結果

問題 No.3030 ミラー・ラビン素数判定法のテスト
ユーザー nonamaenonamae
提出日時 2021-11-04 19:44:33
言語 C
(gcc 12.3.0)
結果
WA  
実行時間 -
コード長 12,032 bytes
コンパイル時間 1,517 ms
コンパイル使用メモリ 45,996 KB
実行使用メモリ 4,388 KB
最終ジャッジ日時 2023-08-05 03:55:41
合計ジャッジ時間 1,883 ms
ジャッジサーバーID
(参考情報)
judge12 / judge14
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,380 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 1 ms
4,380 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 WA -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
権限があれば一括ダウンロードができます

ソースコード

diff #

#pragma region opt
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma endregion opt

#pragma region header
#define _GNU_SOURCE
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <string.h>
#include <time.h>
#pragma endregion header

#pragma region type
/* signed integer */
typedef   int8_t      i8;
typedef   int16_t     i16;
typedef   int32_t     i32;
typedef   int64_t     i64;
typedef __int128_t    i128;
/* unsigned integer */
typedef   uint8_t     u8;
typedef   uint16_t    u16;
typedef   uint32_t    u32;
typedef   uint64_t    u64;
typedef __uint128_t   u128;
/* floating point number */
typedef   float       f32;
typedef   double      f64;
typedef   long double f80;
#pragma endregion type

#pragma region macro
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
#define SWAP(a, b) (((a) ^= (b)), ((b) ^= (a)), ((a) ^= (b)))
#define POPCNT32(a) __builtin_popcount((a))
#define POPCNT64(a) __builtin_popcountll((a))
#define CTZ32(a) __builtin_ctz((a))
#define CLZ32(a) __builtin_clz((a))
#define CTZ64(a) __builtin_ctzll((a))
#define CLZ64(a) __builtin_clzll((a))
#define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1))
#define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1))
#define MSB32(a) ((31) - __builtin_clz((a)))
#define MSB64(a) ((63) - __builtin_clzll((a)))
#define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0))
#define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0))
#define LSBit(a) ((a) & (-(a)))
#define CLSBit(a) ((a) & ((a) - (1)))
#define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a)))))
#define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a)))))
#define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a)))))
#define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a)))))
#define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32))))))
#define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32))))))
#define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s)))))
#define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s)))))
#define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64))))))
#define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64))))))
#define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s)))))
#define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s)))))
#pragma endregion macro

#pragma region io
int read_int(void) {
  // -2147483648 ~ 2147483647 (> 10 ^ 9)
  int c, x = 0, f = 1;
  while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return f * x;
}
i32 in_i32(void) {
  // -2147483648 ~ 2147483647 (> 10 ^ 9)
  i32 c, x = 0, f = 1;
  while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return f * x;
}
u32 in_u32(void) {
  // 0 ~ 4294967295 (> 10 ^ 9)
  u32 c, x = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return x;
}
i64 in_i64(void) {
  // -9223372036854775808 ~ 9223372036854775807 (> 10 ^ 18)
  i64 c, x = 0, f = 1;
  while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return f * x;
}
u64 in_u64(void) {
  // 0 ~ 18446744073709551615 (> 10 ^ 19)
  u64 c, x = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    x = x * 10 + c - 48;
    c = getchar_unlocked();
  }
  return x;
}
static inline void write_int_inner(int x) {
  if (x >= 10) write_int_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void write_int(int x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  write_int_inner(x);
}
static inline void out_i32_inner(i32 x) {
  if (x >= 10) out_i32_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i32(i32 x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  out_i32_inner(x);
}
void out_u32(u32 x) {
  if (x >= 10) out_u32(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
static inline void out_i64_inner(i64 x) {
  if (x >= 10) out_i64_inner(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i64(i64 x) {
  if (x < 0) {
    putchar_unlocked('-');
    x = -x;
  }
  out_i64_inner(x);
}
void out_u64(u64 x) {
  if (x >= 10) out_u64(x / 10);
  putchar_unlocked(x - x / 10 * 10 + 48);
}
void NL(void) { putchar_unlocked('\n'); }
void SP(void) { putchar_unlocked(' '); }
void write_int_array(int *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    write_int(a[i]);
  }
  NL();
}
void out_i32_array(i32 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_i32(a[i]);
  }
  NL();
}
void out_u32_array(u32 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_u32(a[i]);
  }
  NL();
}
void out_i64_array(i64 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_i64(a[i]);
  }
  NL();
}
void out_u64_array(u64 *a, int a_len) {
  for (int i = 0; i < a_len; i++) {
    if (i) SP();
    out_u64(a[i]);
  }
  NL();
}
#pragma endregion io

#pragma region xorshift
const f64 _R_ = 1.0 / 0xffffffffffffffff;
static u64 _xorshift_state_ = 88172645463325252ULL;
u64 next_rand_xorshift(void) {
  _xorshift_state_ = _xorshift_state_ ^ (_xorshift_state_ << 7);
  return _xorshift_state_ = _xorshift_state_ ^ (_xorshift_state_ >> 9);
}
void rand_init_xorshift(u64 seed) {
  _xorshift_state_ += seed;
  (void)next_rand_xorshift();
}
u64 random_range_xorshift(u64 l, u64 r) { return next_rand_xorshift() % (r - l + 1) + l; }
f64 probability_xorshift(void) { return _R_ * next_rand_xorshift(); }
#pragma endregion xorshift

#pragma region binary gcd
u32 bin_gcd_u32(u32 a, u32 b) {
  if (!a || !b) return a | b;
  u32 shift = CTZ32(a | b);
  a >>= CTZ32(a);
  do {
    b >>= CTZ32(b);
    if (a > b) SWAP(a, b);
    b -= a;
  } while (b);
  return a << shift;
}
u64 bin_gcd_u64(u64 a, u64 b) {
  if (!a || !b) return a | b;
  u64 shift = CTZ64(a | b);
  a >>= CTZ64(a);
  do {
    b >>= CTZ64(b);
    if (a > b) SWAP(a, b);
    b -= a;
  } while (b);
  return a << shift;
}
u64 bin_lcm_u64(u32 a, u32 b) { return (u64)a / bin_gcd_u32(a, b) * b; }
#pragma endregion binary gcd

#pragma region m32
typedef uint32_t m32;
m32 _one_m32(u32 mod) { return (u32)-1u % mod + 1; }
m32 _r2_m32(u32 mod) { return (u64)(i64)-1 % mod + 1; }
m32 _inv_m32(u32 mod) {
  u32 inv = mod;
  for (int i = 0; i < 4; ++i) inv *= 2 - inv * mod;
  return inv;
/**
  u32 u = 1, v = 0, x = 1u << 31;
  for (int i = 0; i < 32; i++) {
    if (u & 1) u = (u + mod) >> 1, v = (v >> 1) + x;
    else u >>= 1, v >>= 1;
  }
  return -v;
*/
}
m32 _reduce_m32(u64 a, m32 inv, u32 mod) {
  u32 y = (u32)(a >> 32) - (u32)(((u64)((u32)a * inv) * mod) >> 32);
  return (i32)y < 0 ? y + mod : y;
}
m32 to_m32(u32 a, m32 r2, m32 inv, u32 mod) { return _reduce_m32((u64)a * r2, inv, mod); }
u32 from_m32(m32 A, m32 inv, u32 mod) { return _reduce_m32(A, inv, mod); }
m32 add_m32(m32 A, m32 B, u32 mod) {
  A += B - mod;
  if ((i32)A < 0) A += mod;
  return A;
}
m32 sub_m32(m32 A, m32 B, u32 mod) {
  if ((i32)(A -= B) < 0) A += 2 * mod;
  return A;
}
m32 min_m32(m32 A, u32 mod) { return sub_m32(0u, A, mod); }
m32 mul_m32(m32 A, m32 B, m32 inv, u32 mod) { return _reduce_m32((u64)A * B, inv, mod); }
m32 pow_m32(m32 A, i32 n, m32 inv, u32 mod) {
  m32 ret = _one_m32(mod);
  while (n > 0) {
    if (n & 1) ret = mul_m32(ret, A, inv, mod);
    A = mul_m32(A, A, inv, mod);
    n >>= 1;
  }
  return ret;
}
m32 inv_m32(m32 A, m32 inv, u32 mod) { return pow_m32(A, (i32)mod - 2, inv, mod); }
m32 div_m32(m32 A, m32 B, m32 inv, u32 mod) {
  /* assert(is_prime(mod)); */
  return mul_m32(A, inv_m32(B, inv, mod), inv, mod);
}
m32 in_m32(m32 r2, m32 inv, u32 mod) {
  u32 c, a = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    a = a * 10 + c - 48;
    c = getchar_unlocked();
  }
  return to_m32(a, r2, inv, mod);
}
void out_m32(m32 A, m32 inv, u32 mod) {
  u32 a = from_m32(A, inv, mod);
  out_u32(a);
}
#pragma endregion m32

#pragma region m64
typedef uint64_t m64;
m64 _one_m64(u64 mod) { return (u64)-1ull % mod + 1; }
m64 _r2_m64(u64 mod) { return (u128)(i128)-1 % mod + 1; }
m64 _inv_m64(u64 mod) {
  m64 inv = mod;
  for (int i = 0; i < 5; i++) inv *= 2 - inv * mod;
  return inv;
}
m64 _reduce_m64(u128 a, m64 inv, u64 mod) {
  u64 y = (u64)(a >> 64) - (u64)(((u128)((u64)a * inv) * mod) >> 64);
  return (i64)y < 0 ? y + mod : y;
}
m64 to_m64(u64 a, m64 r2, m64 inv, u64 mod) { return _reduce_m64((u128)a * r2, inv, mod); }
u64 from_m64(m64 A, m64 inv, u64 mod) { return _reduce_m64(A, inv, mod); }
m64 add_m64(m64 A, m64 B, u64 mod) {
  A += B - mod;
  if ((i64)A < 0) A += mod;
  return A;
}
m64 sub_m64(m64 A, m64 B, u64 mod) {
  if ((i64)(A -= B) < 0) A += 2 * mod;
  return A;
}
m64 min_m64(m64 A, u64 mod) { return sub_m64(0ull, A, mod); }
m64 mul_m64(m64 A, m64 B, m64 inv, u64 mod) { return _reduce_m64((u128)A * B, inv, mod); }
m64 pow_m64(m64 A, i64 n, m64 inv, u64 mod) {
  m64 ret = _one_m64(mod);
  while (n > 0) {
    if (n & 1) ret = mul_m64(ret, A, inv, mod);
    A = mul_m64(A, A, inv, mod);
    n >>= 1;
  }
  return ret;
}
m64 inv_m64(m64 A, m64 inv, u64 mod) { return pow_m64(A, (i64)mod - 2, inv, mod); }
m64 div_m64(m64 A, m64 B, m64 inv, u64 mod) {
  /* assert(is_prime(mod)); */
  return mul_m64(A, inv_m64(B, inv, mod), inv, mod);
}
m64 in_m64(m64 r2, m64 inv, u64 mod) {
  u64 c, a = 0;
  while (c = getchar_unlocked(), c < 48 || c > 57);
  while (47 < c && c < 58) {
    a = a * 10 + c - 48;
    c = getchar_unlocked();
  }
  return to_m64(a, r2, inv, mod);
}
void out_m64(m64 A, m64 inv, u64 mod) {
  u64 a = from_m64(A, inv, mod);
  out_u64(a);
}
#pragma endregion m64

#pragma region quadratic_residue
bool euler_criterion(u32 a, m32 r2, m32 inv, u32 mod) { return pow_m32(to_m32(a, r2, inv, mod), (mod - 1) >> 1, inv, mod) == _one_m32(mod); }
int legendre_symbol(u32 a, m32 r2, m32 inv, u32 mod) {
  // assert(a >= 0 && mod & 1 && is_prime(mod));
  int ret;
  if (_reduce_m32((u64)a, inv, mod) == 0) ret = 0;
  else if (euler_criterion(a, r2, inv, mod)) ret = 1;
  else ret = -1;
  return ret;
}
int jacobi_symbol(u64 k, u64 n) {
  // assert(n >= 0 && n & 1);
  u64 j = 1;
  while (k) {
    if ((i64)k < 0) {
      k = -k;
      if ((n & 3) == 3) j = -j;
    }
    int a = CTZ64(k);
    k >>= a;
    if (((n & 7) == 3 || (n & 7) == 5) && (a & 1)) j = -j;
    SWAP(k, n);
    if ((k & n & 3) == 3) j = -j;
    k %= n;
    if (k > n / 2) k -= n;
  }
  return n == 1 ? j : 0;
}
#pragma endregion quadratic_residue

#pragma region solovay_strassen primary test
bool solovay_strassen(u64 n) {
  if (n == 2 || n == 3 || n == 5 || n == 7) return true;
  if (!(n & 1)) return false;
  if (n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
  if (n < 121) return true;
  u64 mod = n;
  m64 r2 = _r2_m64(mod);
  m64 inv = _inv_m64(mod);
  for (int i = 0; i < 15; i++) {
    u64 a = random_range_xorshift(1, n - 1);
    if (1 < bin_gcd_u64(a, n)) return false;
    m64 A = to_m64(a, r2, inv, mod);
    if (jacobi_symbol(a, n) != pow_m64(A, (n - 1) >> 1, inv, mod)) return false;
  }
  return true;
}
#pragma endregion solovay_strassen primary test

void Main(void) {
  int T = read_int();
  while (T--) {
    u64 x = in_u64();
    out_u64(x);
    SP();
    write_int(solovay_strassen(x));
    NL();
  }
}

int main(void) {
  Main();
  return 0;
}
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