結果
| 問題 | No.206 数の積集合を求めるクエリ |
| ユーザー |
 かりあげクン
|
| 提出日時 | 2020-09-02 21:38:04 |
| 言語 | Haskell (9.8.2) |
| 結果 |
CE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 14,941 bytes |
| コンパイル時間 | 292 ms |
| コンパイル使用メモリ | 168,448 KB |
| 最終ジャッジ日時 | 2024-11-14 23:48:32 |
| 合計ジャッジ時間 | 752 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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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
Main.hs:9:28: warning: [GHC-53692] [-Wdeprecated-flags]
-XTypeInType is deprecated: use -XDataKinds and -XPolyKinds instead
|
9 | {-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns #-}
| ^^^^^^^^^^
[1 of 2] Compiling Main ( Main.hs, Main.o )
Main.hs:44:1: error: [GHC-61948]
Could not find module ‘Data.ByteString.Lazy.Builder’.
Perhaps you meant
Data.ByteString.Builder (from bytestring-0.12.1.0)
Data.ByteString.Lazy.Char8 (from bytestring-0.12.1.0)
Data.ByteString.Lazy.ReadInt
Use -v to see a list of the files searched for.
|
44 | import qualified Data.ByteString.Lazy.Builder as BSLB
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Main.hs:48:1: error: [GHC-87110]
Could not load module ‘Data.Graph’.
It is a member of the hidden package ‘containers-0.6.8’.
Use -v to see a list of the files searched for.
|
48 | import qualified Data.Graph as Graph
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Main.hs:49:1: error: [GHC-87110]
Could not load module ‘Data.IntMap’.
It is a member of the hidden package ‘containers-0.6.8’.
Use -v to see a list of the files searched for.
|
49 | import Data.IntMap (IntMap)
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Main.hs:50:1: error: [GHC-87110]
Could not load module ‘Data.IntMap’.
It is a member of the hidden package ‘containers-0.6.8’.
Use -v to see a list of the files searched for.
|
50 | import qualified Data.IntMap as IntMap
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Main.hs:51:1: error: [GHC-87110]
Could not load module ‘Data.IntSet’.
It is a member of the hidden package ‘containers-0.6.8’.
Use -v to see a list of the files searc
ソースコード
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, KindSignatures, LambdaCase #-}
{-# LANGUAGE MagicHash, MultiParamTypeClasses, MultiWayIf #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns #-}
{- base -}
import Control.Applicative
import qualified Control.Arrow as Arrow
import Control.Monad
import Control.Monad.ST
import Data.Bits
import Data.Bool
import Data.Complex
import qualified Data.Char as Char
import qualified Data.Foldable as Foldable
import Data.Function
import qualified Data.List as List
import Data.Maybe
import Data.Monoid
import Data.Ratio
import Data.Ord
import Data.Semigroup
import qualified Data.Word as Word
import Foreign hiding (void)
import GHC.Exts
import Unsafe.Coerce
{- array -}
import qualified Data.Array.IO as ArrIO
import qualified Data.Array.MArray as ArrMA
import qualified Data.Array.ST as ArrST
import qualified Data.Array.Storable as ArrStore
import qualified Data.Array.Unboxed as ArrU
{- bytestring -}
import qualified Data.ByteString as BS
import qualified Data.ByteString.Builder as BSB
import qualified Data.ByteString.Builder.Extra as BSBE
import qualified Data.ByteString.Char8 as BSC8
import qualified Data.ByteString.Lazy as BSL
import qualified Data.ByteString.Lazy.Builder as BSLB
import qualified Data.ByteString.Lazy.Char8 as BSLC8
import qualified Data.ByteString.Unsafe as BSU
{- containers -}
import qualified Data.Graph as Graph
import Data.IntMap (IntMap)
import qualified Data.IntMap as IntMap
import Data.IntSet (IntSet)
import qualified Data.IntSet as IntSet
import qualified Data.Sequence as Seq
import qualified Data.Tree as Tree
{- integer-gmp -}
import GHC.Integer.GMP.Internals
{- vector -}
import qualified Data.Vector as V
import qualified Data.Vector.Generic as VG
import qualified Data.Vector.Generic.Mutable as VGM
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Primitive as VP
import qualified Data.Vector.Primitive.Mutable as VPM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
main :: IO ()
main = do
(l,m,n) <- parse3
a <- parseM l
b <- parseM m
q <- parse1
ax <- VUM.new 262144
forM_ [0..l-1] $ \i -> do
VUM.unsafeWrite ax (a VU.! i - 1) (1 :: Int)
as <- VU.unsafeFreeze ax
bx <- VUM.new 262144
forM_ [0..m-1] $ \i -> do
VUM.unsafeWrite bx (n - b VU.! i) (1 :: Int)
bs <- VU.unsafeFreeze bx
let cx = convolute 262144 as bs
forM_ [0..q-1] $ \i -> do
print $ cx VU.! (n + i)
type Parser a = BSC8.ByteString -> Maybe (a, BSC8.ByteString)
parseInt :: Parser Int
parseInt = fmap (Arrow.second BSC8.tail) . BSC8.readInt
parseChar :: [Char] -> VU.Vector Char
parseChar = VU.fromList
parse1 :: IO Int
parse1 = readLn
parse2 :: IO (Int, Int)
parse2 = (\vec -> (vec VU.! 0, vec VU.! 1)) . VU.unfoldrN 2 parseInt <$> BSC8.getLine
parse3 :: IO (Int, Int, Int)
parse3 = (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2)) . VU.unfoldrN 3 parseInt <$> BSC8.getLine
parse4 :: IO (Int, Int, Int, Int)
parse4 = (\vec -> (vec VU.! 0, vec VU.! 1, vec VU.! 2, vec VU.! 3)) . VU.unfoldrN 4 parseInt <$> BSC8.getLine
parseM :: Int -> IO (VU.Vector Int)
parseM m = VU.unfoldrN m parseInt <$> BSC8.getLine
parseN :: Int -> IO (VU.Vector Int)
parseN n = VU.replicateM n parse1
parseNM :: Int -> Int -> IO (V.Vector (VU.Vector Int))
parseNM n m = V.replicateM n $ VU.unfoldrN m parseInt <$> BSC8.getLine
fi :: Int -> Integer
fi = fromIntegral
fI :: Integer -> Int
fI = fromInteger
gcdInt :: Int -> Int -> Int
gcdInt a b = fI $ gcdInteger (fi a) (fi b)
gcdextInt :: Int -> Int -> (Int, Int)
gcdextInt a b = case gcdExtInteger c d of
(# x, y #) -> (fI x, fI y)
where
c = fromIntegral a
d = fromIntegral b
lcmInt :: Int -> Int -> Int
lcmInt a b = fI $ lcmInteger (fi a) (fi b)
sqrInt :: Int -> Int
sqrInt = fI . sqrInteger . fi
powModInt :: Int -> Int -> Int -> Int
powModInt a n mo = fI $ powModInteger (fi a) (fi n) (fi mo)
recipModInt :: Int -> Int -> Int
recipModInt x n = fI $ recipModInteger (fi x) (fi n)
-------------------------------------------------------------------------------
-- NTT
-------------------------------------------------------------------------------
nextPowerOfTwo :: VU.Vector Int -> VU.Vector Int
nextPowerOfTwo vs
| VU.null vs = VU.singleton 0
| VU.length vs == 1 = vs
| n <- unsafeShiftRL (-1) (countLeadingZeros (VU.length vs - 1)) + 1 = vs VU.++ VU.replicate (n - VU.length vs) 0
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL :: Int -> Int -> Int
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL :: Int -> Int -> Int
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
bitReverse :: Int -> Int
bitReverse
= unsafeCoerce @Word64 @Int
. step 32 0xffffffff00000000 0x00000000ffffffff
. step 16 0xffff0000ffff0000 0x0000ffff0000ffff
. step 08 0xff00ff00ff00ff00 0x00ff00ff00ff00ff
. step 04 0xf0f0f0f0f0f0f0f0 0x0f0f0f0f0f0f0f0f
. step 02 0xcccccccccccccccc 0x3333333333333333
. step 01 0xaaaaaaaaaaaaaaaa 0x5555555555555555
. unsafeCoerce @Int @Word64
where
step :: Int -> Word64 -> Word64 -> Word64 -> Word64
step i ml mr = \ !x -> unsafeShiftR (x .&. ml) i .|. unsafeShiftL (x .&. mr) i
{-# INLINE step #-}
ntt :: Int -> Int -> VU.Vector Int -> VU.Vector Int
ntt p g f = runST $ do
ff <- VU.unsafeThaw $ VU.unsafeBackpermute f
$ VU.generate n ((`unsafeShiftRL` (64 - logN)) . bitReverse)
VU.forM_ (VU.iterateN logN (*2) 2) $ \m -> do
let !unity = powModInt g (quot (p - 1) m) p
let !unities = VU.iterateN (unsafeShiftRL m 1) ((`rem` p) . (* unity)) 1
fix (\loop !k -> when (k < n) $ do
flip VU.imapM_ unities $ \j w -> do
u <- VUM.unsafeRead ff (k + j)
t <- (* w) <$!> VUM.unsafeRead ff (k + j + unsafeShiftRL m 1)
VUM.unsafeWrite ff (k + j) $ rem (u + t) p
VUM.unsafeWrite ff (k + j + unsafeShiftRL m 1) $ mod (u - t) p
loop (k + m)
) 0
VU.unsafeFreeze ff
where
!n = VU.length f
!logN = countTrailingZeros n
{-# INLINE ntt #-}
intt :: Int -> Int -> VU.Vector Int -> VU.Vector Int
intt p g f = VU.map ((`rem` p) . (* n')) $ ntt p (recipModInt g p) f
where
!n' = recipModInt (VU.length f) p
{-# INLINE intt #-}
convolute' :: Int -> Int -> VU.Vector Int -> VU.Vector Int -> VU.Vector Int
convolute' p g xs ys
= intt p g
$ VU.zipWith (\x y -> x * y `rem` p)
(ntt p g $ xs VU.++ VU.replicate n 0)
(ntt p g $ ys VU.++ VU.replicate n 0)
where
!n = VU.length xs
{-# INLINE convolute' #-}
convolute :: Int -> VU.Vector Int -> VU.Vector Int -> VU.Vector Int
convolute n xs ys
= VU.slice 1 (2 * n) $
convolute' 998244353 3
(nextPowerOfTwo $ VU.cons 0 xs)
(nextPowerOfTwo $ VU.cons 0 ys)
-------------------------------------------------------------------------------
#define MOD 1000000007
modulus :: (Num a) => a
modulus = MOD
{-# INLINE modulus #-}
infixr 8 ^%
infixl 7 *%, /%
infixl 6 +%, -%
(+%) :: Int -> Int -> Int
(+%) (I# x#) (I# y#) = case x# +# y# of
r# -> I# (r# -# ((r# >=# MOD#) *# MOD#))
{-# INLINE (+%) #-}
(-%) :: Int -> Int -> Int
(-%) (I# x#) (I# y#) = case x# -# y# of
r# -> I# (r# +# ((r# <# 0#) *# MOD#))
{-# INLINE (-%) #-}
(*%) :: Int -> Int -> Int
(*%) (I# x#) (I# y#) = I# ((x# *# y#) `remInt#` MOD#)
{-# INLINE (*%) #-}
(/%) :: Int -> Int -> Int
(I# x#) /% (I# y#) = go# y# MOD# 1# 0# where
go# a# b# u# v#
| isTrue# (b# ># 0#) = case a# `quotInt#` b# of
q# -> go# b# (a# -# (q# *# b#)) v# (u# -# (q# *# v#))
| otherwise = I# ((x# *# (u# +# MOD#)) `remInt#` MOD#)
{-# INLINE (/%) #-}
(^%) :: Int -> Int -> Int
(^%) x n
| n > 0 = go 1 x n
| n== 0 = 1
| otherwise = go 1 ((/%) 1 x) (-n)
where
go !acc !y !m
| m .&. 1 == 0 = go acc (y *% y) (unsafeShiftR m 1)
| m == 1 = acc *% y
| otherwise = go (acc *% y) (y *% y) (unsafeShiftR (m - 1) 1)
{-# INLINE (^%) #-}
intMod :: (Integral int) => int -> Mint
intMod x = fromIntegral $ mod (fromIntegral x) MOD
{-# INLINE intMod #-}
intModValidate :: Mint -> Bool
intModValidate (Mint x) = 0 <= x && x < MOD
{-# INLINE intModValidate #-}
newtype Mint = Mint { getMint :: Int }
deriving newtype (Eq, Ord, Read)
instance Show Mint where
show (Mint x) = show x
instance Num Mint where
(+) = coerce (+%)
(-) = coerce (-%)
(*) = coerce (*%)
abs = id
signum = const (Mint 1)
fromInteger x = coerce @Int @Mint . fromInteger $ mod x MOD
instance Real Mint where
toRational (Mint x) = toRational x
instance Bounded Mint where
minBound = Mint 0
maxBound = Mint $ MOD - 1
instance Enum Mint where
toEnum = intMod
fromEnum = coerce
instance Fractional Mint where
(Mint x) / (Mint y) = Mint (x /% y)
fromRational q = fromInteger (numerator q) / fromInteger (denominator q)
instance Integral Mint where
quotRem x y = (x / y, x - x / y * y)
toInteger = coerce (toInteger @Int)
newtype instance VUM.MVector s Mint = MV_Mint (VUM.MVector s Int)
newtype instance VU.Vector Mint = V_Mint (VU.Vector Int)
instance VU.Unbox Mint
instance VGM.MVector VUM.MVector Mint where
{-# INLINE basicLength #-}
basicLength (MV_Mint v) = VGM.basicLength v
{-# INLINE basicUnsafeSlice #-}
basicUnsafeSlice i n (MV_Mint v) = MV_Mint $ VGM.basicUnsafeSlice i n v
{-# INLINE basicOverlaps #-}
basicOverlaps (MV_Mint v1) (MV_Mint v2) = VGM.basicOverlaps v1 v2
{-# INLINE basicUnsafeNew #-}
basicUnsafeNew n = MV_Mint `fmap` VGM.basicUnsafeNew n
{-# INLINE basicInitialize #-}
basicInitialize (MV_Mint v) = VGM.basicInitialize v
{-# INLINE basicUnsafeReplicate #-}
basicUnsafeReplicate n x = MV_Mint `fmap` VGM.basicUnsafeReplicate n (coerce x)
{-# INLINE basicUnsafeRead #-}
basicUnsafeRead (MV_Mint v) i = coerce `fmap` VGM.basicUnsafeRead v i
{-# INLINE basicUnsafeWrite #-}
basicUnsafeWrite (MV_Mint v) i x = VGM.basicUnsafeWrite v i (coerce x)
{-# INLINE basicClear #-}
basicClear (MV_Mint v) = VGM.basicClear v
{-# INLINE basicSet #-}
basicSet (MV_Mint v) x = VGM.basicSet v (coerce x)
{-# INLINE basicUnsafeCopy #-}
basicUnsafeCopy (MV_Mint v1) (MV_Mint v2) = VGM.basicUnsafeCopy v1 v2
{-# INLINE basicUnsafeMove #-}
basicUnsafeMove (MV_Mint v1) (MV_Mint v2) = VGM.basicUnsafeMove v1 v2
{-# INLINE basicUnsafeGrow #-}
basicUnsafeGrow (MV_Mint v) n = MV_Mint `fmap` VGM.basicUnsafeGrow v n
instance VG.Vector VU.Vector Mint where
{-# INLINE basicUnsafeFreeze #-}
basicUnsafeFreeze (MV_Mint v) = V_Mint `fmap` VG.basicUnsafeFreeze v
{-# INLINE basicUnsafeThaw #-}
basicUnsafeThaw (V_Mint v) = MV_Mint `fmap` VG.basicUnsafeThaw v
{-# INLINE basicLength #-}
basicLength (V_Mint v) = VG.basicLength v
{-# INLINE basicUnsafeSlice #-}
basicUnsafeSlice i n (V_Mint v) = V_Mint $ VG.basicUnsafeSlice i n v
{-# INLINE basicUnsafeIndexM #-}
basicUnsafeIndexM (V_Mint v) i = coerce `fmap` VG.basicUnsafeIndexM v i
basicUnsafeCopy (MV_Mint mv) (V_Mint v) = VG.basicUnsafeCopy mv v
{-# INLINE elemseq #-}
elemseq _ = seq
fact :: Int -> Mint
fact = VU.unsafeIndex factCache
{-# INLINE fact #-}
recipFact :: Int -> Mint
recipFact = VU.unsafeIndex recipFactCache
{-# INLINE recipFact #-}
invFact :: Int -> Mint
invFact x = recipFact x * fact (x - 1)
{-# INLINE invFact #-}
nPk :: Int -> Int -> Mint
nPk n k
| n < k = 0
| otherwise = fact n * recipFact k
{-# INLINE nPk #-}
nCk :: Int -> Int -> Mint
nCk n k
| n < k = Mint 0
| otherwise = fact n * recipFact (n - k) * recipFact k
{-# INLINE nCk #-}
nHk :: Int -> Int -> Mint
nHk n k
| n < 0 || k < 0 = Mint 0
| k == 0 = Mint 1
| otherwise = nCk (n + k - 1) k
{-# INLINE nHk #-}
#define FACT_CACHE_SIZE 200000
factCacheSize :: Int
factCacheSize = min (modulus - 1) FACT_CACHE_SIZE
{-# INLINE factCacheSize #-}
factCache :: VU.Vector Mint
factCache = VU.scanl' (\ x y -> x * coerce y) (1 :: Mint) $ VU.generate factCacheSize (+ 1)
{-# NOINLINE factCache #-}
recipFactCache :: VU.Vector Mint
recipFactCache = VU.scanr' ((*) . coerce) (1 / factCache VU.! factCacheSize) $ VU.generate factCacheSize (+ 1)
{-# NOINLINE recipFactCache #-}
powN :: Int -> VU.Vector Mint
powN n = VU.scanl' (\acc x -> acc * intMod x) 1 $ VU.replicate factCacheSize n
stirling2nd :: Int -> Int -> Mint
stirling2nd n k = (snd ret) * (recipFact k)
where
xs = zip [0..] $ map f [0..k]
f i = (Mint $ powModInt i n modulus) * (nCk k i)
ret = List.foldl1' g xs
g :: (Int, Mint) -> (Int, Mint) -> (Int, Mint)
g acc x
| odd (k - fst x) = (fst acc + 1, snd acc - snd x)
| otherwise = (fst acc + 1, snd acc + snd x)
lagrangePolynomial :: Int -> VU.Vector Mint -> Int -> IO Mint
lagrangePolynomial k xs t = do
dp <- VUM.replicate (k + 1) (Mint 1)
pd <- VUM.replicate (k + 1) (Mint 1)
forM_ [0 .. k - 1] $ \i -> do
a <- VUM.read dp i
VUM.write dp (i + 1) (intMod (t - i) * a)
forM_ [k, k - 1 .. 1] $ \i -> do
b <- VUM.read pd i
VUM.write pd (i - 1) (intMod (t - i) * b)
ps <- VU.unsafeFreeze dp
qs <- VU.unsafeFreeze pd
lp xs ps qs (Mint 0) 0 k
where
lp :: VU.Vector Mint -> VU.Vector Mint -> VU.Vector Mint -> Mint -> Int -> Int -> IO Mint
lp as ps qs ans i j
| i > j = return ans
| odd (j - i) = lp as ps qs (ans - tmp) (i + 1) j
| otherwise = lp as ps qs (ans + tmp) (i + 1) j
where
tmp = (as VU.! i) * (ps VU.! i) * (qs VU.! i) * (recipFact i) * (recipFact (j - i))
logMod :: Int -> Int -> Int -> Maybe Int
logMod a b p = go 0 b
where
!sp = ceiling . sqrt . fromIntegral $ p
!g = powModInt a (-sp) p
babystep x = a * x `rem` p
giantstep x = g * x `rem` p
table :: IntMap Int
!table = IntMap.fromList $ zip (iterate babystep 1) [0..sp-1]
go !i !x
| i < sp = case IntMap.lookup x table of
Just j -> Just $! i * sp + j
Nothing -> go (i + 1) $ giantstep x
| otherwise = Nothing