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make billiard words script more general

This commit is contained in:
Florian Stecker 2021-10-09 16:33:28 -05:00
parent 5211a60266
commit bcf1510c64
1 changed files with 19 additions and 12 deletions
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31
billiard_words.hs
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@ -2,25 +2,32 @@ import Data.List
import Data.Ord
import Text.Printf
main = do
putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q/fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist, length w <= 100]
main = listWordsUpToLength 22
wordlist = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord p q) | p <- [0..50], q <- [1..50], p <= q]
listWordsUpToLength :: Int -> IO ()
listWordsUpToLength n = do
putStrLn $ unlines [printf "%d/%d\t%.7f\t%d\t%s" p q (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n]
-- putStrLn $ unlines [printf "%d/%d\t%.5f\t%.5f\t%d\t%s" p q (fromIntegral p / fromIntegral q :: Double) (sqrt 3 / (1 + 2*fromIntegral q / fromIntegral p) :: Double) (length w) w | ((p,q),w) <- wordlist (n`div`2) (n`div`2), length w <= n]
wordlist :: Int -> Int -> [((Int,Int),String)]
wordlist pmax qmax = nub $ sortBy (comparing sl) [((p `div` gcd p q, q `div` gcd p q), slopeWord "bca" p q) | p <- [0..50], q <- [0..50], p /= 0 || q /= 0]
where
sl ((p,q),_) = fromIntegral p / fromIntegral q
-- only allows slopes 0 <= p/q <= 1
slopeWord :: Int -> Int -> String
slopeWord p q = concat $ map word $ zipWith step list (tail list)
-- letters: reflection along e_1, reflection along e_2, other one; p,q >= 0
slopeWord :: [Char] -> Int -> Int -> String
slopeWord [x,y,z] p q
| p > q = slopeWord [y,x,z] q p
| otherwise = concat $ map word $ zipWith step list (tail list)
where
p_ = p `div` gcd p q
q_ = q `div` gcd p q
xmax = if (p_-q_) `mod` 3 == 0 then q_ else 3*q_ :: Int
list = [(x,(x*p) `div` q) | x <- [0..xmax]]
step (x1,y1) (x2,y2) = ((x1-y1) `mod` 3, y2-y1)
word (0,0) = "bc"
word (1,0) = "ab"
word (2,0) = "ca"
word (0,1) = "baca"
word (1,1) = "acbc"
word (2,1) = "cbab"
word (0,0) = [z,x]
word (1,0) = [y,z]
word (2,0) = [x,y]
word (0,1) = [z,y,x,y]
word (1,1) = [y,x,z,x]
word (2,1) = [x,z,y,z]