With your help, the Elves manage to find the right parts and fix all of the machines. Now, they just need to send the command to boot up the machines and get the sand flowing again.
The machines are far apart and wired together with long cables. The cables don't connect to the machines directly, but rather to communication modules attached to the machines that perform various initialization tasks and also act as communication relays.
Modules communicate using pulses. Each pulse is either a high pulse or a low pulse. When a module sends a pulse, it sends that type of pulse to each module in its list of destination modules.
There are several different types of modules:
Flip-flop modules (prefix %) are either on or off; they are initially off. If a flip-flop module receives a high pulse, it is ignored and nothing happens. However, if a flip-flop module receives a low pulse, it flips between on and off. If it was off, it turns on and sends a high pulse. If it was on, it turns off and sends a low pulse.
Conjunction modules (prefix &) remember the type of the most recent pulse received from each of their connected input modules; they initially default to remembering a low pulse for each input. When a pulse is received, the conjunction module first updates its memory for that input. Then, if it remembers high pulses for all inputs, it sends a low pulse; otherwise, it sends a high pulse.
There is a single broadcast module (named broadcaster). When it receives a pulse, it sends the same pulse to all of its destination modules.
Here at Desert Machine Headquarters, there is a module with a single button on it called, aptly, the button module. When you push the button, a single low pulse is sent directly to the broadcaster module.
After pushing the button, you must wait until all pulses have been delivered and fully handled before pushing it again. Never push the button if modules are still processing pulses.
Pulses are always processed in the order they are sent. So, if a pulse is sent to modules a, b, and c, and then module a processes its pulse and sends more pulses, the pulses sent to modules b and c would have to be handled first.
The module configuration (your puzzle input) lists each module. The name of the module is preceded by a symbol identifying its type, if any. The name is then followed by an arrow and a list of its destination modules. For example:
12345broadcaster -> a, b, c
%a -> b
%b -> c
%c -> inv
&inv -> aIn this module configuration, the broadcaster has three destination modules named a, b, and c. Each of these modules is a flip-flop module (as indicated by the % prefix).a outputs to b which outputs to c which outputs to another module named inv.inv is a conjunction module (as indicated by the & prefix) which, because it has only one input, acts like an inverter (it sends the opposite of the pulse type it receives); it outputs to a.
By pushing the button once, the following pulses are sent:
123456789101112button -low-> broadcaster
broadcaster -low-> a
broadcaster -low-> b
broadcaster -low-> c
a -high-> b
b -high-> c
c -high-> inv
inv -low-> a
a -low-> b
b -low-> c
c -low-> inv
inv -high-> aAfter this sequence, the flip-flop modules all end up off, so pushing the button again repeats the same sequence.
Here's a more interesting example:
12345broadcaster -> a
%a -> inv, con
&inv -> b
%b -> con
&con -> outputThis module configuration includes the broadcaster, two flip-flops (named a and b), a single-input conjunction module (inv), a multi-input conjunction module (con), and an untyped module named output (for testing purposes). The multi-input conjunction module con watches the two flip-flop modules and, if they're both on, sends a low pulse to the output module.
Here's what happens if you push the button once:
12345678button -low-> broadcaster
broadcaster -low-> a
a -high-> inv
a -high-> con
inv -low-> b
con -high-> output
b -high-> con
con -low-> outputBoth flip-flops turn on and a low pulse is sent to output! However, now that both flip-flops are on and con remembers a high pulse from each of its two inputs, pushing the button a second time does something different:
123456button -low-> broadcaster
broadcaster -low-> a
a -low-> inv
a -low-> con
inv -high-> b
con -high-> outputFlip-flop a turns off! Now, con remembers a low pulse from module a, and so it sends only a high pulse to output.
Push the button a third time:
12345678button -low-> broadcaster
broadcaster -low-> a
a -high-> inv
a -high-> con
inv -low-> b
con -low-> output
b -low-> con
con -high-> outputThis time, flip-flop a turns on, then flip-flop b turns off. However, before b can turn off, the pulse sent to con is handled first, so it briefly remembers all high pulses for its inputs and sends a low pulse to output. After that, flip-flop b turns off, which causes con to update its state and send a high pulse to output.
Finally, with a on and b off, push the button a fourth time:
123456button -low-> broadcaster
broadcaster -low-> a
a -low-> inv
a -low-> con
inv -high-> b
con -high-> outputThis completes the cycle: a turns off, causing con to remember only low pulses and restoring all modules to their original states.
To get the cables warmed up, the Elves have pushed the button 1000 times. How many pulses got sent as a result (including the pulses sent by the button itself)?
In the first example, the same thing happens every time the button is pushed: 8 low pulses and 4 high pulses are sent. So, after pushing the button 1000 times, 8000 low pulses and 4000 high pulses are sent. Multiplying these together gives 32000000.
In the second example, after pushing the button 1000 times, 4250 low pulses and 2750 high pulses are sent. Multiplying these together gives 11687500.
Consult your module configuration; determine the number of low pulses and high pulses that would be sent after pushing the button 1000 times, waiting for all pulses to be fully handled after each push of the button.What do you get if you multiply the total number of low pulses sent by the total number of high pulses sent?
Check the comments in the code below.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203import abc
from dataclasses import dataclass, field
from pathlib import Path
from typing import Literal
import pytest
State = Literal["Low", "High"]
@dataclass
class Event:
from_module: str
to_module: str
state: State
@dataclass
class BaseModule(abc.ABC):
key: str
next_modules: list[str]
@property
@abc.abstractmethod
def output(self) -> State: ...
@abc.abstractmethod
def pulse(self, module: str, state: State) -> list[Event]: ...
@dataclass
class Broadcast(BaseModule):
@property
def output(self) -> State:
return "Low"
def pulse(self, module: str, state: State) -> list[Event]:
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
@dataclass
class FlipFlop(BaseModule):
on: bool = False
@property
def output(self) -> State:
if self.on:
return "High"
return "Low"
def pulse(self, module: str, state: State) -> list[Event]:
if state == "High":
return []
elif state == "Low":
self.on = not self.on
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
@dataclass
class Conjunction(BaseModule):
inputs: dict[str, State] = field(default_factory=dict)
@property
def output(self) -> State:
if all([state == "High" for state in self.inputs.values()]):
return "Low"
return "High"
def add_input(self, module: str) -> None:
self.inputs[module] = "Low"
def pulse(self, module: str, state: State) -> list[Event]:
self.inputs[module] = state
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
def runner(document: list[str]) -> int:
module_map: dict[str, BaseModule] = {}
conjunctions: set[str] = set()
# Parse inputs to a "module map"
# Also pull out the conjunction keys
for line in document:
key, output = line.split(" -> ")
outputs = [value.strip() for value in output.split(",")]
if key == "broadcaster":
module_map[key] = Broadcast(key=key, next_modules=outputs)
elif key.startswith("%"):
key = key.replace("%", "")
module_map[key] = FlipFlop(key=key, next_modules=outputs)
elif key.startswith("&"):
key = key.replace("&", "")
module_map[key] = Conjunction(key=key, next_modules=outputs)
conjunctions.add(key)
else:
raise ValueError
# Run through all modules
# If they have any conjunctions, update said conjunction
for key, module in module_map.items():
for next_module in module.next_modules:
if next_module in conjunctions:
# Add to module inputs
conjunction_module = module_map[next_module]
assert isinstance(conjunction_module, Conjunction)
conjunction_module.add_input(key)
# Get the initial output state of all modules
initial_state: dict[str, State] = {}
for key, module in module_map.items():
initial_state[key] = module.output
# Callback for comparing against initial state
def matches_initial_state() -> bool:
for _key, _module in module_map.items():
if initial_state[_key] != _module.output:
return False
return True
steps_to_cycle = 0
button_presses = 0
pulses: dict[State, int] = {
"High": 0, # 11
"Low": 0, # 17
}
events: list[Event] = []
while steps_to_cycle < 1 or not matches_initial_state():
events.append(Event(to_module="broadcaster", from_module="button", state="Low"))
button_presses += 1
pulses["Low"] += 1
while events:
steps_to_cycle += 1
event = events.pop(0)
if event.to_module not in module_map:
continue
event_module = module_map[event.to_module]
new_events = event_module.pulse(event.from_module, event.state)
events += new_events
for new_event in new_events:
pulses[new_event.state] += 1
if button_presses >= 1000:
break
button_cycles = 1000 // button_presses
return (pulses["Low"] * button_cycles * pulses["High"]) * button_cycles
@pytest.mark.parametrize(
"filename,output",
[
("example-1.txt", 32000000),
("example-2.txt", 11687500),
("example-3.txt", 731517480),
],
)
def test_runner(filename: str, output: int) -> None:
with open(Path(__file__).with_name(filename)) as file:
result = runner(file.read().splitlines())
assert result == output
Answer: 731,517,480
The final machine responsible for moving the sand down to Island Island has a module attached named rx. The machine turns on when a single low pulse is sent to rx.
Reset all modules to their default states. Waiting for all pulses to be fully handled after each button press, what is the fewest number of button presses required to deliver a single low pulse to the module named rx?
Find the inputs to rx and count the number of button presses required to switch their outputs to High. Then just calculate the least common multiple of these button presses.
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200import abc
import math
from dataclasses import dataclass, field
from pathlib import Path
from typing import Literal
import pytest
State = Literal["Low", "High"]
@dataclass
class Event:
from_module: str
to_module: str
state: State
@dataclass
class BaseModule(abc.ABC):
key: str
next_modules: list[str]
@property
@abc.abstractmethod
def output(self) -> State: ...
@abc.abstractmethod
def pulse(self, module: str, state: State) -> list[Event]: ...
@dataclass
class Broadcast(BaseModule):
@property
def output(self) -> State:
return "Low"
def pulse(self, module: str, state: State) -> list[Event]:
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
@dataclass
class FlipFlop(BaseModule):
on: bool = False
@property
def output(self) -> State:
if self.on:
return "High"
return "Low"
def pulse(self, module: str, state: State) -> list[Event]:
if state == "High":
return []
elif state == "Low":
self.on = not self.on
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
@dataclass
class Conjunction(BaseModule):
inputs: dict[str, State] = field(default_factory=dict)
@property
def output(self) -> State:
if all([state == "High" for state in self.inputs.values()]):
return "Low"
return "High"
def add_input(self, module: str) -> None:
self.inputs[module] = "Low"
def pulse(self, module: str, state: State) -> list[Event]:
self.inputs[module] = state
return [
Event(
from_module=self.key,
to_module=next_module,
state=self.output,
)
for next_module in self.next_modules
]
def runner(document: list[str]) -> int:
module_map: dict[str, BaseModule] = {}
conjunctions: set[str] = set()
# Parse inputs to a "module map"
# Also pull out the conjunction keys
for line in document:
key, output = line.split(" -> ")
outputs = [value.strip() for value in output.split(",")]
if key == "broadcaster":
module_map[key] = Broadcast(key=key, next_modules=outputs)
elif key.startswith("%"):
key = key.replace("%", "")
module_map[key] = FlipFlop(key=key, next_modules=outputs)
elif key.startswith("&"):
key = key.replace("&", "")
module_map[key] = Conjunction(key=key, next_modules=outputs)
conjunctions.add(key)
else:
raise ValueError
# Run through all modules
# If they have any conjunctions, update said conjunction
for key, module in module_map.items():
for next_module in module.next_modules:
if next_module in conjunctions:
# Add to module inputs
conjunction_module = module_map[next_module]
assert isinstance(conjunction_module, Conjunction)
conjunction_module.add_input(key)
# Get the initial output state of all modules
initial_state: dict[str, State] = {}
for key, module in module_map.items():
initial_state[key] = module.output
# Callback for comparing against initial state
def matches_initial_state() -> bool:
for _key, _module in module_map.items():
if initial_state[_key] != _module.output:
return False
return True
rx_caller = module_map["kh"]
assert isinstance(rx_caller, Conjunction)
triggers: dict[str, float] = {_input: math.inf for _input in rx_caller.inputs}
button_presses = 0
events: list[Event] = []
while button_presses < 1 or not matches_initial_state():
events.append(Event(to_module="broadcaster", from_module="button", state="Low"))
button_presses += 1
while events:
event = events.pop(0)
if event.to_module not in module_map:
continue
event_module = module_map[event.to_module]
new_events = event_module.pulse(event.from_module, event.state)
events += new_events
if event_module.key in triggers and event_module.output == "High":
triggers[event_module.key] = min(
triggers[event_module.key], button_presses
)
if all([value != math.inf for value in triggers.values()]):
break
return math.lcm(*triggers.values())
@pytest.mark.parametrize(
"filename,output",
[
("example-3.txt", 244178746156661),
],
)
def test_runner(filename: str, output: int) -> None:
with open(Path(__file__).with_name(filename)) as file:
result = runner(file.read().splitlines())
assert result == output
Answer: 244,178,746,156,661
| Day | Part 1 Time | Part 1 Rank | Part 2 Time | Part 2 Rank |
|---|---|---|---|---|
| 20 | 02:00:44 | 3,521 | 02:15:45 | 1,801 |
I got stuck for a long time (at least ~45 minutes) just trying to figure out how the modules actually worked. I had a solution that worked for the first input but not the second. And when I fixed the code to work for the second input, it broke for the first. I really just needed to read the prompt carefully 🙃.
The second part was surprisingly easy. I've seen enough problems to know when to pull out math.lcm.
I did try running the problem without using math.lcm, but considering that my answer was 244,178,746,156,661, I don't think that would've ever finished.