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 |
 Yu_212
|
| 提出日時 | 2023-12-08 15:56:50 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 1,895 ms / 9,973 ms |
| コード長 | 20,186 bytes |
| コンパイル時間 | 3,852 ms |
| コンパイル使用メモリ | 102,192 KB |
| 実行使用メモリ | 55,700 KB |
| 最終ジャッジ日時 | 2024-09-27 02:51:10 |
| 合計ジャッジ時間 | 10,825 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 10 |
ソースコード
import java.io.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.StreamSupport;
import static java.lang.Math.*;
public class Main {
static In in = new In();
static Out out = new Out(false, false);
static final long inf = 0x1fffffffffffffffL;
static final int iinf = 0x3fffffff;
static final double eps = 1e-9;
static long mod = 998244353;
void solve() {
int n = in.nextInt();
for (int i = 0; i < n; i++) {
long x = in.nextLong();
if (x < 1L << 62) {
out.println(x, PrimeUtils.isPrime(x) ? 1 : 0);
} else {
out.println(x, BigInteger.valueOf(x).isProbablePrime(Integer.MAX_VALUE) ? 1 : 0);
}
}
}
public static void main(String... args) {
new Main().solve();
out.flush();
}
}
class BigMontgomery {
private final long n, r2, nInv;
public BigMontgomery(long n) {
long r2 = (1L << 62) % n;
for (int i = 0; i < 66; i++) {
r2 <<= 1;
if (r2 >= n) {
r2 -= n;
}
}
long nInv = n;
for (int i = 0; i < 5; ++i) {
nInv *= 2 - n * nInv;
}
this.n = n;
this.r2 = r2;
this.nInv = nInv;
}
private static long high(long x, long y) {
return multiplyHigh(x, y) + ((x >> 63) & y) + ((y >> 63) & x);
}
private long mr(long x) {
return high(-nInv * x, n) + (x == 0 ? 0 : 1);
}
private long mr2(long x, long y) {
return high(x, y) + high(-nInv * x * y, n) + (x * y == 0 ? 0 : 1);
}
public long mul(long x, long y) {
long r = mr2(mr2(x, r2), y);
return r < n ? r : r - n;
}
public long pow(long x, long y) {
long z = mr2(x, r2);
long r = 1;
while (y > 0) {
if ((y & 1) == 1) {
r = mr2(r, z);
}
z = mr2(z, z);
y >>= 1;
}
return r < n ? r : r - n;
}
}
class PrimeUtils {
private static final int[] bases = {15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560, 3128, 5212, 2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028, 2213, 6219, 620, 3763, 4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113, 7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556, 2206, 3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344, 17, 15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903, 737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41, 19875, 3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315, 978, 233, 3003, 2562, 2994, 10587, 10030, 2377, 1902, 5354, 4447, 1555, 263, 27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784, 1661, 524, 3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031, 2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336, 579, 165, 1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788, 434, 8085, 17618, 727, 3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183, 8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674, 411, 522, 1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785, 1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42, 4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816, 5197, 13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708, 418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194};
private static final SieveOfEratosthenes sieve = new SieveOfEratosthenes();
private static final int USE_SIEVE_LIMIT = 5000000;
public static int getMinPrimeFactor(int n) {
return sieve.minPrimeFactor(n);
}
public static int getNthPrime(int n) {
return sieve.nthPrime(n);
}
public static boolean isPrime(int n) {
if (n == 2 || n == 3 || n == 5 || n == 7) {
return true;
}
if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) {
return false;
}
if (n < 121) {
return n > 1;
}
long h = n;
h = ((h >> 16) ^ h) * 0x45D9F3B;
h = ((h >> 16) ^ h) * 0x45D9F3B;
h = ((h >> 16) ^ h) & 0xFF;
int a = bases[(int)h];
return millerRabin(n, a, new BigMontgomery(n));
}
private static boolean millerRabin(long n, long a, BigMontgomery bm) {
long d = n - 1;
int s = 0;
while ((d & 1) == 0) {
s++;
d >>= 1;
}
long x = bm.pow(a, d);
if (x == 1) {
return true;
}
for (int r = 0; r < s; r++) {
if (x == n - 1) {
return true;
}
x = bm.mul(x, x);
}
return false;
}
public static boolean isPrime(long n) {
if (n <= Integer.MAX_VALUE) {
return isPrime((int)n);
}
BigMontgomery bm = new BigMontgomery(n);
for (long a : new long[] {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (!millerRabin(n, a, bm)) {
return false;
}
}
return true;
}
public static List<Integer> getPrimesLessThan(int n) {
List<Integer> primes = new ArrayList<>();
for (int prime : sieve) {
if (prime >= n) {
break;
}
primes.add(prime);
}
return primes;
}
public static List<Integer> getNPrimes(int n) {
List<Integer> primes = new ArrayList<>();
for (int i = 0; i < n; i++) {
primes.add(sieve.nthPrime(i));
}
return primes;
}
public static Map<Integer, Integer> factorize(int n) {
if (n <= USE_SIEVE_LIMIT) {
return factorize0(n);
} else {
return factorize1(n);
}
}
// O(N + Q * logN)
private static Map<Integer, Integer> factorize0(int n) {
Map<Integer, Integer> primeFactors = new LinkedHashMap<>();
while (n > 1) {
int primeFactor = getMinPrimeFactor(n);
int count = 0;
while (getMinPrimeFactor(n) == primeFactor) {
count++;
n /= primeFactor;
}
primeFactors.put(primeFactor, count);
}
return primeFactors;
}
// O(√N + Q * √N / logN)
private static Map<Integer, Integer> factorize1(int n) {
Map<Integer, Integer> primeFactors = new LinkedHashMap<>();
int c = n;
for (int prime : sieve) {
int count = 0;
while (c % prime == 0) {
count++;
c /= prime;
}
if (count > 0) {
primeFactors.put(prime, count);
}
if (prime * prime >= n) {
break;
}
}
if (c > 1) {
primeFactors.put(c, 1);
}
return primeFactors;
}
public static List<Integer> divisors(int n) {
List<Integer> divisors = new ArrayList<>();
divisors.add(1);
Map<Integer, Integer> primeFactors = factorize(n);
for (Map.Entry<Integer, Integer> entry : primeFactors.entrySet()) {
int exp = entry.getValue();
int s = divisors.size();
for (int i = 0; i < s; i++) {
int v = 1;
for (int j = 0; j < exp; j++) {
v *= entry.getKey();
divisors.add(divisors.get(i) * v);
}
}
}
Collections.sort(divisors);
return divisors;
}
}
class SieveOfEratosthenes implements Iterable<Integer> {
private final List<Integer> primes = new ArrayList<>();
private int[] table;
public SieveOfEratosthenes() {
this(1000);
}
public SieveOfEratosthenes(int initialCapacity) {
calcTable(initialCapacity);
}
private void calcTable(int n) {
int oldCapacity = 0;
int[] newTable = new int[n];
if (table != null) {
oldCapacity = table.length;
System.arraycopy(table, 0, newTable, 0, oldCapacity);
}
table = newTable;
for (int i = oldCapacity; i < n; i++) {
table[i] = i;
}
for (int i = 2; i < n; i++) {
if (i >= oldCapacity && table[i] == i) {
primes.add(i);
}
for (int prime : primes) {
if (prime > table[i] || (long)prime * i >= n) {
break;
}
table[prime * i] = prime;
}
}
}
private void grow(int minCapacity) {
int oldCapacity = table.length;
int newCapacity = (int)min(Integer.MAX_VALUE, max(minCapacity, (long)oldCapacity + (oldCapacity >> 1)));
calcTable(newCapacity);
}
public int minPrimeFactor(int n) {
if (table.length <= n) {
grow(n + 1);
}
return table[n];
}
public int nthPrime(int n) {
while (primes.size() <= n) {
grow(table.length + 1);
}
return primes.get(n);
}
public int countLessThan(int n) {
while (primes.get(primes.size() - 1) < n) {
grow(table.length + 1);
}
int left = -1;
int right = primes.size();
while (right - left > 1) {
int mid = (left + right) / 2;
if (primes.get(mid) < n) {
left = mid;
} else {
right = mid;
}
}
return right;
}
public Map<Integer, Integer> factorize(int n) {
Map<Integer, Integer> primeFactors = new LinkedHashMap<>();
while (n > 1) {
int primeFactor = minPrimeFactor(n);
int exp = 0;
while (n % primeFactor == 0) {
n /= primeFactor;
exp++;
}
primeFactors.put(primeFactor, exp);
}
return primeFactors;
}
public long sumOfDivisors(int n) {
long prod = 1;
while (n > 1) {
int primeFactor = minPrimeFactor(n);
int factor = 1;
long sum = 1;
while (n % primeFactor == 0) {
n /= primeFactor;
factor *= primeFactor;
sum += factor;
}
prod *= sum;
}
return prod;
}
public List<Integer> divisors(int n) {
List<Integer> divisors = new ArrayList<>();
divisors.add(1);
Map<Integer, Integer> primeFactors = factorize(n);
for (Map.Entry<Integer, Integer> entry : primeFactors.entrySet()) {
int exp = entry.getValue();
int s = divisors.size();
for (int i = 0; i < s; i++) {
int v = 1;
for (int j = 0; j < exp; j++) {
v *= entry.getKey();
divisors.add(divisors.get(i) * v);
}
}
}
Collections.sort(divisors);
return divisors;
}
public IntStream stream() {
int characteristics = Spliterator.ORDERED | Spliterator.DISTINCT | Spliterator.SORTED | Spliterator.NONNULL | Spliterator.IMMUTABLE;
Spliterator.OfInt spliterator = Spliterators.spliteratorUnknownSize(iterator(), characteristics);
return StreamSupport.intStream(spliterator, false);
}
@Override
public PrimitiveIterator.OfInt iterator() {
return new PrimitiveIterator.OfInt() {
private int i = 0;
@Override
public int nextInt() {
return nthPrime(i++);
}
@Override
public boolean hasNext() {
return true;
}
};
}
}
class In {
private final BufferedInputStream reader = new BufferedInputStream(System.in);
private final byte[] buffer = new byte[0x10000];
private int i = 0;
private int length = 0;
public int read() {
if (i == length) {
i = 0;
try {
length = reader.read(buffer);
} catch (IOException ignored) {
}
if (length == -1) {
return 0;
}
}
if (length <= i) {
throw new RuntimeException();
}
return buffer[i++];
}
public String next() {
StringBuilder builder = new StringBuilder();
int b = read();
while (b < '!' || '~' < b) {
b = read();
}
while ('!' <= b && b <= '~') {
builder.appendCodePoint(b);
b = read();
}
return builder.toString();
}
public String nextLine() {
StringBuilder builder = new StringBuilder();
int b = read();
while (b != 0 && b != '\r' && b != '\n') {
builder.appendCodePoint(b);
b = read();
}
if (b == '\r') {
read();
}
return builder.toString();
}
public int nextInt() {
long val = nextLong();
if (val < Integer.MIN_VALUE || Integer.MAX_VALUE < val) {
throw new NumberFormatException();
}
return (int)val;
}
public long nextLong() {
int b = read();
while (b < '!' || '~' < b) {
b = read();
}
boolean neg = false;
if (b == '-') {
neg = true;
b = read();
}
long n = 0;
int c = 0;
while ('0' <= b && b <= '9') {
n = n * 10 + b - '0';
b = read();
c++;
}
if (c == 0 || c >= 2 && n == 0) {
throw new NumberFormatException();
}
return neg ? -n : n;
}
public double nextDouble() {
return Double.parseDouble(next());
}
public char[] nextCharArray() {
return next().toCharArray();
}
public String[] nextStringArray(int n) {
String[] s = new String[n];
for (int i = 0; i < n; i++) {
s[i] = next();
}
return s;
}
public char[][] nextCharMatrix(int n, int m) {
char[][] a = new char[n][m];
for (int i = 0; i < n; i++) {
a[i] = next().toCharArray();
}
return a;
}
public int[] nextIntArray(int n) {
int[] a = new int[n];
for (int i = 0; i < n; i++) {
a[i] = nextInt();
}
return a;
}
public int[] nextIntArray(int n, IntUnaryOperator op) {
int[] a = new int[n];
for (int i = 0; i < n; i++) {
a[i] = op.applyAsInt(nextInt());
}
return a;
}
public int[][] nextIntMatrix(int h, int w) {
int[][] a = new int[h][w];
for (int i = 0; i < h; i++) {
a[i] = nextIntArray(w);
}
return a;
}
public long[] nextLongArray(int n) {
long[] a = new long[n];
for (int i = 0; i < n; i++) {
a[i] = nextLong();
}
return a;
}
public long[] nextLongArray(int n, LongUnaryOperator op) {
long[] a = new long[n];
for (int i = 0; i < n; i++) {
a[i] = op.applyAsLong(nextLong());
}
return a;
}
public long[][] nextLongMatrix(int h, int w) {
long[][] a = new long[h][w];
for (int i = 0; i < h; i++) {
a[i] = nextLongArray(w);
}
return a;
}
public List<List<Integer>> nextGraph(int n, int m, boolean directed) {
List<List<Integer>> res = new ArrayList<>();
for (int i = 0; i < n; i++) {
res.add(new ArrayList<>());
}
for (int i = 0; i < m; i++) {
int u = nextInt() - 1;
int v = nextInt() - 1;
res.get(u).add(v);
if (!directed) {
res.get(v).add(u);
}
}
return res;
}
}
class Out {
private final PrintWriter out = new PrintWriter(System.out);
private final PrintWriter err = new PrintWriter(System.err);
public boolean autoFlush;
public boolean enableDebug;
public Out(boolean autoFlush, boolean enableDebug) {
this.autoFlush = autoFlush;
this.enableDebug = enableDebug;
}
public void debug(Object... args) {
if (!enableDebug) {
return;
}
if (args == null || args.getClass() != Object[].class) {
args = new Object[] {args};
}
StackTraceElement stackTrace = Thread.currentThread().getStackTrace()[2];
err.print(String.format("[%40s] ", stackTrace.toString()));
err.println(Arrays.stream(args).map(obj -> format(obj, true)).collect(Collectors.joining(" ")));
err.flush();
}
private String format(Object obj, boolean canMultiline) {
if (obj == null) return "null";
Class<?> clazz = obj.getClass();
if (clazz == Double.class) return String.format("%.10f", obj);
if (clazz == int[].class) return Arrays.toString((int[])obj);
if (clazz == long[].class) return Arrays.toString((long[])obj);
if (clazz == char[].class) return String.valueOf((char[])obj);
if (clazz == boolean[].class) return IntStream.range(0, ((boolean[])obj).length).mapToObj(i -> ((boolean[])obj)[i] ? "1" : "0").collect(Collectors.joining());
if (clazz == double[].class) return Arrays.toString(Arrays.stream((double[])obj).mapToObj(a -> format(a, false)).toArray());
if (canMultiline && clazz.isArray() && clazz.componentType().isArray()) return Arrays.stream((Object[])obj).map(a -> format(a, false)).collect(Collectors.joining("\n"));
if (clazz == Object[].class) return Arrays.toString(Arrays.stream((Object[])obj).map(a -> format(a, false)).toArray());
if (clazz.isArray()) return Arrays.toString((Object[])obj);
return String.valueOf(obj);
}
public void println(Object... args) {
if (args == null || args.getClass() != Object[].class) {
args = new Object[] {args};
}
out.println(Arrays.stream(args)
.map(obj -> obj instanceof Double ? String.format("%.10f", obj) : String.valueOf(obj))
.collect(Collectors.joining(" ")));
if (autoFlush) {
out.flush();
}
}
public void println(char a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(int a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(long a) {
out.println(a);
if (autoFlush) {
out.flush();
}
}
public void println(double a) {
out.println(String.format("%.10f", a));
if (autoFlush) {
out.flush();
}
}
public void println(String s) {
out.println(s);
if (autoFlush) {
out.flush();
}
}
public void println(char[] s) {
out.println(String.valueOf(s));
if (autoFlush) {
out.flush();
}
}
public void println(int[] a) {
StringJoiner joiner = new StringJoiner(" ");
for (int i : a) {
joiner.add(Integer.toString(i));
}
out.println(joiner);
if (autoFlush) {
out.flush();
}
}
public void println(long[] a) {
StringJoiner joiner = new StringJoiner(" ");
for (long i : a) {
joiner.add(Long.toString(i));
}
out.println(joiner);
if (autoFlush) {
out.flush();
}
}
public void flush() {
err.flush();
out.flush();
}
}