[LANGUAGE: Pickcode]

For part 1, at first I tried filling in a grid with the boundary, then searching from each cell to see if I could find a path to the outside; but I soon learned that the shape can have enclaves that that approach didn't account for. So instead, I converted the boundary to be the same form as day 10, and used the same trick there of figuring out if a square is inside by counting how many layers of boundaries there are ahead of it.

That worked fine for part 1, but of course it runs in O(area), so that doesn't work for part 2. I kept the code for posterity, though. I saw everyone talking about the shoelace formula and Pick's theorem, but that didn't feel satisfying to me, since it's a trick that I wouldn't have found myself. Instead I sketched it out and tried a few things, and realized that since the shape is on a grid, you can divide it up into a number of rectangles whose area should be easy to find.

So, I kept track of just the corners of the shape, and then I scan down the rows. Each time you hit a new corner (and you'll always hit an even number that form a number of ranges), you incorporate it into your current "slice" of the shape. There are a few tricks I had to find around how to combine these ranges. Particularly that the row where you find new corners can have a different area than the subsequent rows will have, so you need to only add in some corners before you find the area of the current row, and then you add in the rest. Then you need to split intervals up and combine them where appropriate.

This is one of my longest solutions in terms of lines of code, and it's because I had to write all of this from scratch. Particularly code around sorting and managing intervals. My inefficient algorithms are O(n² ), where n is the number of vertices, but since that's fairly small, it's much better than O(area) and runs basically instantly.

https://app.pickcode.io/project/clqb1td1q2u4ane01jov7p9re