結果

問題 No.308 素数は通れません
コンテスト
ユーザー こまる
提出日時 2020-10-07 23:37:46
言語 Haskell
(9.10.1)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 3,005 bytes
コンパイル時間 264 ms
コンパイル使用メモリ 150,144 KB
最終ジャッジ日時 2024-11-15 05:01:24
合計ジャッジ時間 773 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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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:3:1: 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.
  |
3 | import qualified GHC.Integer.GMP.Internals as GMP
  | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

ソースコード

diff # 

{-# LANGUAGE BangPatterns #-}
import           Data.Bits                 (Bits (unsafeShiftL, unsafeShiftR), FiniteBits (countTrailingZeros))
import qualified GHC.Integer.GMP.Internals as GMP

main :: IO ()
main = do
  n <- readLn :: IO Integer
  if n < 50
    then putStrLn $ ["0","1","2","3","3","5","5","7","7","7","7","11","11","13","13","7","7","17","8","19","19","19","7","23","23","23","8","8","8","29","8","31","8","8","8","8","8","37","8","8","8","41","8","43","8","8","8","47","8","14","8"] !! (fromInteger n)
    else if n `mod` 8 == 1 && isPrime (n - 8)
      then putStrLn "14"
      else putStrLn "8"

isPrime :: Integer -> Bool
isPrime k
  | k <= 3 = k == 2 || k == 3
  | even k = False
  | otherwise = millerRabin k
  where
    millerRabin :: Integer -> Bool
    millerRabin n
      | n < 18446744073709551616     = millerRabinSmall (fromInteger n)
      | n < 318665857834031151167461 = loop [2,3,5,7,11,13,17,19,23,29,31,37]
      | otherwise                    = loop [2,3,5,7,11,13,17,19,23,29,31,37,41]
      where
        !m = n - 1
        !s = cTZ m 0
        !d = m .>>. s
        cTZ :: Integer -> Int -> Int
        cTZ !i !cnt
          | odd i     = cnt
          | otherwise = cTZ (i .>>. 1) (cnt + 1)
        {-# INLINE cTZ #-}
        check1 :: Integer -> Bool
        check1 a = GMP.powModInteger a d n /= 1
        {-# INLINE check1 #-}
        check2 :: Integer -> Int -> Bool
        check2 a i = (GMP.powModInteger a (d * (1 .<<. i)) n) /= m
        {-# INLINE check2 #-}
        loop [] = True
        loop (a:as)
          | check1 a && allok = False
          | otherwise = loop as
          where
            allok = all (check2 a) [0..(s - 1)]

millerRabinSmall :: Int -> Bool
millerRabinSmall n
  | n < 2047                = loop [2]
  | n < 1373653             = loop [2,3]
  | n < 9080191             = loop [31,73]
  | n < 25326001            = loop [2,3,5]
  | n < 4759123141          = loop [2,7,61]
  | n < 1122004669633       = loop [2,13,23,1662803]
  | n < 2152302898747       = loop [2,3,5,7,11]
  | n < 3474749660383       = loop [2,3,5,7,11,13]
  | n < 341550071728321     = loop [2,3,5,7,11,13,17]
  | otherwise               = loop [2,325,9375,28178,450775,9780504,1795265022]
  where
    !m = n - 1
    !s = countTrailingZeros m
    !d = m .>>. s
    check3 :: Int -> Bool
    check3 a = powModInt a d n /= 1
    {-# INLINE check3 #-}
    check4 :: Int -> Int -> Bool
    check4 a i = (powModInt a (d * (1 .<<. i)) n) /= m
    {-# INLINE check4 #-}
    loop [] = True
    loop (a:as)
      | check3 a && allok = False
      | otherwise = loop as
      where
        allok = all (check4 a) [0..(s - 1)]

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

infixl 8 .>>., .<<.
(.>>.) :: Bits i => i -> Int -> i
(.>>.) = unsafeShiftR
{-# INLINE (.>>.) #-}

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