結果

問題 No.206 数の積集合を求めるクエリ
コンテスト
ユーザー こまる
提出日時 2020-10-13 23:24:39
言語 Haskell
(9.10.1)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 8,412 bytes
コンパイル時間 183 ms
コンパイル使用メモリ 155,520 KB
最終ジャッジ日時 2024-11-14 23:51:55
合計ジャッジ時間 892 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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コンパイルメッセージ
Loaded package environment from /home/judge/.ghc/x86_64-linux-9.8.2/environments/default
[1 of 2] Compiling Main             ( Main.hs, Main.o )

Main.hs:15:1: error: [GHC-87110]
    Could not load module ‘GHC.Integer.GMP.Internals’.
    It is a member of the hidden package ‘integer-gmp-1.1’.
    Use -v to see a list of the files searched for.
   |
15 | import qualified GHC.Integer.GMP.Internals         as GMP
   | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

ソースコード

diff # 

{-# LANGUAGE BangPatterns    #-}
{-# LANGUAGE MagicHash       #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE UnboxedTuples   #-}

import           Control.Arrow
import           Control.Monad
import           Control.Monad.ST
import           Data.Bits
import           GHC.Exts
import qualified Data.ByteString.Char8             as BSC8
import qualified Data.Vector.Fusion.Stream.Monadic as VFSM
import qualified Data.Vector.Unboxed               as VU
import qualified Data.Vector.Unboxed.Mutable       as VUM
import qualified GHC.Integer.GMP.Internals         as GMP



type Parser a = BSC8.ByteString -> Maybe (a, BSC8.ByteString)
parseInt :: Parser Int
parseInt = fmap (second BSC8.tail) . BSC8.readInt
parseM :: Int -> IO (VU.Vector Int)
parseM m = VU.unfoldrN m parseInt <$> BSC8.getLine



infixl 8 .<<., .>>., .>>>.
infixl 6 .^.

(.<<.) :: Bits b => b -> Int -> b
(.<<.) = unsafeShiftL
{-# INLINE (.<<.) #-}

(.>>.) :: Bits b => b -> Int -> b
(.>>.) = unsafeShiftR
{-# INLINE (.>>.) #-}

(.>>>.) :: Int -> Int -> Int
(.>>>.) (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE (.>>>.) #-}

(.^.) :: Bits b => b -> b -> b
(.^.) = xor
{-# INLINE (.^.) #-}



stream :: Monad m => Int -> Int -> VFSM.Stream m Int
stream !l !r = VFSM.Stream step l
  where
    step x
      | x < r     = return $ VFSM.Yield x (x + 1)
      | otherwise = return $ VFSM.Done
    {-# INLINE [0] step #-}
{-# INLINE [1] stream #-}

rep :: Monad m => Int -> (Int -> m ()) -> m ()
rep n = flip VFSM.mapM_ (stream 0 n)
{-# INLINE rep #-}

streamR :: Monad m => Int -> Int -> VFSM.Stream m Int
streamR !l !r = VFSM.Stream step (r - 1)
  where
    step x
      | x >= l = return $ VFSM.Yield x (x - 1)
      | otherwise = return VFSM.Done
    {-# INLINE [0] step #-}
{-# INLINE [1] streamR #-}

rev :: Monad m => Int -> (Int -> m ()) -> m ()
rev n = flip VFSM.mapM_ (streamR 0 n)
{-# INLINE rev #-}

rev1 :: Monad m => Int -> (Int -> m ()) -> m ()
rev1 n = flip VFSM.mapM_ (streamR 1 (n + 1))
{-# INLINE rev1 #-}

streamStep :: Monad m => Int -> Int -> Int -> VFSM.Stream m Int
streamStep !l !r !d = VFSM.Stream step l
  where
    step x
      | x < r = return $ VFSM.Yield x (x + d)
      | otherwise = return VFSM.Done
    {-# INLINE [0] step #-}
{-# INLINE [1] streamStep #-}

encode32x2 :: Int -> Int -> Int
encode32x2 x y = x .<<. 32 .|. y
{-# INLINE encode32x2 #-}

decode32x2 :: Int -> (Int, Int)
decode32x2 xy =
    let !x = xy .>>>. 32
        !y = xy .&. 0xffffffff
    in (x, y)
{-# INLINE decode32x2 #-}

fi :: Int -> Integer
fi = fromIntegral
{-# INLINE fi #-}

fI :: Integer -> Int
fI = fromInteger
{-# INLINE fI #-}

powModInt :: Int -> Int -> Int -> Int
powModInt a n mo = fI $ GMP.powModInteger (fi a) (fi n) (fi mo)
{-# INLINE powModInt #-}

recipModInt :: Int -> Int -> Int
recipModInt a mo = fI $ GMP.recipModInteger (fi a) (fi mo)



data NTTRunner = NTTRunner
  { pNR    :: !Int
  , gNR    :: !Int
  , ipNR   :: !Word
  , sesNR  :: !(VU.Vector Int)
  , siesNR :: !(VU.Vector Int)
  }

buildNTTRunner :: Int -> Int -> NTTRunner
buildNTTRunner pNR gNR = NTTRunner{..}
  where
    ipNR = quot (complement 0) (fromIntegral pNR) + 1
    ctz = countTrailingZeros (pNR - 1)
    !e  = powModInt gNR ((pNR - 1) .>>. ctz) pNR
    !ie = recipModInt e pNR
    es  = VU.reverse $ VU.iterateN (ctz - 1) (\x -> x *% x) e
    ies = VU.reverse $ VU.iterateN (ctz - 1) (\x -> x *% x) ie
    sesNR  = VU.zipWith (*%) es  $ VU.scanl' (*%) 1 ies
    siesNR = VU.zipWith (*%) ies $ VU.scanl' (*%) 1 es
    x *% y = x * y `rem` pNR

addNR :: NTTRunner -> Int -> Int -> Int
addNR (NTTRunner (I# m#) _ _ _ _) (I# x#) (I# y#)
  = case x# +# y# of
    z# -> I# (z# -# ((z# >=# m#) *# m#))
{-# INLINE addNR #-}

subNR :: NTTRunner -> Int -> Int -> Int
subNR (NTTRunner (I# m#) _ _ _ _) (I# x#) (I# y#)
  = case x# -# y# of
    z# -> I# (z# +# ((z# <# 0#) *# m#))
{-# INLINE subNR #-}

mulNR :: NTTRunner -> Int -> Int -> Int
mulNR (NTTRunner (I# m0#) _ (W# im#) _ _) (I# x#) (I# y#)
  = case timesWord# (int2Word# x#) (int2Word# y#) of
      z# -> case timesWord2# z# im# of
        (# q#, _ #) -> case minusWord# z# (timesWord# q# m#) of
          v#  | isTrue# (geWord# v# m#) -> I# (word2Int# (plusWord# v# m#))
              | otherwise -> I# (word2Int# v#)
  where
    m# = int2Word# m0#
{-# INLINE mulNR #-}

butterfly :: NTTRunner -> VUM.STVector s Int -> ST s ()
butterfly nr@NTTRunner{..} mvec = do
  flip VFSM.mapM_ (stream 1 (h + 1)) $ \ph -> do
    let !w = 1 .<<. (ph - 1)
        !p = 1 .<<. (h - ph)
    void $ VFSM.foldlM'
      (\acc s -> do
        let offset = s .<<. (h - ph + 1)
        flip VFSM.mapM_ (stream offset (offset + p)) $ \i -> do
          l <- VUM.unsafeRead mvec i
          r <- mulNR nr acc <$!> VUM.unsafeRead mvec (i + p)
          VUM.unsafeWrite mvec (i + p) $ subNR nr l r
          VUM.unsafeWrite mvec i $ addNR nr l r
        return $! mulNR nr acc $ VU.unsafeIndex siesNR (countTrailingZeros (complement s))
      ) 1 (stream 0 w)
    where
      n  = VUM.length mvec
      !h = head [i | i <- [0 ..], n <= 1 .<<. i]
{-# INLINE butterfly #-}

invButterfly :: NTTRunner -> VUM.STVector s Int -> ST s ()
invButterfly nr@NTTRunner{..} mvec = void $ do
  flip VFSM.mapM_ (streamR 1 (h + 1)) $ \ph -> do
    let !w = 1 .<<. (ph - 1)
        !p = 1 .<<. (h - ph)
    VFSM.foldlM'
      (\acc s -> do
        let offset = s .<<. (h - ph + 1)
        flip VFSM.mapM_ (stream offset (offset + p)) $ \i -> do
          l <- VUM.unsafeRead mvec i
          r <- VUM.unsafeRead mvec (i + p)
          VUM.unsafeWrite mvec (i + p) $ mulNR nr acc (pNR + l - r)
          VUM.unsafeWrite mvec i $ addNR nr l r
        return $! mulNR nr acc $ VU.unsafeIndex sesNR (countTrailingZeros (complement s))
      ) 1 (stream 0 w)
  where
    n  = VUM.length mvec
    !h = head [i | i <- [0..], n <= 1 .<<. i]
{-# INLINE invButterfly #-}

growToPowerOfTwo :: VU.Vector Int -> VU.Vector Int
growToPowerOfTwo v
  | VU.null v = VU.singleton 0
  | VU.length v == 1 = v
  | n <- (-1) .>>>. (countTrailingZeros (VU.length v - 1)) + 1
    = v VU.++ VU.replicate (n - VU.length v) 0

ntt :: Int -> Int -> VU.Vector Int -> VU.Vector Int
ntt p g = VU.modify (butterfly nr)
  where
    nr = buildNTTRunner p g

intt :: Int -> Int -> VU.Vector Int -> VU.Vector Int
intt p g f = VU.map (mulNR nr invn) $ VU.modify (invButterfly nr) f
  where
    nr    = buildNTTRunner p g
    !invn = recipModInt (VU.length f) p

convolute :: Int -> Int -> VU.Vector Int -> VU.Vector Int -> VU.Vector Int
convolute p g xs ys = VU.create $ do
  mxs <- VUM.replicate len 0
  VU.unsafeCopy (VUM.take n mxs) xs
  butterfly nr mxs
  mys <- VUM.replicate len 0
  VU.unsafeCopy (VUM.take m mys) ys
  butterfly nr mys
  rep len $ \i -> do
    yi <- VUM.unsafeRead mys i
    VUM.unsafeModify mxs (mulNR nr yi) i
  invButterfly nr mxs
  rep (n + m - 1) $ \i -> do
    VUM.unsafeModify mxs (mulNR nr ilen) i
  return $ VUM.take (n + m - 1) mxs
    where
      !nr   = buildNTTRunner p g
      n     = VU.length xs
      m     = VU.length ys
      !h    = head [i | i <- [0..], n + m - 1 <= 1 .<<. i]
      !len  = 1 .<<. h
      !ilen = recipModInt len p

multiply :: VU.Vector Int -> VU.Vector Int -> Int -> VU.Vector Int
multiply ax bx mo = ret
  where
    m1 = 167772161
    m2 = 469762049
    m3 = 1224736769
    g  = 3
    x  = convolute m1 g ax bx
    y  = convolute m2 g ax bx
    z  = convolute m3 g ax bx
    !m1invm2  = recipModInt m1 m2
    !m12invm3 = recipModInt (m1 * m2) m3
    !m12mod   = m1 * m2 `mod` mo
    !v1 = VU.zipWith func1 y x
    func1 !yi !xi =
      let c = (yi - xi) * m1invm2 `mod` m2
      in if c < 0 then c + m2 else c
    !v2 = VU.zipWith3 func2 z x v1
    func2 !zi !xi !v1i =
      let d = (zi - (xi + m1 * v1i) `mod` m3) * m12invm3 `mod` m3
      in if d < 0 then d + m3 else d
    !ret = VU.zipWith3 func3 x v1 v2
    func3 !xi !v1i !v2i =
      let e = (xi + m1 * v1i + m12mod * v2i) `mod` mo
      in if e < 0 then e + mo else e




main :: IO ()
main = do
  [l, m, n] <- map read . words <$> getLine
  as <- parseM l
  bs <- parseM m
  q  <- readLn :: IO Int
  ax <- VUM.new 262144
  bx <- VUM.new 262144 
  rep l $ \i -> VUM.unsafeWrite ax (as VU.! i - 1) (1 :: Int)
  rep m $ \i -> VUM.unsafeWrite bx (n - bs VU.! i) (1 :: Int)
  a <- VU.unsafeFreeze ax
  b <- VU.unsafeFreeze bx
  let c = convolute 998244353 3 a b
  putStr . unlines . map show . VU.toList . VU.drop (n - 1) $ VU.take (n + q - 1) c
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