結果

問題 No.577 Prime Powerful Numbers
ユーザー Ryuhei MoriRyuhei Mori
提出日時 2017-10-28 01:58:48
言語 C
(gcc 12.3.0)
結果
AC  
実行時間 11 ms / 2,000 ms
コード長 4,414 bytes
コンパイル時間 362 ms
コンパイル使用メモリ 33,152 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-22 00:13:49
合計ジャッジ時間 909 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
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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
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 1 ms
6,820 KB
testcase_03 AC 3 ms
6,816 KB
testcase_04 AC 1 ms
5,248 KB
testcase_05 AC 11 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 11 ms
5,248 KB
testcase_08 AC 3 ms
5,248 KB
testcase_09 AC 3 ms
5,248 KB
testcase_10 AC 1 ms
5,248 KB
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ソースコード

diff # 

#include <stdio.h>
#include <stdint.h>

typedef __int128 int128_t;
typedef unsigned __int128 uint128_t;

uint64_t ex_gcd(uint64_t y){
  int i;
  uint64_t u, v;
  u = 1; v = 0;
  uint64_t x = 1LL<<63;

  for(i=0;i<64;i++){
    if(u&1){
      u = (u + y) / 2;
      v = v/2 + x;
    }
    else {
      u >>= 1; v >>= 1;
    }
  }

  return v;
} 


static inline uint64_t MR(uint128_t x, uint64_t m, uint64_t n){
  uint64_t z = ((uint128_t) ((uint64_t) x * m) * n + x) >> 64;
  return z < n ? z : z - n;
}

static inline uint64_t RM(uint64_t x, uint64_t r2, uint64_t m, uint64_t n){
  return MR((uint128_t) r2 * x, m, n);
}

// k > 0
static inline uint64_t modpow64(uint64_t a, uint64_t k, uint64_t m, uint64_t n){
  uint64_t r;
  for(r=a,--k;k;k/=2){
    if(k&1) r = MR((uint128_t)r*a, m, n);
    a = MR((uint128_t) a*a, m, n);
  }
  return r;
}

static inline uint32_t modpow32(uint32_t a, uint32_t k, uint32_t n){
  uint32_t r;
  for(r=1;k;k/=2){
    if(k&1) r = (uint64_t)r*a%n;
    a = (uint64_t) a*a%n;
  }
  return r;
}

uint64_t sieve;

void make_sieve(){
  const uint32_t ps[] = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127};
  int i;
  for(i=0;i<sizeof(ps)/sizeof(ps[0]);i++){
    sieve |= 1 << (ps[i]/2);
  }
}

static inline int is_primesmall(uint32_t n){
  return sieve & (1 << (n/2));
}

int is_prime32(uint32_t n){
  static const uint32_t as32[] = {2, 7, 61};
  int i, j, r;
  uint32_t d;
  r = __builtin_ctz(n-1);
  d = (n-1) >> r;
  for(i=0;i<3;i++){
    uint32_t a = as32[i] % n;
    if(a == 0) return 1;
    uint32_t t = modpow32(a, d, n);
    if(t == 1) continue;
    for(j=0;t!=n-1;j++){
      if(j == r-1) return 0;
      t = (uint64_t) t * t % n;
      if(t == 1) return 0;
    }
  }
  return 1;
}


int is_prime64(uint64_t n){
  static const uint64_t as64[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  int i, j, r;
  uint64_t d, one, mone, r2, m;
  if(n < (1LL << 32)) return is_prime32(n);
  r = __builtin_ctzll(n-1);
  d = (n-1) >> r;
  m = ex_gcd(n);
  one = -1ULL % n + 1;
  mone = n - one;
  r2 = (uint128_t) (int128_t) -1 % n + 1;
  for(i=0;i<7;i++){
    uint64_t a = RM(as64[i], r2, m, n);
    if(a == 0) return 1;
    uint64_t t = modpow64(a, d, m, n);
    if(t == one) continue;
    for(j=0;t!=mone;j++){
      if(j == r-1) return 0;
      t = MR((uint128_t) t * t, m, n);
//      if(t == one) return 0;
    }
  }
  return 1;
}

int is_prime(uint64_t n){
  if(n <= 1) return 0;
  if(n <= 3) return 1;
  if(!(n & 1)) return 0;
  if(n < 128) return is_primesmall(n);
  if(n < (1LL << 32)) return is_prime32(n);
  return is_prime64(n);
}

// y is odd
uint64_t gcd64(uint64_t x, uint64_t y){
  if(x==0) return y;
  x >>= __builtin_ctzll(x);
  while(x!=y){
    if(x < y){
      y -= x;
      y >>= __builtin_ctzll(y);
    }
    else {
      x -= y;
      x >>= __builtin_ctzll(x);
    }
  }
  return x;
}

int is_power64(uint64_t n, uint64_t p){
  int i;
  uint64_t a[49];
  uint64_t x;
  a[0] = p;
  a[1] = p * p;
  for(i=1; a[i] <= n && a[i] > a[i-1]; i++){
    a[i+1] = a[i] * a[i];
  }
/*
  if(a[--i] == n) return 1;
  while(i){
    if(n % a[i]) return 0;
    n /= a[i];
    while(i > 0 && n < a[--i]) ;
  }
*/
  x = a[--i];
  if(x == n) return 1;
  for(--i; i>=0;--i){
    uint64_t y = x * a[i];
    if(y == n) return 1;
    else if(y < x) return 0;
    else if(y < n) x = y;
  }
  return 0;
}

uint64_t is_primepower64(uint64_t n){
  uint64_t i;
  if(n <= 1) return 0;
  if(!(n&(n-1))) return 2;
  if(!(n&1)) return 0;

//return is_prime64(n);

  uint64_t s, m, r2, one;
  m = ex_gcd(n);
  one = -1UL % n + 1;
  r2 = (uint128_t) (int128_t) -1 % n + 1;

  uint64_t y = 2;
  uint64_t x = one << 1;
  if(x >= n) x -= n;
  uint64_t in = MR((uint128_t)modpow64(x, n, m, n), m, n);
  uint64_t inmi = in >= y ? in - y : in + n - y;
  uint64_t p = gcd64(inmi, n);

//fprintf(stderr, "%ld\n", p);

  if(p < 128) return is_power64(n, p) && is_prime(p);
  else return is_prime(p) && is_power64(n, p);
//  return is_prime64(p);
}


int main(){
  int i, q;

  make_sieve();
  scanf("%d", &q);
  for(i=0;i<q;i++){
    uint64_t n;
    scanf("%ld", &n);
    if(n<=2) puts("No");
    else if((n&1)==0) puts("Yes");
    else {
      uint64_t j;
      for(j=2; j<n; j<<=1){
        if(is_primepower64(n-j)){
          break;
        }
      }
      if(j>=n) puts("No"); else puts("Yes");
    }
  }
  return 0;
}
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