結果
| 問題 |
No.8030 ミラー・ラビン素数判定法のテスト
|
| ユーザー |
 nonamae
|
| 提出日時 | 2022-07-09 22:15:30 |
| 言語 | C (gcc 13.3.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,691 bytes |
| コンパイル時間 | 967 ms |
| コンパイル使用メモリ | 43,704 KB |
| 実行使用メモリ | 6,820 KB |
| 最終ジャッジ日時 | 2024-12-31 18:55:36 |
| 合計ジャッジ時間 | 2,032 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 8 WA * 2 |
ソースコード
#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
typedef int8_t i8;
typedef int16_t i16;
typedef int32_t i32;
typedef int64_t i64;
typedef __int128_t i128;
typedef uint8_t u8;
typedef uint16_t u16;
typedef uint32_t u32;
typedef uint64_t u64;
typedef __uint128_t u128;
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
// -2147483648 ～ 2147483647 (> 10 ^ 9)
i32 in_i32(void) {
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;
}
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);
}
// -9223372036854775808 ～ 9223372036854775807 (> 10 ^ 18)
i64 in_i64(void) {
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;
}
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);
}
// 0 ～ 4294967295 (> 10 ^ 9)
u32 in_u32(void) {
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;
}
void out_u32(u32 x) {
if (x >= 10) out_u32(x / 10);
putchar_unlocked(x - x / 10 * 10 + 48);
}
// 0 ～ 18446744073709551615 (> 10 ^ 19)
u64 in_u64(void) {
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;
}
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(' '); }
#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
u64 bin_gcd(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;
}
#pragma endregion binary gcd
#pragma region jacobi symbol
int jacobi(i64 a, u64 n) {
u64 t;
int j = 1;
while (a) {
if (a < 0) {
a = -a;
if ((n & 3) == 3) j = -j;
}
int s = CTZ64(a);
a >>= s;
if (((n & 7) == 3 || (n & 7) == 5) && (s & 1)) j = -j;
if ((a & n & 3) == 3) j = -j;
t = a, a = n, n = t;
a %= n;
if (a > n / 2) a -= n;
}
return n == 1 ? j : 0;
}
#pragma endregion jacobi symbol
#pragma region montgomery_64bit
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 N_m64(u64 mod) {
m64 N = mod;
for (int i = 0; i < 5; i++) N *= 2 - N * mod;
return N;
}
m64 reduce_m64(u128 a, m64 N, u64 mod) {
u64 y = (u64)(a >> 64) - (u64)(((u128)((u64)a * N) * mod) >> 64);
return (i64)y < 0 ? y + mod : y;
}
m64 to_m64(u64 a, m64 r2, m64 N, u64 mod) {
return reduce_m64((u128)a * r2, N, mod);
}
u64 from_m64(m64 A, m64 N, u64 mod) {
return reduce_m64(A, N, 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 N, u64 mod) {
return reduce_m64((u128)A * B, N, mod);
}
m64 pow_m64(m64 A, i64 n, m64 one, m64 N, u64 mod) {
m64 ret = one;
while (n > 0) {
if (n & 1) ret = mul_m64(ret, A, N, mod);
A = mul_m64(A, A, N, mod);
n >>= 1;
}
return ret;
}
m64 inv_m64(m64 A, m64 one, m64 N, u64 mod) {
return pow_m64(A, (i64)mod - 2, one, N, mod);
}
m64 div_m64(m64 A, m64 B, m64 one, m64 N, u64 mod) {
/* assert(is_prime(mod)); */
return mul_m64(A, inv_m64(B, one, N, mod), N, mod);
}
m64 in_m64(m64 r2, m64 N, 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, N, mod);
}
void out_m64(m64 A, m64 N, u64 mod) {
u64 a = from_m64(A, N, mod);
out_u64(a);
}
#pragma endregion montgomery_64bit
#pragma region Solovay_Strassen_primarity_test
u32 is_prime(u64 n) {
if (n <= 1) return 0;
if (n <= 3) return 1;
if (!(n & 1)) return 0;
const u64 mod = n;
const u64 r2 = r2_m64(n);
const u64 N = N_m64(n);
const u64 one = one_m64(n);
const u64 rev = reduce_m64((u128)(n - 1) * r2, N, n);
for (int _ = 0; _ < 7; ++_) {
u32 a = random_range_xorshift(2u, ((n - 1) > ((1ull << 32) - 1)) ? 1u << 31 : n - 1);
int x = jacobi(a, n);
u64 y = (x == -1) ? rev : ((x == 0) ? 0 : one);
if (y == 0 || y != pow_m64(to_m64(a, r2, N, mod), (mod - 1) / 2, one, N, mod)) return 0;
}
return 1;
}
#pragma endregion Solovay_Strassen_primarity_test
int main(void) {
u64 Q = in_u64();
while (Q--) {
u64 x = in_u64();
out_u64(x);
SP();
out_u32(is_prime(x));
NL();
}
return 0;
}