結果

問題 No.36 素数が嫌い！
ユーザー むらためむらため
提出日時 2017-08-13 14:52:34
言語 Nim
(2.0.2)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 3,269 bytes
コンパイル時間 812 ms
コンパイル使用メモリ 57,720 KB
最終ジャッジ日時 2023-09-12 14:27:36
合計ジャッジ時間 1,190 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
このコードへのチャレンジ（β）
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。

コンパイルメッセージ
/home/judge/data/code/Main.nim(1, 50) Warning: Use the new 'sugar' module instead; future is deprecated [Deprecated]
/home/judge/data/code/Main.nim(41, 25) template/generic instantiation of `toSeq` from here
/nim-1.6.12/lib/pure/collections/sequtils.nim(846, 18) Error: type mismatch: got <HSlice[system.int, system.cint]>
but expected one of:
iterator items(a: cstring): char
  first type mismatch at position: 1
  required type for a: cstring
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items(a: string): char
  first type mismatch at position: 1
  required type for a: string
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items(n: NimNode): NimNode
  first type mismatch at position: 1
  required type for n: NimNode
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[IX, T](a: array[IX, T]): T
  first type mismatch at position: 1
  required type for a: array[IX, T]
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[T: Ordinal](s: Slice[T]): T
  first type mismatch at position: 1
  required type for s: Slice[items.T]
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[T: char](a: openArray[T]): T
  first type mismatch at position: 1
  required type for a: openArray[T: char]
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[T: enum and Ordinal](E: typedesc[T]): T
  first type mismatch at position: 1
  required type for E: typedesc[T: enum and Ordinal]
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[T: not char](a: openArray[T]): lent2 T
  first type mismatch at position: 1
  required type for a: openArray[T: not char]
  but expression ':tmp_486539464' is of type: HSlice[system.int, system.cint]
iterator items[T](a: seq[T]): lent2 T
  first type mismatch at position: 1
  required type

ソースコード

diff # 

import sequtils,strutils,strscans,algorithm,math,future,macros
template get*():string = stdin.readLine()

proc millerRabinIsPrime(n:int):bool = # O(log n)
  proc ctz(n:int):cint{.importC: "__builtin_ctz", noDecl .} # 01<0000> -> 4
  proc power(x,n:int,modulo:int = 0): int =
    proc mul(x,n,modulo:int):int =
      if n == 0: return 0
      if n == 1: return x
      result = mul(x,n div 2,modulo) mod modulo
      result = (result * 2) mod modulo
      result = (result + x * (n mod 2 == 1).int) mod modulo
      if n == 0: return 1
    if n == 1: return x
    let
      pow_2 = power(x,n div 2,modulo)
      odd = if n mod 2 == 1: x else: 1
    if modulo > 0:
      const maybig = int.high.float.sqrt.int div 2
      if pow_2 > maybig or odd > maybig:
        result = mul(pow_2,pow_2,modulo)
        result = mul(result,odd,modulo)
      else:
        result = (pow_2 * pow_2) mod modulo
        result = (result * odd) mod modulo
    else:
      return pow_2 * pow_2 * odd

  if n <= 1 : return false
  if n div 2 == 0: return false
  if n == 2 or n == 3 or n == 5: return true
  let
    s = ctz(n - 1)
    d = (n - 1) div (1 shl s)
  var a_list = @[2, 7, 61]
  if n >= 4_759_123_141 and n < 341_550_071_728_321:
    a_list = @[2, 3, 5, 7, 11, 13, 17]
  if n in a_list : return true
  for a in a_list:
    if power(a,d,n) == 1 : continue
    let notPrime = toSeq(0..<s).allIt(power(a,d*(1 shl it),n) != n-1)
    if notPrime : return false
  return true


proc squareFormFactor(n:int):int =
  proc check(k:int):int =
    #echo k
    proc √(x:int):int = x.float.sqrt.int
    if n <= 1 : return n
    if n mod 2 == 0 : return 2
    if √(n) * √(n) == n : return √(n)
    var P,Q = newSeq[int]()
    block:
      P &= √(k * n)
      Q &= 1
      Q &= k * n - P[0]*P[0]
    while √(Q[^1]) * √(Q[^1]) != Q[^1]:
      let b = (√(k * n) + P[^1] ) div Q[^1]
      P &= b * Q[^1] - P[^1]
      Q &= Q[^2] + b * (P[^2] - P[^1])
    block:
      if Q[^1] == 0 : return check(k + 1)
      let
        b = (√(k * n) - P[^1] ) div Q[^1]
        P0 = b * √(Q[^1]) + P[^1]
        Q0 = √(Q[^1])
        Q1 = (k*n - P0*P0) div Q0
      (P,Q) = (@[P0], @[ Q0, Q1 ])
    while true:
      let b = (√(k * n) + P[^1] ) div Q[^1]
      P &= b * Q[^1] - P[^1]
      Q &= Q[^2] + b * (P[^2] - P[^1])
      if P[^1] == P[^2] or Q[^1] == Q[^2]: break
    let f = gcd(n,P[^1])
    if f != 1 and f != n : return f
    else: return check(k+1)
  return check(1)


proc getPrimes(n:int):seq[int] = # [2,3,5,...n]
  proc getIsPrimes(n:int) :seq[bool] = # [0...n] O(n loglog n)
    result = newSeqWith(n+1,true)
    result[0] = false
    result[1] = false
    for i in 2..n.float.sqrt.int :
      if not result[i]: continue
      for j in countup(i*2,n,i):
        result[j] = false
  let isPrimes = getIsPrimes(n)
  result = @[]
  for i,p in isPrimes:
    if p : result &= i



let N = get().parseInt()
if N == 1 :
  echo "NO"
  quit()
if millerRabinIsPrime(N):
  echo "NO"
  quit()
let primes = getPrimes(N.float.cbrt.int + 1)
for p in primes:
  if N mod p != 0: continue
  if millerRabinIsPrime(N div p):
    echo "NO"
  else:
    echo "YES"
  quit()

let sff = squareFormFactor(N)
if millerRabinIsPrime(N div sff) and millerRabinIsPrime(sff):
  echo "NO"
else: echo "YES"
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