結果
| 問題 | No.206 数の積集合を求めるクエリ |
| ユーザー |
 こまる
|
| 提出日時 | 2020-10-13 23:24:39 |
| 言語 | Haskell (9.8.2) |
| 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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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
ただし、clay言語の場合は開発者のデバッグのため、公開されます。
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
{-# 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