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 |
![]() |
提出日時 | 2017-10-24 16:03:39 |
言語 | C++11 (gcc 11.4.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 12,225 bytes |
コンパイル時間 | 2,062 ms |
コンパイル使用メモリ | 192,312 KB |
実行使用メモリ | 6,820 KB |
最終ジャッジ日時 | 2024-11-18 15:57:19 |
合計ジャッジ時間 | 2,688 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
(要ログイン)
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
6,820 KB |
testcase_01 | AC | 2 ms
6,820 KB |
testcase_02 | AC | 2 ms
6,820 KB |
testcase_03 | AC | 2 ms
6,816 KB |
testcase_04 | WA | - |
testcase_05 | WA | - |
testcase_06 | WA | - |
testcase_07 | WA | - |
testcase_08 | WA | - |
testcase_09 | WA | - |
ソースコード
#include <bits/stdc++.h> using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define fi first #define se second #define mt make_tuple #define mp make_pair template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } #define exists find_if #define forall all_of using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>; using ld = long double; using vld = vector<ld>; using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; } using Pos = complex<double>; template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{}; template<class Ch, class Tr, class Tuple, size_t... Is> void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; } template<class Ch, class Tr, class... Args> auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; } ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; } template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template <typename T> ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template <typename T, typename U> ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template <typename T, typename U> ostream &operator<<(ostream &o, const unordered_map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;} string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); return s; } template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;}; string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); } struct ci : public iterator<forward_iterator_tag, ll> { ll n; ci(const ll n) : n(n) { } bool operator==(const ci& x) { return n == x.n; } bool operator!=(const ci& x) { return !(*this == x); } ci &operator++() { n++; return *this; } ll operator*() const { return n; } }; static const double EPS = 1e-14; static const long long INF = 1e18; static const long long mo = 1e9+7; #define ldout fixed << setprecision(40) // 素数の個数はO(n / log n) /**********************************************************/ // 素数テーブルの作成 /**********************************************************/ // 素数テーブル構築: O(n log n) #define MAX_NUM 20000000 ll prime_size = -1; bool is_prime[MAX_NUM]; vector<ll> primes; // 素数リスト void sieve_of_atkin(ll N) { ll sqrtN = sqrt(N); int n; for (int z = 1; z <= 5; z += 4) { for (int y = z; y <= sqrtN; y += 6) { for (int x = 1; x <= sqrtN && (n = 4*x*x+y*y) <= N; ++x) is_prime[n] = !is_prime[n]; for (int x = y+1; x <= sqrtN && (n = 3*x*x-y*y) <= N; x += 2) is_prime[n] = !is_prime[n]; } } for (int z = 2; z <= 4; z += 2) { for (int y = z; y <= sqrtN; y += 6) { for (int x = 1; x <= sqrtN && (n = 3*x*x+y*y) <= N; x += 2) is_prime[n] = !is_prime[n]; for (int x = y+1; x <= sqrtN && (n = 3*x*x-y*y) <= N; x += 2) is_prime[n] = !is_prime[n]; } } for (int y = 3; y <= sqrtN; y += 6) { for (int z = 1; z <= 2; ++z) { for (int x = z; x <= sqrtN && (n = 4*x*x+y*y) <= N; x += 3) is_prime[n] = !is_prime[n]; } } for (int n = 5; n <= sqrtN; ++n) if (is_prime[n]) for (int k = n*n; k <= N; k+=n*n) is_prime[k] = false; is_prime[2] = is_prime[3] = true; } void sieve_of_eratosthenes(ll n) { for (ll i = 2; i < n; ++i) is_prime[i] = true; for (ll i = 2; i*i < n; ++i) if (is_prime[i]) for (ll j = i*i; j < n; j+=i) is_prime[j] = false; for (ll i = 0; i < n; i++) if (is_prime[i]) primes.push_back(i); } void constructPrime(ll n) { assert(n < MAX_NUM); prime_size = n; #if 1 sieve_of_atkin(n); #else sieve_of_eratosthenes(n); #endif primes.reserve(1.2*n*log(n)); // 素数定理よりn>100でOK rep(i, n) if (is_prime[i]) { primes.pb(i); } } /**********************************************************/ // 以下はよく行う処理のテンプレート // そのままは大抵使えないので、改造するつもりで。 /**********************************************************/ // 素因数分解 // // 小さい素数から見ていって、割れたら割って素因数リストに追加する // 残ったnが素数リストよりも大きければ、そのnは素数だと見なして返す。 unordered_map<ll, ll> factorize(ll n) { if (n <= 1) return unordered_map<ll, ll>(); unordered_map<ll, ll> divisors_list; ll prime; for (ll i = 0; (prime = primes[i]) && n >= prime * prime; ) if (n % prime) i++; else divisors_list[prime]++, n /= prime; if (n != 1) divisors_list[n]++; return divisors_list; } // [0, n]の範囲を全て素因数分解する。「飛び飛びの」高速化。結構速い。 // n < 1,000,000で150ms // n < 10,000,000で1000ms // // 配列rem[i]は、初めiが入っている。 // 素数pを下から見るが、rem[i]を全て見る必要はなく、rem[p*i]だけでいい。 vector<unordered_map<ll, ll>> factorizeRange(ll n) { vector<unordered_map<ll, ll>> fact(n+1); vector<ll> rem(n+1); rep(i, n+1) rem[i] = i; for (auto x : primes) for (ll i = x; i <= n; i += x) while (rem[i] % x == 0) rem[i] /= x, fact[i][x]++; return fact; } // lcm(a) // a[i] < 1e7 unordered_map<ll, ll> lcmSmall(set<ll>& a) { if (!a.size()) return unordered_map<ll, ll>(); ll n = *(prev(a.end())); vector<ll> rem(n+1); rep(i, n+1) rem[i] = i; unordered_map<ll, ll> ret; for (auto x : primes) { ll max_c = 0; for (ll i = x; i <= n; i += x) if (a.count(i)) { ll c = 0; while (rem[i] % x == 0) rem[i] /= x, c++; chmax(max_c, c); } if (max_c) ret[x] = max_c; } return ret; } // lcm(a) // a[i]>1e7 unordered_map<ll, ll> lcmLarge(set<ll>& a) { if (!a.size()) return unordered_map<ll, ll>(); unordered_map<ll, ll> ret; for (auto n : a) { auto d = factorize(n); for (auto x : d) chmax(ret[x.fi], x.se); } return ret; } // 約数を全列挙する。 // // 約数を試し割りするより、n=1000000で4倍くらい早い。 vector<ll> divisors(ll n) { vector<ll> divisors_list; auto counter = factorize(n); divisors_list.push_back(1); for (auto x : counter) { ll tmp_size = divisors_list.size(); ll p = 1; for (ll i = 0; i < x.second; i++) { p *= x.first; for (ll j = 0; j < tmp_size; j++) divisors_list.push_back(divisors_list[j] * p); } } return divisors_list; } ll getDivisorsNum(ll n) { unordered_map<ll, ll> divisors_list = factorize(n); map<ll, ll> num; rep(i, divisors_list.size()) num[divisors_list[i]]++; ll p = 1; for (auto x : num) p *= x.second + 1; return p; } /**********************************************************/ // 前処理なしの素数判定 /**********************************************************/ #define ull unsigned long long // dla n < 2^32: inline ull mul(ull a, ull b, ull mod) { return (a*b) % mod; } const int _k = 25; const ull _mask = (1<<_k)-1; ull mul (ull a, ull b, ull mod) { // zaĹ‚: b, mod < 2^(64-_k) ull result = 0; while (a) { ull temp = (b * (a & _mask)) % mod; result = (result + temp) % mod; a >>= _k; b = (b << _k) % mod; } return result; } ull pow(ull a, ull w, ull mod) { ull res = 1; while (w){ if (w&1) res = mul(res, a, mod); a = mul(a, a, mod); w /= 2; } return res; } bool primetest(ull n, int a) { if (a > n-1) return 1; ull d = n-1; int s = 0; while (!(d&1)) { d /= 2; s++; } ull x = pow(a, d, n); if (x == 1 || x == n-1) return 1; rep(i,s-1){ x = mul(x, x, n); if (x == 1) return 0; if (x == n-1) return 1; } return 0; } bool isPrime(ull n) { if (n < 4) return n > 1; bool pr = n%2; if (n < (1LL << 32)) { for (int a : {2,7,61}) pr = pr && primetest(n,a); } else if (n < (1LL << 48)) { for (int a : {2,3,5,7,11,13,17}) pr = pr && primetest(n,a); } else { for (int a : {2,325,9375,28178,450775,9780504,1795265022}) pr = pr && primetest(n,a); } return pr; } // O(n^0.25) // ローのアルゴリズム // 計算結果はrho_retに保存される map<ull,int> rho_ret; // {p, k}, pの素因数がk個存在 ull find_factor(ull z) { if (!(z&1)) return 2; ull c = rand() % z, x = 2, y = 2, d = 1; while (d == 1) { ull tp = (mul(y,y,z) + c) % z; y = (mul(tp,tp,z) + c) % z; x = (mul(x,x,z) + c) % z; d = __gcd(x>y ? x-y : y-x, z); } return d; } void rhofact_rec(ull z) { if (z==1) return; if (isPrime(z)) { rho_ret[z]++; return; } while(1) { ull f = find_factor(z); if (f != z) { rhofact_rec(f); rhofact_rec(z/f); break; } } } void rho(ull z) { rho_ret.clear(); rhofact_rec(z); } // ガウス素数=複素数の素数判定 bool isGaussianPrime(ll a, ll b) { if (a < 0) a = -a; if (b < 0) b = -b; if (a == 0) return b % 4 == 3 && is_prime[b]; if (b == 0) return a % 4 == 3 && is_prime[a]; return is_prime[a*a+b*b]; } // 区間篩 // O( n log n ). const ll N = 100000000; // MAXPRIME const ll M = 10000; // SQRT(N) const ll K = 6000000; // NUMBER OF PRIMES, CHOOSE 9/8 * N / LOG(N) vector<ll> iterativeSieve() { static ll p[K], table[M]; for (ll i = 2; i < M; ++i) p[i] = i; for (ll i = 2; i*i < M; ++i) if (p[i]) for (ll j = i*i; j < M; j += i) p[j] = 0; p[0] = p[1] = 0; ll num = remove(p, p+M, 0) - p; for (ll m = M; m < N; m += M) { for (ll x = m; x < m+M; ++x) table[x-m] = x; for (ll i = 0, j; p[i]*p[i] < m+M; ++i) { if (p[i] >= m) j = p[i] * p[i]; else if (m % p[i] == 0) j = m; else j = m - (m % p[i]) + p[i]; for (; j < m+M; j += p[i]) table[j-m] = 0; } num = remove_copy(table, table+M, p+num, 0) - p; } return vector<ll>(p, p+num); } ll n = 1000000; int main(void) { ll n; cin >> n; rep(i, n) { ll x; cin >> x; cout << x << " " << isPrime(x) << endl; } return 0; }