Magic squares of doubly even order: Difference between revisions

| rem n 4 > 0 = []

| otherwise =

splitEvery n $

-- Taken directly from the integer series where True

-- and from the reverse of that series where False

zipWith

(\x i ->

if x

then i

else limit - i)

series

[1 .. sqr]

where

sqr = n * n

limit = sqr + 1

series

-- For integer powers of 2, the (append not) 'magic' series directly

-- yields the truth table that we need

| isPowerOf 2 n = magicSeries $ floor (logBase 2 (fromIntegral sqr))

-- where n is not an integer power of 2, we can replicate a

-- minimum truth table, horizontally and vertically

| otherwise =

concat . concat . concat . scale $

scale <$> splitEvery 4 (magicSeries 4)

scale = replicate $ quot n 4

isPowerOf k n = until (\x -> rem x k /= 0) (`quot` k) n == 1

-- Summed and checked---------------------------------------------------

where

square = magicSquare n

h:t =

sum <$>

square ++ -- rows

transpose square ++ -- cols

diagonals square -- diagonals

diagonals xs = flip (zipWith (!!)) [0 ..] <$> [xs, reverse xs]