{-

- Solution to Project Euler problem 205

- Copyright (c) Project Nayuki. All rights reserved.

-

- https://www.nayuki.io/page/project-euler-solutions

- https://github.com/nayuki/Project-Euler-solutions

-}

import Data.Ratio ((%))

import Numeric (showFFloat)

main = putStrLn (ans "")

numer = sum [(ninePyramidalPdf !! i) * (sum (take i sixCubicPdf)) | i <- [0 .. ((length ninePyramidalPdf) - 1)]]

denom = (sum ninePyramidalPdf) * (sum sixCubicPdf)

ans = showFFloat (Just 7) (fromRational (numer % denom))

pyramidalDiePdf = [0, 1, 1, 1, 1] :: [Integer]

ninePyramidalPdf = (iterate (convolve pyramidalDiePdf) [1]) !! 9

cubicDiePdf = [0, 1, 1, 1, 1, 1, 1] :: [Integer]

sixCubicPdf = (iterate (convolve cubicDiePdf) [1]) !! 6

convolve :: [Integer] -> [Integer] -> [Integer]

convolve as bs = let

m = length as

n = length bs

func i = sum [(as !! j) * (bs !! (i - j)) | j <- [(max 0 (i - (n - 1))) .. (min i (m - 1))]]

in map func [0 .. (m + n - 2)]