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Advent of Code
--- Day 12: Garden Groups ---
Why not search for the Chief Historian near the [16]gardener and his
[17]massive farm? There's plenty of food, so The Historians grab something
to eat while they search.
You're about to settle near a complex arrangement of garden plots when
some Elves ask if you can lend a hand. They'd like to set up fences around
each region of garden plots, but they can't figure out how much fence they
need to order or how much it will cost. They hand you a map (your puzzle
input) of the garden plots.
Each garden plot grows only a single type of plant and is indicated by a
single letter on your map. When multiple garden plots are growing the same
type of plant and are touching (horizontally or vertically), they form a
region. For example:
AAAA
BBCD
BBCC
EEEC
This 4x4 arrangement includes garden plots growing five different types of
plants (labeled A, B, C, D, and E), each grouped into their own region.
In order to accurately calculate the cost of the fence around a single
region, you need to know that region's area and perimeter.
The area of a region is simply the number of garden plots the region
contains. The above map's type A, B, and C plants are each in a region of
area 4. The type E plants are in a region of area 3; the type D plants are
in a region of area 1.
Each garden plot is a square and so has four sides. The perimeter of a
region is the number of sides of garden plots in the region that do not
touch another garden plot in the same region. The type A and C plants are
each in a region with perimeter 10. The type B and E plants are each in a
region with perimeter 8. The lone D plot forms its own region with
perimeter 4.
Visually indicating the sides of plots in each region that contribute to
the perimeter using - and |, the above map's regions' perimeters are
measured as follows:
+-+-+-+-+
|A A A A|
+-+-+-+-+ +-+
|D|
+-+-+ +-+ +-+
|B B| |C|
+ + + +-+
|B B| |C C|
+-+-+ +-+ +
|C|
+-+-+-+ +-+
|E E E|
+-+-+-+
Plants of the same type can appear in multiple separate regions, and
regions can even appear within other regions. For example:
OOOOO
OXOXO
OOOOO
OXOXO
OOOOO
The above map contains five regions, one containing all of the O garden
plots, and the other four each containing a single X plot.
The four X regions each have area 1 and perimeter 4. The region containing
21 type O plants is more complicated; in addition to its outer edge
contributing a perimeter of 20, its boundary with each X region
contributes an additional 4 to its perimeter, for a total perimeter of 36.
Due to "modern" business practices, the price of fence required for a
region is found by multiplying that region's area by its perimeter. The
total price of fencing all regions on a map is found by adding together
the price of fence for every region on the map.
In the first example, region A has price 4 * 10 = 40, region B has price 4
* 8 = 32, region C has price 4 * 10 = 40, region D has price 1 * 4 = 4,
and region E has price 3 * 8 = 24. So, the total price for the first
example is 140.
In the second example, the region with all of the O plants has price 21 *
36 = 756, and each of the four smaller X regions has price 1 * 4 = 4, for
a total price of 772 (756 + 4 + 4 + 4 + 4).
Here's a larger example:
RRRRIICCFF
RRRRIICCCF
VVRRRCCFFF
VVRCCCJFFF
VVVVCJJCFE
VVIVCCJJEE
VVIIICJJEE
MIIIIIJJEE
MIIISIJEEE
MMMISSJEEE
It contains:
• A region of R plants with price 12 * 18 = 216.
• A region of I plants with price 4 * 8 = 32.
• A region of C plants with price 14 * 28 = 392.
• A region of F plants with price 10 * 18 = 180.
• A region of V plants with price 13 * 20 = 260.
• A region of J plants with price 11 * 20 = 220.
• A region of C plants with price 1 * 4 = 4.
• A region of E plants with price 13 * 18 = 234.
• A region of I plants with price 14 * 22 = 308.
• A region of M plants with price 5 * 12 = 60.
• A region of S plants with price 3 * 8 = 24.
So, it has a total price of 1930.
What is the total price of fencing all regions on your map?
Your puzzle answer was 1522850.
--- Part Two ---
Fortunately, the Elves are trying to order so much fence that they qualify
for a bulk discount!
Under the bulk discount, instead of using the perimeter to calculate the
price, you need to use the number of sides each region has. Each straight
section of fence counts as a side, regardless of how long it is.
Consider this example again:
AAAA
BBCD
BBCC
EEEC
The region containing type A plants has 4 sides, as does each of the
regions containing plants of type B, D, and E. However, the more complex
region containing the plants of type C has 8 sides!
Using the new method of calculating the per-region price by multiplying
the region's area by its number of sides, regions A through E have prices
16, 16, 32, 4, and 12, respectively, for a total price of 80.
The second example above (full of type X and O plants) would have a total
price of 436.
Here's a map that includes an E-shaped region full of type E plants:
EEEEE
EXXXX
EEEEE
EXXXX
EEEEE
The E-shaped region has an area of 17 and 12 sides for a price of 204.
Including the two regions full of type X plants, this map has a total
price of 236.
This map has a total price of 368:
AAAAAA
AAABBA
AAABBA
ABBAAA
ABBAAA
AAAAAA
It includes two regions full of type B plants (each with 4 sides) and a
single region full of type A plants (with 4 sides on the outside and 8
more sides on the inside, a total of 12 sides). Be especially careful when
counting the fence around regions like the one full of type A plants; in
particular, each section of fence has an in-side and an out-side, so the
fence does not connect across the middle of the region (where the two B
regions touch diagonally). (The Elves would have used the Möbius Fencing
Company instead, but their contract terms were too one-sided.)
The larger example from before now has the following updated prices:
• A region of R plants with price 12 * 10 = 120.
• A region of I plants with price 4 * 4 = 16.
• A region of C plants with price 14 * 22 = 308.
• A region of F plants with price 10 * 12 = 120.
• A region of V plants with price 13 * 10 = 130.
• A region of J plants with price 11 * 12 = 132.
• A region of C plants with price 1 * 4 = 4.
• A region of E plants with price 13 * 8 = 104.
• A region of I plants with price 14 * 16 = 224.
• A region of M plants with price 5 * 6 = 30.
• A region of S plants with price 3 * 6 = 18.
Adding these together produces its new total price of 1206.
What is the new total price of fencing all regions on your map?
Your puzzle answer was 953738.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, you should [18]return to your Advent calendar and try
another puzzle.
If you still want to see it, you can [19]get your puzzle input.
References
Visible links
1. https://adventofcode.com/
2. https://adventofcode.com/2024/about
3. https://adventofcode.com/2024/events
4. https://cottonbureau.com/people/advent-of-code
5. https://adventofcode.com/2024/settings
6. https://adventofcode.com/2024/auth/logout
7. Advent of Code Supporter
https://adventofcode.com/2024/support
8. https://adventofcode.com/2024
9. https://adventofcode.com/2024
10. https://adventofcode.com/2024/support
12. https://adventofcode.com/2024/leaderboard
13. https://adventofcode.com/2024/stats
16. https://adventofcode.com/2023/day/5
17. https://adventofcode.com/2023/day/21
18. https://adventofcode.com/2024
19. https://adventofcode.com/2024/day/12/input