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 tute7627
提出日時 2020-09-04 19:06:02
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 30 ms / 9,973 ms
コード長 6,677 bytes
コンパイル時間 2,419 ms
コンパイル使用メモリ 204,544 KB
最終ジャッジ日時 2025-01-14 04:41:15
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
other AC * 10
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 # 

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
namespace FastPrimeFactorization {

  template< typename word, typename dword, typename sword >
  struct UnsafeMod {
    UnsafeMod() : x(0) {}

    UnsafeMod(word _x) : x(init(_x)) {}

    bool operator==(const UnsafeMod &rhs) const {
      return x == rhs.x;
    }

    bool operator!=(const UnsafeMod &rhs) const {
      return x != rhs.x;
    }

    UnsafeMod &operator+=(const UnsafeMod &rhs) {
      if((x += rhs.x) >= mod) x -= mod;
      return *this;
    }

    UnsafeMod &operator-=(const UnsafeMod &rhs) {
      if(sword(x -= rhs.x) < 0) x += mod;
      return *this;
    }

    UnsafeMod &operator*=(const UnsafeMod &rhs) {
      x = reduce(dword(x) * rhs.x);
      return *this;
    }

    UnsafeMod operator+(const UnsafeMod &rhs) const {
      return UnsafeMod(*this) += rhs;
    }

    UnsafeMod operator-(const UnsafeMod &rhs) const {
      return UnsafeMod(*this) -= rhs;
    }

    UnsafeMod operator*(const UnsafeMod &rhs) const {
      return UnsafeMod(*this) *= rhs;
    }

    UnsafeMod pow(uint64_t e) const {
      UnsafeMod ret(1);
      for(UnsafeMod base = *this; e; e >>= 1, base *= base) {
        if(e & 1) ret *= base;
      }
      return ret;
    }

    word get() const {
      return reduce(x);
    }

    static constexpr int word_bits = sizeof(word) * 8;

    static word modulus() {
      return mod;
    }

    static word init(word w) {
      return reduce(dword(w) * r2);
    }

    static void set_mod(word m) {
      mod = m;
      inv = mul_inv(mod);
      r2 = -dword(mod) % mod;
    }

    static word reduce(dword x) {
      word y = word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits);
      return sword(y) < 0 ? y + mod : y;
    }

    static word mul_inv(word n, int e = 6, word x = 1) {
      return !e ? x : mul_inv(n, e - 1, x * (2 - x * n));
    }

    static word mod, inv, r2;

    word x;
  };

  using uint128_t = __uint128_t;

  using Mod64 = UnsafeMod< uint64_t, uint128_t, int64_t >;
  template<> uint64_t Mod64::mod = 0;
  template<> uint64_t Mod64::inv = 0;
  template<> uint64_t Mod64::r2 = 0;

  using Mod32 = UnsafeMod< uint32_t, uint64_t, int32_t >;
  template<> uint32_t Mod32::mod = 0;
  template<> uint32_t Mod32::inv = 0;
  template<> uint32_t Mod32::r2 = 0;

  bool miller_rabin_primality_test_uint64(uint64_t n) {
    Mod64::set_mod(n);
    uint64_t d = n - 1;
    while(d % 2 == 0) d /= 2;
    Mod64 e{1}, rev{n - 1};
    // http://miller-rabin.appspot.com/  < 2^64
    for(uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
      if(n <= a) break;
      uint64_t t = d;
      Mod64 y = Mod64(a).pow(t);
      while(t != n - 1 && y != e && y != rev) {
        y *= y;
        t *= 2;
      }
      if(y != rev && t % 2 == 0) return false;
    }
    return true;
  }

  bool miller_rabin_primality_test_uint32(uint32_t n) {
    Mod32::set_mod(n);
    uint32_t d = n - 1;
    while(d % 2 == 0) d /= 2;
    Mod32 e{1}, rev{n - 1};
    for(uint32_t a : {2, 7, 61}) {
      if(n <= a) break;
      uint32_t t = d;
      Mod32 y = Mod32(a).pow(t);
      while(t != n - 1 && y != e && y != rev) {
        y *= y;
        t *= 2;
      }
      if(y != rev && t % 2 == 0) return false;
    }
    return true;
  }

  bool is_prime(uint64_t n) {
    if(n == 2) return true;
    if(n == 1 || n % 2 == 0) return false;
    if(n < uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n);
    return miller_rabin_primality_test_uint64(n);
  }

  uint64_t pollard_rho(uint64_t n) {
    if(is_prime(n)) return n;
    if(n % 2 == 0) return 2;
    Mod64::set_mod(n);
    uint64_t d;
    Mod64 one{1};
    for(Mod64 c{one};; c += one) {
      Mod64 x{2}, y{2};
      do {
        x = x * x + c;
        y = y * y + c;
        y = y * y + c;
        d = __gcd((x - y).get(), n);
      } while(d == 1);
      if(d < n) return d;
    }
    assert(0);
  }

  vector< uint64_t > prime_factor(uint64_t n) {
    if(n <= 1) return {};
    uint64_t p = pollard_rho(n);
    if(p == n) return {p};
    auto l = prime_factor(p);
    auto r = prime_factor(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
  }
};
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n;cin>>n;
  while(n--){
    ll x;cin>>x;
    auto k=FastPrimeFactorization::is_prime(x);
    cout<<x spa k<<endl;
  }
  return 0;
}
0