rules_dict = dict([rule.split(": ") for rule in rules])
     rule_0 = re.compile(dfs(rules_dict, "0", 0))
     total = sum([1 for message in messages if rule_0.fullmatch(message)])
@@ -109,5 +111,112 @@ def part_1():
     print(f"There are {total} messages completely matching rule 0")
 
 
+# --- Part Two ---
+
+# As you look over the list of messages, you realize your matching rules
+# aren't quite right. To fix them, completely replace rules 8: 42 and 11: 42 31
+# with the following:
+
+# 8: 42 | 42 8
+# 11: 42 31 | 42 11 31
+
+# This small change has a big impact: now, the rules do contain loops, and the
+# list of messages they could hypothetically match is infinite. You'll need to
+# determine how these changes affect which messages are valid.
+
+# Fortunately, many of the rules are unaffected by this change; it might help
+# to start by looking at which rules always match the same set of values and
+# how those rules (especially rules 42 and 31) are used by the new versions of
+# rules 8 and 11.
+
+# (Remember, you only need to handle the rules you have; building a solution
+# that could handle any hypothetical combination of rules would be
+# significantly more difficult.)
+
+# For example:
+
+# 42: 9 14 | 10 1
+# 9: 14 27 | 1 26
+# 10: 23 14 | 28 1
+# 1: "a"
+# 11: 42 31
+# 5: 1 14 | 15 1
+# 19: 14 1 | 14 14
+# 12: 24 14 | 19 1
+# 16: 15 1 | 14 14
+# 31: 14 17 | 1 13
+# 6: 14 14 | 1 14
+# 2: 1 24 | 14 4
+# 0: 8 11
+# 13: 14 3 | 1 12
+# 15: 1 | 14
+# 17: 14 2 | 1 7
+# 23: 25 1 | 22 14
+# 28: 16 1
+# 4: 1 1
+# 20: 14 14 | 1 15
+# 3: 5 14 | 16 1
+# 27: 1 6 | 14 18
+# 14: "b"
+# 21: 14 1 | 1 14
+# 25: 1 1 | 1 14
+# 22: 14 14
+# 8: 42
+# 26: 14 22 | 1 20
+# 18: 15 15
+# 7: 14 5 | 1 21
+# 24: 14 1
+
+# abbbbbabbbaaaababbaabbbbabababbbabbbbbbabaaaa
+# bbabbbbaabaabba
+# babbbbaabbbbbabbbbbbaabaaabaaa
+# aaabbbbbbaaaabaababaabababbabaaabbababababaaa
+# bbbbbbbaaaabbbbaaabbabaaa
+# bbbababbbbaaaaaaaabbababaaababaabab
+# ababaaaaaabaaab
+# ababaaaaabbbaba
+# baabbaaaabbaaaababbaababb
+# abbbbabbbbaaaababbbbbbaaaababb
+# aaaaabbaabaaaaababaa
+# aaaabbaaaabbaaa
+# aaaabbaabbaaaaaaabbbabbbaaabbaabaaa
+# babaaabbbaaabaababbaabababaaab
+# aabbbbbaabbbaaaaaabbbbbababaaaaabbaaabba
+
+# Without updating rules 8 and 11, these rules only match three messages:
+# bbabbbbaabaabba, ababaaaaaabaaab, and ababaaaaabbbaba.
+
+# However, after updating rules 8 and 11, a total of 12 messages match:
+
+#     bbabbbbaabaabba
+#     babbbbaabbbbbabbbbbbaabaaabaaa
+#     aaabbbbbbaaaabaababaabababbabaaabbababababaaa
+#     bbbbbbbaaaabbbbaaabbabaaa
+#     bbbababbbbaaaaaaaabbababaaababaabab
+#     ababaaaaaabaaab
+#     ababaaaaabbbaba
+#     baabbaaaabbaaaababbaababb
+#     abbbbabbbbaaaababbbbbbaaaababb
+#     aaaaabbaabaaaaababaa
+#     aaaabbaabbaaaaaaabbbabbbaaabbaabaaa
+#     aabbbbbaabbbaaaaaabbbbbababaaaaabbaaabba
+
+# After updating rules 8 and 11, how many messages completely match rule 0?
+
+
+def part_2():
+    rules.append("8: 42 | 42 8")
+    rules.append("11: 42 31 | 42 11 31")
+    rules_dict = dict([rule.split(": ") for rule in rules])
+    rule_0 = re.compile(dfs(rules_dict, "0", 0))
+    total = sum([1 for message in messages if rule_0.fullmatch(message)])
+
+    print(
+        f"After updating rules 8 and 11, there are still "
+        f"{total} messages completely matching rule 0"
+    )
+
+
 if __name__ == "__main__":
     part_1()
+    part_2()