2021 Day 16
This commit is contained in:
Akumatic
parent
5712f7df20
commit
99b0fe5972
134
2021/16/README.md
Normal file
134
2021/16/README.md
Normal file
@ -0,0 +1,134 @@
|
||||
# 2021 Day 16: Packet Decoder
|
||||
Copyright (c) Eric Wastl
|
||||
#### [Direct Link](https://adventofcode.com/2021/day/16)
|
||||
|
||||
## Part 1
|
||||
|
||||
As you leave the cave and reach open waters, you receive a transmission from the Elves back on the ship.
|
||||
|
||||
The transmission was sent using the Buoyancy Interchange Transmission System (BITS), a method of packing numeric expressions into a binary sequence. Your submarine's computer has saved the transmission in [hexadecimal](https://en.wikipedia.org/wiki/Hexadecimal) (your puzzle input).
|
||||
|
||||
The first step of decoding the message is to convert the hexadecimal representation into binary. Each character of hexadecimal corresponds to four bits of binary data:
|
||||
|
||||
```
|
||||
0 = 0000
|
||||
1 = 0001
|
||||
2 = 0010
|
||||
3 = 0011
|
||||
4 = 0100
|
||||
5 = 0101
|
||||
6 = 0110
|
||||
7 = 0111
|
||||
8 = 1000
|
||||
9 = 1001
|
||||
A = 1010
|
||||
B = 1011
|
||||
C = 1100
|
||||
D = 1101
|
||||
E = 1110
|
||||
F = 1111
|
||||
```
|
||||
|
||||
The BITS transmission contains a single **packet** at its outermost layer which itself contains many other packets. The hexadecimal representation of this packet might encode a few extra `0` bits at the end; these are not part of the transmission and should be ignored.
|
||||
|
||||
Every packet begins with a standard header: the first three bits encode the packet **version**, and the next three bits encode the packet **type ID**. These two values are numbers; all numbers encoded in any packet are represented as binary with the most significant bit first. For example, a version encoded as the binary sequence `100` represents the number `4`.
|
||||
|
||||
Packets with type ID `4` represent a **literal value**. Literal value packets encode a single binary number. To do this, the binary number is padded with leading zeroes until its length is a multiple of four bits, and then it is broken into groups of four bits. Each group is prefixed by a `1` bit except the last group, which is prefixed by a `0` bit. These groups of five bits immediately follow the packet header. For example, the hexadecimal string `D2FE28` becomes:
|
||||
|
||||
```
|
||||
110100101111111000101000
|
||||
VVVTTTAAAAABBBBBCCCCC
|
||||
```
|
||||
|
||||
Below each bit is a label indicating its purpose:
|
||||
|
||||
- The three bits labeled `V` (`110`) are the packet version, `6`.
|
||||
- The three bits labeled `T` (`100`) are the packet type ID, `4`, which means the packet is a literal value.
|
||||
- The five bits labeled `A` (`10111`) start with a `1` (not the last group, keep reading) and contain the first four bits of the number, `0111`.
|
||||
- The five bits labeled `B` (`11110`) start with a `1` (not the last group, keep reading) and contain four more bits of the number, `1110`.
|
||||
- The five bits labeled `C` (`00101`) start with a `0` (last group, end of packet) and contain the last four bits of the number, `0101`.
|
||||
- The three unlabeled `0` bits at the end are extra due to the hexadecimal representation and should be ignored.
|
||||
|
||||
So, this packet represents a literal value with binary representation `011111100101`, which is `2021` in decimal.
|
||||
|
||||
Every other type of packet (any packet with a type ID other than `4`) represent an **operator** that performs some calculation on one or more sub-packets contained within. Right now, the specific operations aren't important; focus on parsing the hierarchy of sub-packets.
|
||||
|
||||
An operator packet contains one or more packets. To indicate which subsequent binary data represents its sub-packets, an operator packet can use one of two modes indicated by the bit immediately after the packet header; this is called the **length type ID**:
|
||||
|
||||
- If the length type ID is `0`, then the next **15** bits are a number that represents the **total length in bits** of the sub-packets contained by this packet.
|
||||
- If the length type ID is `1`, then the next **11** bits are a number that represents the **number of sub-packets immediately contained** by this packet.
|
||||
|
||||
Finally, after the length type ID bit and the 15-bit or 11-bit field, the sub-packets appear.
|
||||
|
||||
For example, here is an operator packet (hexadecimal string `38006F45291200`) with length type ID `0` that contains two sub-packets:
|
||||
|
||||
```
|
||||
00111000000000000110111101000101001010010001001000000000
|
||||
VVVTTTILLLLLLLLLLLLLLLAAAAAAAAAAABBBBBBBBBBBBBBBB
|
||||
```
|
||||
|
||||
- The three bits labeled `V` (`001`) are the packet version, `1`.
|
||||
- The three bits labeled `T` (`110`) are the packet type ID, `6`, which means the packet is an operator.
|
||||
- The bit labeled `I` (`0`) is the length type ID, which indicates that the length is a 15-bit number representing the number of bits in the sub-packets.
|
||||
- The 15 bits labeled `L` (`000000000011011`) contain the length of the sub-packets in bits, `27`.
|
||||
- The 11 bits labeled `A` contain the first sub-packet, a literal value representing the number `10`.
|
||||
- The 16 bits labeled `B` contain the second sub-packet, a literal value representing the number `20`.
|
||||
|
||||
After reading 11 and 16 bits of sub-packet data, the total length indicated in `L` (27) is reached, and so parsing of this packet stops.
|
||||
|
||||
As another example, here is an operator packet (hexadecimal string `EE00D40C823060`) with length type ID `1` that contains three sub-packets:
|
||||
|
||||
```
|
||||
11101110000000001101010000001100100000100011000001100000
|
||||
VVVTTTILLLLLLLLLLLAAAAAAAAAAABBBBBBBBBBBCCCCCCCCCCC
|
||||
```
|
||||
|
||||
- The three bits labeled `V` (`111`) are the packet version, `7`.
|
||||
- The three bits labeled `T` (`011`) are the packet type ID, `3`, which means the packet is an operator.
|
||||
- The bit labeled `I` (1) is the length type ID, which indicates that the length is a 11-bit number representing the number of sub-packets.
|
||||
- The 11 bits labeled `L` (`00000000011`) contain the number of sub-packets, `3`.
|
||||
- The 11 bits labeled `A` contain the first sub-packet, a literal value representing the number `1`.
|
||||
- The 11 bits labeled `B` contain the second sub-packet, a literal value representing the number `2`.
|
||||
- The 11 bits labeled `C` contain the third sub-packet, a literal value representing the number `3`.
|
||||
|
||||
After reading 3 complete sub-packets, the number of sub-packets indicated in `L` (3) is reached, and so parsing of this packet stops.
|
||||
|
||||
For now, parse the hierarchy of the packets throughout the transmission and **add up all of the version numbers**.
|
||||
|
||||
Here are a few more examples of hexadecimal-encoded transmissions:
|
||||
|
||||
- `8A004A801A8002F478` represents an operator packet (version 4) which contains an operator packet (version 1) which contains an operator packet (version 5) which contains a literal value (version 6); this packet has a version sum of **`16`**.
|
||||
- `620080001611562C8802118E34` represents an operator packet (version 3) which contains two sub-packets; each sub-packet is an operator packet that contains two literal values. This packet has a version sum of **`12`**.
|
||||
- `C0015000016115A2E0802F182340` has the same structure as the previous example, but the outermost packet uses a different length type ID. This packet has a version sum of **`23`**.
|
||||
- `A0016C880162017C3686B18A3D4780` is an operator packet that contains an operator packet that contains an operator packet that contains five literal values; it has a version sum of **`31`**.
|
||||
|
||||
Decode the structure of your hexadecimal-encoded BITS transmission; **what do you get if you add up the version numbers in all packets?**
|
||||
|
||||
## Part 2
|
||||
|
||||
Now that you have the structure of your transmission decoded, you can calculate the value of the expression it represents.
|
||||
|
||||
Literal values (type ID `4`) represent a single number as described above. The remaining type IDs are more interesting:
|
||||
|
||||
- Packets with type ID `0` are **sum** packets - their value is the sum of the values of their sub-packets. If they only have a single sub-packet, their value is the value of the sub-packet.
|
||||
- Packets with type ID `1` are **product** packets - their value is the result of multiplying together the values of their sub-packets. If they only have a single sub-packet, their value is the value of the sub-packet.
|
||||
- Packets with type ID `2` are **minimum** packets - their value is the minimum of the values of their sub-packets.
|
||||
- Packets with type ID `3` are **maximum** packets - their value is the maximum of the values of their sub-packets.
|
||||
- Packets with type ID `5` are **greater than** packets - their value is **1** if the value of the first sub-packet is greater than the value of the second sub-packet; otherwise, their value is **0**. These packets always have exactly two sub-packets.
|
||||
- Packets with type ID `6` are **less than** packets - their value is **1** if the value of the first sub-packet is less than the value of the second sub-packet; otherwise, their value is **0**. These packets always have exactly two sub-packets.
|
||||
- Packets with type ID `7` are equal to packets - their value is **1** if the value of the first sub-packet is equal to the value of the second sub-packet; otherwise, their value is **0**. These packets always have exactly two sub-packets.
|
||||
|
||||
Using these rules, you can now work out the value of the outermost packet in your BITS transmission.
|
||||
|
||||
For example:
|
||||
|
||||
- `C200B40A82` finds the sum of `1` and `2`, resulting in the value **`3`**.
|
||||
- `04005AC33890` finds the product of `6` and `9`, resulting in the value **`54`**.
|
||||
- `880086C3E88112` finds the minimum of `7`, `8`, and `9`, resulting in the value **`7`**.
|
||||
- `CE00C43D881120` finds the maximum of `7`, `8`, and `9`, resulting in the value **`9`**.
|
||||
- `D8005AC2A8F0` produces **`1`**, because `5` is less than `15`.
|
||||
- `F600BC2D8F` produces **`0`**, because `5` is not greater than `15`.
|
||||
- `9C005AC2F8F0` produces **`0`**, because `5` is not equal to `15`.
|
||||
- `9C0141080250320F1802104A08` produces **`1`**, because `1` + `3` = `2` * `2`.
|
||||
|
||||
**What do you get if you evaluate the expression represented by your hexadecimal-encoded BITS transmission?**
|
||||
92
2021/16/code.py
Normal file
92
2021/16/code.py
Normal file
@ -0,0 +1,92 @@
|
||||
# SPDX-License-Identifier: MIT
|
||||
# Copyright (c) 2021 Akumatic
|
||||
#
|
||||
# https://adventofcode.com/2021/day/16
|
||||
|
||||
def read_file(filename: str = "input.txt") -> str:
|
||||
with open(f"{__file__.rstrip('code.py')}{filename}", "r") as f:
|
||||
return f.read().strip()
|
||||
|
||||
def hex2bin(hex_str: str) -> str:
|
||||
return "".join(bin(int(h, 16))[2:].zfill(4) for h in hex_str)
|
||||
|
||||
def decode_packet(packet: str) -> tuple:
|
||||
# packet header
|
||||
version = int(packet[:3], 2)
|
||||
type_id = int(packet[3: 6], 2)
|
||||
size = 6
|
||||
payload = list()
|
||||
|
||||
if type_id == 4: # literal value
|
||||
for i in range(6, len(packet), 5):
|
||||
payload.append(packet[i+1: i+5])
|
||||
size += 5
|
||||
if packet[i] == "0":
|
||||
break
|
||||
payload = int("".join(payload), 2)
|
||||
|
||||
else: # operator
|
||||
size += 1
|
||||
if packet[6] == "0": # length in bits of the subpacket
|
||||
sub_size = int(packet[7: 22], 2)
|
||||
size += 15 + sub_size
|
||||
data = packet[22:]
|
||||
i = 0
|
||||
while i < sub_size:
|
||||
decoded_sub = decode_packet(data[i:])
|
||||
payload.append(decoded_sub)
|
||||
i += decoded_sub[2]
|
||||
else: # packet[6] == 1, number of sub-packets
|
||||
sub_amount = int(packet[7: 18], 2)
|
||||
size += 11
|
||||
data = packet[size:]
|
||||
for i in range(sub_amount):
|
||||
decoded_sub = decode_packet(data)
|
||||
payload.append(decoded_sub)
|
||||
size += decoded_sub[2]
|
||||
data = packet[size:]
|
||||
|
||||
return version, type_id, size, payload
|
||||
|
||||
def sum_versions(payload: tuple) -> int:
|
||||
if payload[1] == 4:
|
||||
return payload[0]
|
||||
return payload[0] + sum(sum_versions(sub) for sub in payload[3])
|
||||
|
||||
def payload_value(payload: tuple) -> int:
|
||||
# literal values
|
||||
if payload[1] == 4:
|
||||
return payload[3]
|
||||
|
||||
values = [payload_value(sub) for sub in payload[3]]
|
||||
|
||||
if payload[1] == 0: # sum
|
||||
return sum(values)
|
||||
elif payload[1] == 1: # product
|
||||
prod = 1
|
||||
for value in values:
|
||||
prod *= value
|
||||
return prod
|
||||
elif payload[1] == 2: # minimum
|
||||
return min(values)
|
||||
elif payload[1] == 3: # maximum
|
||||
return max(values)
|
||||
elif payload[1] == 5: # greater than
|
||||
return 1 if values[0] > values[1] else 0
|
||||
elif payload[1] == 6: # less than
|
||||
return 1 if values[0] < values[1] else 0
|
||||
else: # payload[1] == 7, equal to
|
||||
return 1 if values[0] == values[1] else 0
|
||||
|
||||
def part1(hex_value: str) -> int:
|
||||
data = decode_packet(hex2bin(hex_value))
|
||||
return sum_versions(data)
|
||||
|
||||
def part2(hex_value: str) -> int:
|
||||
data = decode_packet(hex2bin(hex_value))
|
||||
return payload_value(data)
|
||||
|
||||
if __name__ == "__main__":
|
||||
vals = read_file()
|
||||
print(f"Part 1: {part1(vals)}")
|
||||
print(f"Part 2: {part2(vals)}")
|
||||
1
2021/16/input.txt
Normal file
1
2021/16/input.txt
Normal file
@ -0,0 +1 @@
|
||||
620D7B005DF2549DF6D51466E599E2BF1F60016A3F980293FFC16E802B325332544017CC951E3801A19A3C98A7FF5141004A48627F21A400C0C9344EBA4D9345D987A8393D43D000172329802F3F5DE753D56AB76009080350CE3B44810076274468946009E002AD2D9936CF8C4E2C472400732699E531EDDE0A4401F9CB9D7802F339DE253B00CCE77894EC084027D4EFFD006C00D50001098B708A340803118E0CC5C200A1E691E691E78EA719A642D400A913120098216D80292B08104DE598803A3B00465E7B8738812F3DC39C46965F82E60087802335CF4BFE219BA34CEC56C002EB9695BDAE573C1C87F2B49A3380273709D5327A1498C4F6968004EC3007E1844289240086C4D8D5174C01B8271CA2A880473F19F5024A5F1892EF4AA279007332980CA0090252919DEFA52978ED80804CA100622D463860200FC608FB0BC401888B09E2A1005B725FA25580213C392D69F9A1401891CD617EAF4A65F27BC5E6008580233405340D2BBD7B66A60094A2FE004D93F99B0CF5A52FF3994630086609A75B271DA457080307B005A68A6665F3F92E7A17010011966A350C92AA1CBD52A4E996293BEF5CBFC3480085994095007009A6A76DF136194E27CE34980212B0E6B3940B004C0010A8631E20D0803F0F21AC2020085B401694DA4491840D201237C0130004222BC3F8C2200DC7686B14A67432E0063801AC05C3080146005101362E0071010EC403E19801000340A801A002A118012C0200B006AC4015088018000B398019399C2FC432013E3003551006E304108AA000844718B51165F35FA89802F22D3801374CE3C3B2B8B5B7DDC11CC011C0090A6E92BF5226E92BF5327F3FD48750036898CC7DD9A14238DD373C6E70FBCA0096536673DC9C7770D98EE19A67308154B7BB799FC8CE61EE017CFDE2933FBE954C69864D1E5A1BCEC38C0179E5E98280
|
||||
2
2021/16/solution.txt
Normal file
2
2021/16/solution.txt
Normal file
@ -0,0 +1,2 @@
|
||||
Part 1: 883
|
||||
Part 2: 1675198555015
|
||||
27
2021/16/test_code.py
Normal file
27
2021/16/test_code.py
Normal file
@ -0,0 +1,27 @@
|
||||
# SPDX-License-Identifier: MIT
|
||||
# Copyright (c) 2021 Akumatic
|
||||
|
||||
from code import part1, part2, read_file, hex2bin, decode_packet
|
||||
|
||||
def test():
|
||||
assert decode_packet(hex2bin("D2FE28")) == (6, 4, 21, 2021)
|
||||
assert decode_packet(hex2bin("38006F45291200")) == (1, 6, 49, [(6, 4, 11, 10), (2, 4, 16, 20)])
|
||||
assert decode_packet(hex2bin("EE00D40C823060")) == (7, 3, 51, [(2, 4, 11, 1), (4, 4, 11, 2), (1, 4, 11, 3)])
|
||||
print("Passed decoding tests")
|
||||
assert part1("8A004A801A8002F478") == 16
|
||||
assert part1("620080001611562C8802118E34") == 12
|
||||
assert part1("C0015000016115A2E0802F182340") == 23
|
||||
assert part1("A0016C880162017C3686B18A3D4780") == 31
|
||||
print("Passed Part 1")
|
||||
assert part2("C200B40A82") == 3
|
||||
assert part2("04005AC33890") == 54
|
||||
assert part2("880086C3E88112") == 7
|
||||
assert part2("CE00C43D881120") == 9
|
||||
assert part2("D8005AC2A8F0") == 1
|
||||
assert part2("F600BC2D8F") == 0
|
||||
assert part2("9C005AC2F8F0") == 0
|
||||
assert part2("9C0141080250320F1802104A08") == 1
|
||||
print("Passed Part 2")
|
||||
|
||||
if __name__ == "__main__":
|
||||
test()
|
||||
@ -30,7 +30,7 @@ Collect stars by solving puzzles. Two puzzles will be made available on each day
|
||||
| 13 | :white_check_mark: | :white_check_mark: | [Solution](13/code.py) | [Day 13](https://adventofcode.com/2021/day/13) |
|
||||
| 14 | :white_check_mark: | :white_check_mark: | [Solution](14/code.py) | [Day 14](https://adventofcode.com/2021/day/14) |
|
||||
| 15 | :white_check_mark: | :white_check_mark: | [Solution](15/code.py) | [Day 15](https://adventofcode.com/2021/day/15) |
|
||||
| 16 | | | | |
|
||||
| 16 | :white_check_mark: | :white_check_mark: | [Solution](16/code.py) | [Day 16](https://adventofcode.com/2021/day/16) |
|
||||
| 17 | | | | |
|
||||
| 18 | | | | |
|
||||
| 19 | | | | |
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user