feat: day_12 (first challenge)

Author: lauthieb

day_12/README.md

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+# Day 12: Garden Groups
+
+[https://adventofcode.com/2024/day/12](https://adventofcode.com/2024/day/12)
+
+## Description
+
+### Part One
+
+Why not search for the Chief Historian near the [gardener](https://adventofcode.com/2023/day/5) and his [massive farm](https://adventofcode.com/2023/day/21)? 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 <span title="I originally wanted to title this puzzle &quot;Fencepost Problem&quot;, but I was afraid someone would then try to count fenceposts by mistake and experience a fencepost problem.">fences</span> 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?_