Day 5: If You Give A Seed A Fertilizer

Completed in ~2 hours, 32 minutes.

5,566ᵗʰ worldwide.

2023-12-05

You take the boat and find the gardener right where you were told he would be: managing a giant "garden" that looks more to you like a farm.

"A water source? Island Island is the water source!" You point out that Snow Island isn't receiving any water.

"Oh, we had to stop the water because we ran out of sand to filter it with! Can't make snow with dirty water. Don't worry, I'm sure we'll get more sand soon; we only turned off the water a few days... weeks... oh no." His face sinks into a look of horrified realization.

"I've been so busy making sure everyone here has food that I completely forgot to check why we stopped getting more sand! There's a ferry leaving soon that is headed over in that direction - it's much faster than your boat. Could you please go check it out?"

You barely have time to agree to this request when he brings up another. "While you wait for the ferry, maybe you can help us with our food production problem. The latest Island Island Almanac just arrived and we're having trouble making sense of it."

The almanac (your puzzle input) lists all of the seeds that need to be planted. It also lists what type of soil to use with each kind of seed, what type of fertilizer to use with each kind of soil, what type of water to use with each kind of fertilizer, and so on. Every type of seed, soil, fertilizer and so on is identified with a number, but numbers are reused by each category - that is, soil 123 and fertilizer 123 aren't necessarily related to each other.

For example:

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seeds: 79 14 55 13

seed-to-soil map:
50 98 2
52 50 48

soil-to-fertilizer map:
0 15 37
37 52 2
39 0 15

fertilizer-to-water map:
49 53 8
0 11 42
42 0 7
57 7 4

water-to-light map:
88 18 7
18 25 70

light-to-temperature map:
45 77 23
81 45 19
68 64 13

temperature-to-humidity map:
0 69 1
1 0 69

humidity-to-location map:
60 56 37
56 93 4

The almanac starts by listing which seeds need to be planted: seeds 79, 14, 55, and 13.

The rest of the almanac contains a list of maps which describe how to convert numbers from a source category into numbers in a destination category. That is, the section that starts with seed-to-soil map: describes how to convert a seed number (the source) to a soil number (the destination). This lets the gardener and his team know which soil to use with which seeds, which water to use with which fertilizer, and so on.

Rather than list every source number and its corresponding destination number one by one, the maps describe entire ranges of numbers that can be converted. Each line within a map contains three numbers: the destination range start, the source range start, and the range length.

Consider again the example seed-to-soil map:

The first line has a destination range start of 50, a source range start of 98, and a range length of 2. This line means that the source range starts at 98 and contains two values: 98 and 99. The destination range is the same length, but it starts at 50, so its two values are 50 and 51. With this information, you know that seed number 98 corresponds to soil number 50 and that seed number 99 corresponds to soil number 51.

The second line means that the source range starts at 50 and contains 48 values: 50, 51, ..., 96, 97. This corresponds to a destination range starting at 52 and also containing 48 values: 52, 53, ..., 98, 99. So, seed number 53 corresponds to soil number 55.

Any source numbers that aren't mapped correspond to the same destination number. So, seed number 10 corresponds to soil number 10.

So, the entire list of seed numbers and their corresponding soil numbers looks like this:

With this map, you can look up the soil number required for each initial seed number:

Seed number 79 corresponds to soil number 81.
Seed number 14 corresponds to soil number 14.
Seed number 55 corresponds to soil number 57.
Seed number 13 corresponds to soil number 13.

The gardener and his team want to get started as soon as possible, so they'd like to know the closest location that needs a seed. Using these maps, find the lowest location number that corresponds to any of the initial seeds. To do this, you'll need to convert each seed number through other categories until you can find its corresponding location number. In this example, the corresponding types are:

Seed 79, soil 81, fertilizer 81, water 81, light 74, temperature 78, humidity 78, location 82.
Seed 14, soil 14, fertilizer 53, water 49, light 42, temperature 42, humidity 43, location 43.
Seed 55, soil 57, fertilizer 57, water 53, light 46, temperature 82, humidity 82, location 86.
Seed 13, soil 13, fertilizer 52, water 41, light 34, temperature 34, humidity 35, location 35.

So, the lowest location number in this example is 35.

What is the lowest location number that corresponds to any of the initial seed numbers?

For each seed, push it through all the layers of mapping with range/bounds checking.

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from pathlib import Path

import pytest


def runner(document: list[str], seeds: list[int]) -> int:
    locations: list[int] = []

    mode = "seed-to-soil-map:"

    for seed in seeds:
        soil = 0
        fertilizer = 0
        water = 0
        light = 0
        temperature = 0
        humidity = 0
        location = 0

        for line in document:
            if not line:
                pass

            elif ":" in line:
                mode = line

                if mode == "seed-to-soil map:":
                    soil = seed

                if mode == "soil-to-fertilizer map:":
                    fertilizer = soil

                if mode == "fertilizer-to-water map:":
                    water = fertilizer

                if mode == "water-to-light map:":
                    light = water

                if mode == "light-to-temperature map:":
                    temperature = light

                if mode == "temperature-to-humidity map:":
                    humidity = temperature

                if mode == "humidity-to-location map:":
                    location = humidity

            else:
                destination_start_str, source_start_str, range_length_str = line.split(
                    " "
                )

                destination_start = int(destination_start_str)
                source_start = int(source_start_str)
                range_length = int(range_length_str)

                if (
                    mode == "seed-to-soil map:"
                    and source_start <= seed < source_start + range_length
                ):
                    soil = seed + (destination_start - source_start)

                if (
                    mode == "soil-to-fertilizer map:"
                    and source_start <= soil < source_start + range_length
                ):
                    fertilizer = soil + (destination_start - source_start)

                if (
                    mode == "fertilizer-to-water map:"
                    and source_start <= fertilizer < source_start + range_length
                ):
                    water = fertilizer + (destination_start - source_start)

                if (
                    mode == "water-to-light map:"
                    and source_start <= water < source_start + range_length
                ):
                    light = water + (destination_start - source_start)

                if (
                    mode == "light-to-temperature map:"
                    and source_start <= light < source_start + range_length
                ):
                    temperature = light + (destination_start - source_start)

                if (
                    mode == "temperature-to-humidity map:"
                    and source_start <= temperature < source_start + range_length
                ):
                    humidity = temperature + (destination_start - source_start)

                if (
                    mode == "humidity-to-location map:"
                    and source_start <= humidity < source_start + range_length
                ):
                    location = humidity + (destination_start - source_start)

        locations.append(location)

    return min(locations)


@pytest.mark.parametrize(
    "filename,seeds,total",
    [
        ("example-1.txt", [79, 14, 55, 13], 35),
        (
            "example-2.txt",
            [
                1972667147,
                405592018,
                1450194064,
                27782252,
                348350443,
                61862174,
                3911195009,
                181169206,
                626861593,
                138786487,
                2886966111,
                275299008,
                825403564,
                478003391,
                514585599,
                6102091,
                2526020300,
                15491453,
                3211013652,
                546191739,
            ],
            662197086,
        ),
    ],
)
def test_runner(filename: str, seeds: list[int], total: int) -> None:
    with open(Path(__file__).with_name(filename)) as file:
        result = runner(file.read().splitlines(), seeds)

        assert result == total

Answer: 662,197,086

Everyone will starve if you only plant such a small number of seeds. Re-reading the almanac, it looks like the seeds: line actually describes ranges of seed numbers.

The values on the initial seeds: line come in pairs. Within each pair, the first value is the start of the range and the second value is the length of the range. So, in the first line of the example above:

seeds: 79 14 55 13

This line describes two ranges of seed numbers to be planted in the garden. The first range starts with seed number 79 and contains 14 values: 79, 80, ..., 91, 92. The second range starts with seed number 55 and contains 13 values: 55, 56, ..., 66, 67.

Now, rather than considering four seed numbers, you need to consider a total of 27 seed numbers.

In the above example, the lowest location number can be obtained from seed number 82, which corresponds to soil 84, fertilizer 84, water 84, light 77, temperature 45, humidity 46, and location 46. So, the lowest location number is 46.

Consider all of the initial seed numbers listed in the ranges on the first line of the almanac.What is the lowest location number that corresponds to any of the initial seed numbers?

Instead of iterating through one seed at a time, we instead fully check each layer one at a time. To fully check a layer, iterate through each seed/range combination, and see where the bounds of the seeds are in comparison to the bounds of each position-set. There are five possible scenarios, which I'll demonstrate with some examples:

Seed start/stop = [5, 10], position start/stop = [6, 9]: Seed range fully contains the position range
Seed start/stop = [5, 9], position start/stop = [6, 10]: Seed range overlaps the position range on the high end
Seed start/stop = [6, 10], position start/stop = [5, 9]: Seed range overlaps the position range on the low end
Seed start/stop = [6, 9], position start/stop = [5, 10]: Seed range is fully contained within the position range
Seed start/stop = [1, 5], position start/stop = [6, 10]: Seed range does not overlap the position range

Depending on what scenario occurs, we need to add more checks to the current layer and/or add more checks to the next layer.

By checking bounds, we can cover an enormous range of values very quickly.

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from collections.abc import Iterator
from dataclasses import dataclass
from pathlib import Path
from typing import Any

import pytest


@dataclass(frozen=True)
class Location:
    start: int
    end: int


@dataclass(frozen=True)
class Map:
    start: int
    end: int
    offset: int


def chunks(data: list[Any], size: int) -> Iterator[list[Any]]:
    """Yield successive chunks from data."""
    for i in range(0, len(data), size):
        yield data[i : i + size]


def runner(document: list[str], seeds: list[int]) -> int:
    modes = [
        "seed-to-soil map:",
        "soil-to-fertilizer map:",
        "fertilizer-to-water map:",
        "water-to-light map:",
        "light-to-temperature map:",
        "temperature-to-humidity map:",
        "humidity-to-location map:",
        "final",
    ]

    mode_to_locations: dict[str, list[Location]] = {
        "seed-to-soil map:": [
            Location(start=start, end=start + size - 1)
            for start, size in chunks(seeds, 2)
        ],
        "soil-to-fertilizer map:": [],
        "fertilizer-to-water map:": [],
        "water-to-light map:": [],
        "light-to-temperature map:": [],
        "temperature-to-humidity map:": [],
        "humidity-to-location map:": [],
    }

    mode_to_map: dict[str, list[Map]] = {
        "seed-to-soil map:": [],
        "soil-to-fertilizer map:": [],
        "fertilizer-to-water map:": [],
        "water-to-light map:": [],
        "light-to-temperature map:": [],
        "temperature-to-humidity map:": [],
        "humidity-to-location map:": [],
    }

    mode = "seed-to-soil map:"

    for line in document:
        if not line:
            pass

        elif ":" in line:
            mode = line

        else:
            destination_start_str, source_start_str, range_length_str = line.split(" ")

            destination_start = int(destination_start_str)
            source_start = int(source_start_str)
            range_length = int(range_length_str)

            mode_to_map[mode].append(
                Map(
                    start=source_start,
                    end=source_start + range_length - 1,
                    offset=destination_start - source_start,
                )
            )

    for index, mode in enumerate(modes[:-1]):
        maps = mode_to_map[mode]
        locations = mode_to_locations[mode]

        next_locations: list[Location] = []

        while locations:
            location = locations.pop()
            found = False

            for map in maps:
                if (
                    map.start <= location.start <= map.end
                    and map.start <= location.end <= map.end
                ):
                    next_locations.append(
                        Location(
                            start=location.start + map.offset,
                            end=location.end + map.offset,
                        )
                    )
                    found = True
                    break

                elif map.start <= location.start <= map.end:
                    next_locations.append(
                        Location(
                            start=location.start + map.offset,
                            end=map.end + map.offset,
                        )
                    )
                    locations.append(
                        Location(
                            start=map.end + 1,
                            end=location.end,
                        )
                    )
                    found = True
                    break

                elif map.start <= location.end <= map.end:
                    locations.append(
                        Location(
                            start=location.start,
                            end=map.start - 1,
                        )
                    )
                    next_locations.append(
                        Location(
                            start=map.start + map.offset,
                            end=location.end + map.offset,
                        )
                    )
                    found = True
                    break

                elif map.start > location.start and map.end < location.end:
                    locations.append(
                        Location(
                            start=map.end + 1,
                            end=location.end,
                        )
                    )
                    locations.append(
                        Location(
                            start=location.start,
                            end=map.start - 1,
                        )
                    )
                    next_locations.append(
                        Location(
                            start=map.start + map.offset,
                            end=map.end + map.offset,
                        )
                    )
                    found = True
                    break

            if not found:
                next_locations.append(location)

        mode_to_locations[modes[index + 1]] = next_locations

    final_locations = mode_to_locations["final"]

    return min([location.start for location in final_locations])


@pytest.mark.parametrize(
    "filename,seeds,total",
    [
        ("example-1.txt", [79, 14, 55, 13], 46),
        (
            "example-2.txt",
            [
                1972667147,
                405592018,
                1450194064,
                27782252,
                348350443,
                61862174,
                3911195009,
                181169206,
                626861593,
                138786487,
                2886966111,
                275299008,
                825403564,
                478003391,
                514585599,
                6102091,
                2526020300,
                15491453,
                3211013652,
                546191739,
            ],
            52510809,
        ),
    ],
)
def test_runner(filename: str, seeds: list[int], total: int) -> None:
    with open(Path(__file__).with_name(filename)) as file:
        result = runner(file.read().splitlines(), seeds)

        assert result == total

Answer: 52,510,809

Day	Part 1 Time	Part 1 Rank	Part 2 Time	Part 2 Rank
5	00:35:47	4,028	02:31:26	5,566

This was very hard to reason about and work through 😖.

I'm just happy I made it through this problem without needing to go super late into the night.

Fletcher Easton

Day 5: If You Give A Seed A Fertilizer

Part 1 – Prompt #

Part 1 – Solution #

Part 2 – Prompt #

Part 2 – Solution #

Recap #