Ticket #4005: 5.hs

module Main (main) where

data Radical = H | C Radical Radical Radical

three_partitions :: Int -> [(Int,Int,Int)]
three_partitions m =
  [ (i,j,k) | i <- [0..(div m 3)], j <- [i..(div (m-i) 2)], k <- [m - (i+j)]]

remainders :: [a] -> [[a]]
remainders [] = []
remainders (r:rs) = (r:rs) : (remainders rs)

radical_generator :: [[Radical]]
radical_generator = radicals
 where radicals = [H] : [rads_of_size_n radicals j | j <- [1..13]]

rads_of_size_n :: [[Radical]] -> Int -> [Radical]
rads_of_size_n radicals n =
  [ (C ri rj rk)
  | (i,j,k)  <- (three_partitions (n-1)),
    (ri:ris) <- (remainders (radicals!!i)),
    (rj:rjs) <- (remainders (if (i==j) then (ri:ris) else radicals!!j)),
    rk       <- (if (j==k) then (rj:rjs) else radicals!!k)]

data Paraffin = CCP Radical Radical Radical Radical

four_partitions :: [(Int,Int,Int,Int)]
four_partitions =
    [(0,0,13,13), (0,1,12,13), (0,2,11,13), (0,2,12,12), (0,3,10,13),
     (0,3,11,12), (0,4,9,13),  (0,4,10,12), (0,4,11,11), (0,5,8,13),
     (0,5,9,12),  (0,5,10,11), (0,6,7,13),  (0,6,8,12),  (0,6,9,11),
     (0,6,10,10), (0,7,7,12),  (0,7,8,11),  (0,7,9,10),  (0,8,8,10),
     (0,8,9,9),   (1,1,11,13), (1,1,12,12), (1,2,10,13), (1,2,11,12),
     (1,3,9,13),  (1,3,10,12), (1,3,11,11), (1,4,8,13),  (1,4,9,12),
     (1,4,10,11), (1,5,7,13),  (1,5,8,12),  (1,5,9,11),  (1,5,10,10),
     (1,6,6,13),  (1,6,7,12),  (1,6,8,11),  (1,6,9,10),  (1,7,7,11),
     (1,7,8,10),  (1,7,9,9),   (1,8,8,9),   (2,2,9,13),  (2,2,10,12),
     (2,2,11,11), (2,3,8,13),  (2,3,9,12),  (2,3,10,11), (2,4,7,13),
     (2,4,8,12),  (2,4,9,11),  (2,4,10,10), (2,5,6,13),  (2,5,7,12),
     (2,5,8,11),  (2,5,9,10),  (2,6,6,12),  (2,6,7,11),  (2,6,8,10),
     (2,6,9,9),   (2,7,7,10),  (2,7,8,9),   (2,8,8,8),   (3,3,7,13),
     (3,3,8,12),  (3,3,9,11),  (3,3,10,10), (3,4,6,13),  (3,4,7,12),
     (3,4,8,11),  (3,4,9,10),  (3,5,5,13),  (3,5,6,12),  (3,5,7,11),
     (3,5,8,10),  (3,5,9,9),   (3,6,6,11),  (3,6,7,10),  (3,6,8,9),
     (3,7,7,9),   (3,7,8,8),   (4,4,5,13),  (4,4,6,12),  (4,4,7,11),
     (4,4,8,10),  (4,4,9,9),   (4,5,5,12),  (4,5,6,11),  (4,5,7,10),
     (4,5,8,9),   (4,6,6,10),  (4,6,7,9),   (4,6,8,8),   (4,7,7,8),
     (5,5,5,11),  (5,5,6,10),  (5,5,7,9),   (5,5,8,8),   (5,6,6,9),
     (5,6,7,8),   (5,7,7,7),   (6,6,6,8),   (6,6,7,7)]

ccp_generator :: [[Radical]] -> [Paraffin]
ccp_generator radicals =
  [ (CCP ri rj rk rl)
  | (i,j,k,l) <- four_partitions,
    (ri:ris)  <- (remainders (radicals!!i)),
    (rj:rjs)  <- (remainders (if (i==j) then (ri:ris) else radicals!!j)),
    (rk:rks)  <- (remainders (if (j==k) then (rj:rjs) else radicals!!k)),
    rl        <- (if (k==l) then (rk:rks) else radicals!!l)]

paraffins_until :: Int
paraffins_until = length (ccp_generator radicals)
 where
  radicals = radical_generator

main :: IO ()
main = print paraffins_until