2023: d20: ex2: add solution

2023/d20/ex2/ex2.py

@@ -0,0 +1,128 @@
+#!/usr/bin/env python
+
+import enum
+import itertools
+import math
+import sys
+from collections import defaultdict, deque
+from typing import NamedTuple
+
+
+class ModuleType(enum.StrEnum):
+    FLIP_FLOP = "%"
+    CONJUNCTION = "&"
+    BROADCAST = "broadcaster"
+
+
+class Pulse(enum.IntEnum):
+    LOW = 0
+    HIGH = 1
+
+
+class Rule(NamedTuple):
+    module_type: ModuleType
+    destinations: list[str]
+
+
+Modules = dict[str, Rule]
+
+
+def solve(input: list[str]) -> int:
+    def parse_rule(line: str) -> tuple[str, Rule]:
+        module, outputs = line.split(" -> ")
+
+        name: str
+        module_type: ModuleType
+
+        if module != "broadcaster":
+            name = module[1:]
+            module_type = ModuleType(module[0])
+        else:
+            name = module
+            module_type = ModuleType(module)
+
+        return name, Rule(module_type, outputs.split(", "))
+
+    def parse(input: list[str]) -> Modules:
+        return dict(map(parse_rule, input))
+
+    def compute_inputs(modules: Modules) -> dict[str, list[str]]:
+        inputs: dict[str, list[str]] = defaultdict(list)
+
+        for src, rule in modules.items():
+            for dst in rule.destinations:
+                inputs[dst].append(src)
+
+        return inputs
+
+    def count_buttons(modules: Modules) -> int:
+        def count_buttons_for(
+            wanted_src: str,
+            wanted_dst: str,
+            pulse_wanted: Pulse,
+        ) -> int:
+            inputs = compute_inputs(modules)
+            last_pulse: dict[str, Pulse] = defaultdict(lambda: Pulse.LOW)
+
+            for i in itertools.count(start=1):
+                queue: deque[tuple[Pulse, str]] = deque([(Pulse.LOW, "broadcaster")])
+
+                while queue:
+                    pulse, name = queue.popleft()
+
+                    mod = modules.get(name)
+
+                    # This is for unknown outputs
+                    if mod is None:
+                        continue
+
+                    new_pulse: Pulse
+                    match mod.module_type:
+                        case ModuleType.FLIP_FLOP:
+                            if pulse == Pulse.HIGH:
+                                continue
+                            new_pulse = Pulse(1 - last_pulse[name])
+                        case ModuleType.CONJUNCTION:
+                            high_inputs = all(
+                                last_pulse[input] == Pulse.HIGH
+                                for input in inputs[name]
+                            )
+                            new_pulse = Pulse.LOW if high_inputs else Pulse.HIGH
+                        case ModuleType.BROADCAST:
+                            new_pulse = pulse
+
+                    last_pulse[name] = new_pulse
+                    for dst in mod.destinations:
+                        queue.append((new_pulse, dst))
+                        # We found the pulse we wanted, report the number of button presses
+                        if (
+                            new_pulse == pulse_wanted
+                            and name == wanted_src
+                            and dst == wanted_dst
+                        ):
+                            return i
+
+            assert False  # Sanity check
+
+        inputs = compute_inputs(modules)
+        # The input has a single conjunction leading to "rx"
+        # So we want to compute when all of *its* inputs are high at the same time
+        assert len(inputs["rx"]) == 1  # Sanity check
+        rx_input = inputs["rx"][0]
+        assert modules[rx_input].module_type == ModuleType.CONJUNCTION  # Sanity check
+        # Shortcut: assume that the high pulse output is cyclic
+        return math.lcm(
+            *(count_buttons_for(mod, rx_input, Pulse.HIGH) for mod in inputs[rx_input])
+        )
+
+    modules = parse(input)
+    return count_buttons(modules)
+
+
+def main() -> None:
+    input = sys.stdin.read().splitlines()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()