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 |
 はむこ
|
| 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 | 2,152 ms |
| コンパイル使用メモリ | 192,288 KB |
| 実行使用メモリ | 5,376 KB |
| 最終ジャッジ日時 | 2024-04-29 12:44:41 |
| 合計ジャッジ時間 | 2,925 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（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 | 2 ms
5,248 KB |
| testcase_01 | AC | 1 ms
5,376 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 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) { // zał: 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;
}