Runs in 10 ms. I was stuck for most of the day on the bdv and cdv instructions, as I didn't read that the numerator was still register A. Once I got past that, it was pretty straight forward.
Haskell. For part 2 I just wrote 10000 text files and went through them by hand. I quickly noticed that every 103 seconds, an image started to form, so it didn't take that long to find the tree.
Haskell, 14 ms. The hardest part was the parser today. I somehow thought that the buttons could have negative values in X or Y too, so it's a bit overcomplicated.
haskell
import Text.ParserCombinators.ReadP
int, signedInt :: ReadP Int
int = read <$> (many1 $ choice $ map char ['0' .. '9'])
signedInt = ($) <$> choice [id <$ char '+', negate <$ char '-'] <*> int
machine :: ReadP ((Int, Int), (Int, Int), (Int, Int))
machine = do
string "Button A: X"
xa <- signedInt
string ", Y"
ya <- signedInt
string "\nButton B: X"
xb <- signedInt
string ", Y"
yb <- signedInt
string "\nPrize: X="
x0 <- int
string ", Y="
y0 <- int
return ((xa, ya), (xb, yb), (x0, y0))
machines :: ReadP [((Int, Int), (Int, Int), (Int, Int))]
machines = sepBy machine (string "\n\n")
calc :: ((Int, Int), (Int, Int), (Int, Int)) -> Maybe (Int, Int)
calc ((ax, ay), (bx, by), (x0, y0)) = case
( (x0 * by - y0 * bx) `divMod` (ax * by - ay * bx)
, (x0 * ay - y0 * ax) `divMod` (bx * ay - by * ax)
) of
((a, 0), (b, 0)) -> Just (a, b)
_ -> Nothing
enlarge :: (a, b, (Int, Int)) -> (a, b, (Int, Int))
enlarge (u, v, (x0, y0)) = (u, v, (10000000000000 + x0, 10000000000000 + y0))
solve :: [((Int, Int), (Int, Int), (Int, Int))] -> Int
solve ts = sum
[ 3 * a + b
| Just (a, b) <- map calc ts
]
main :: IO ()
main = do
ts <- fst . last . readP_to_S machines <$> getContents
mapM_ (print . solve) [ts, map enlarge ts]
You're right, I had it backwards. Hydrostatic equilibrium makes it that the combined force vector of gravity and the centrifugal force is perpendicular to the planet surface everywhere.
This. Planets are in hydrostatic equilibrium, meaning that the combined acceleration by gravity and the centrifugal "force" is equal all over the world (except for local differences due to mountains and dense crust).
That's an interesting perspective. Do you think it would be better to have separate legal documentation in German, which you then can refer to in your comments?
Really going the extra mile looking for the original image, thanks!