    {-# LANGUAGE TypeSynonymInstances, MultiParamTypeClasses #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  XMonad.Layout.HintedGrid
    -- Copyright   :  (c) Lukas Mai
    -- License     :  BSD-style (see LICENSE)
    --
    -- Maintainer  :  <l.mai@web.de>
    -- Stability   :  unstable
    -- Portability :  unportable
    --
    -- A not so simple layout that attempts to put all windows in a square grid
    -- while obeying their size hints.
    --
    -----------------------------------------------------------------------------

    module XMonad.Layout.HintedGrid (
        -- * Usage
        -- $usage
        Grid(..), arrange, defaultRatio
    ) where

    import Prelude hiding ((.))

    import XMonad
    import XMonad.StackSet

    import Control.Monad.State
    import Data.List
    import Data.Ord

    infixr 9 .
    (.) :: (Functor f) => (a -> b) -> f a -> f b
    (.) = fmap

    -- $usage
    -- You can use this module with the following in your @~\/.xmonad\/xmonad.hs@:
    --
    -- > import XMonad.Layout.HintedGrid
    --
    -- Then edit your @layoutHook@ by adding the 'Grid' layout:
    --
    -- > myLayout = Grid False ||| Full ||| etc..
    -- > main = xmonad defaultConfig { layoutHook = myLayout }
    --
    -- You can also specify an aspect ratio for Grid to strive for with the
    -- GridRatio constructor:
    --
    -- > myLayout = GridRatio (4/3) False ||| etc.
    --
    -- For more detailed instructions on editing the layoutHook see
    -- "XMonad.Doc.Extending#Editing_the_layout_hook".

    -- | Automatic mirroring of hinted layouts doesn't work very well, so this
    -- 'Grid' comes with built-in mirroring. @Grid False@ is the normal layout,
    -- @Grid True@ is the mirrored variant (rotated by 90 degrees).
    data Grid a = Grid Bool | GridRatio Double Bool deriving (Read, Show)

    defaultRatio :: Double
    defaultRatio = 16/9

    instance LayoutClass Grid Window where
        doLayout (Grid m)        r w = doLayout (GridRatio defaultRatio m) r w
        doLayout (GridRatio d m) r w = flip (,) Nothing . arrange d m r (integrate w)

    replicateS :: Int -> (a -> (b, a)) -> a -> ([b], a)
    replicateS n = runState . replicateM n . State

    doColumn :: Dimension -> Dimension -> Dimension -> [(D -> D)] -> [D]
    doColumn width height k adjs =
        let
            (ind, fs) = unzip . sortBy (comparing $ snd . ($ (width, height)) . snd) . zip [0 :: Int ..] $ adjs
            (_, ds) = doC height k fs
        in
        map snd . sortBy (comparing fst) . zip ind $ ds
        where
        doC h _ [] = (h, [])
        doC h n (f : fs) = (adj :) . doC (h - h') (n - 1) fs
            where
            adj@(_, h') = f (width, h `div` n)

    doRect :: Dimension -> Dimension -> Dimension -> [[D -> D]] -> [Rectangle]
    doRect height = doR
        where
        doR _ _ [] = []
        doR width n (c : cs) =
            let
                v = fromIntegral $ length c
                c' = doColumn (width `div` n) height v c
                (ws, hs) = unzip c'
                maxw = maximum ws
                height' = sum hs
                hbonus = height - height'
                hsingle = hbonus `div` v
                hoffset = hsingle `div` 2
                width' = width - maxw
                ys = map ((height -) . subtract hoffset) . scanl1 (+) . map (hsingle +) $ hs
                xs = map ((width' +) . (`div` 2) . (maxw -)) $ ws
            in
            zipWith3 (\x y (w, h) -> Rectangle (fromIntegral x) (fromIntegral y) w h) xs ys c' ++ doR width' (n - 1) cs

    -- | The internal function for computing the grid layout.
    arrange :: Double -> Bool -> Rectangle -> [Window] -> X [(Window, Rectangle)]
    arrange aspectRatio mirror (Rectangle rx ry rw rh) wins = do
        proto <- mapM mkAdjust wins
        let
            adjs = map (\f -> twist . f . twist) proto
            rs = arrange' aspectRatio (twist (rw, rh)) adjs
            rs' = map (\(Rectangle x y w h) -> uncurry (uncurry Rectangle (twist (x, y))) (twist (w, h))) rs
        return . zip wins . map (\r -> r{ rect_x = rect_x r + rx, rect_y = rect_y r + ry }) $ rs'
        where
        twist
            | mirror = \(a, b) -> (b, a)
            | otherwise = id

    arrange' :: Double -> D -> [D -> D] -> [Rectangle]
    arrange' aspectRatio (rw, rh) adjs = reverse $ doRect rh rw (fromIntegral ncolumns) (ecols ++ cols)
        where
        nwindows = length adjs
        ncolumns = max 1 . round . sqrt $ fromIntegral nwindows * fromIntegral rw / (fromIntegral rh * aspectRatio)
        nrows = nwindows `div` ncolumns
        nextras = nwindows - ncolumns * nrows
        (ecols, adjs') = replicateS nextras (splitAt (nrows + 1)) $ reverse adjs
        (cols, _) = replicateS (ncolumns - nextras) (splitAt nrows) adjs'