結果

問題 No.577 Prime Powerful Numbers
ユーザー 37zigen37zigen
提出日時 2017-10-14 14:57:57
言語 Java21
(openjdk 21)
結果
TLE  
実行時間 -
コード長 4,653 bytes
コンパイル時間 3,377 ms
コンパイル使用メモリ 79,496 KB
実行使用メモリ 78,776 KB
最終ジャッジ日時 2024-11-17 18:43:36
合計ジャッジ時間 18,708 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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 95 ms
42,972 KB
testcase_01 AC 543 ms
78,776 KB
testcase_02 AC 56 ms
42,120 KB
testcase_03 TLE -
testcase_04 AC 124 ms
37,628 KB
testcase_05 TLE -
testcase_06 AC 883 ms
38,880 KB
testcase_07 TLE -
testcase_08 AC 1,830 ms
38,596 KB
testcase_09 TLE -
testcase_10 AC 54 ms
76,868 KB
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ソースコード

diff # 

import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		new Main().run();
	}

	// n = p^aで表せるか判定
	boolean check2(long n) {
		if (isPrime(n))
			return true;
		long fa = factor(n);
		while (!isPrime(fa))
			fa = factor(fa);
		while (n % fa == 0)
			n /= fa;
		if (n != 1)
			return false;
		else
			return true;
	}

	boolean check(long n) {
		if (n == 1 || n == 2 || n == 3) {
			return false;
		}
		if (n % 2 == 0) {
			return true;
		}
		for (int i = 0; i < 63; ++i) {
			long m = n - (1L << i);
			if (m < 0) {
				return false;
			}
			if (check2(m)) {
				return true;
			}
		}
		throw new AssertionError();
	}

	long factor(long n) {
		if (n < 1e6) {
			for (int i = 2; i * i <= n; ++i) {
				if (n % i == 0)
					return i;
			}
			throw new AssertionError();
		}
		for (int i = 2; i < 1000; ++i) {
			if (n % i == 0)
				return i;
		}
		int Lim = (int) (Math.sqrt(Math.sqrt(n)));
		for (int c = 1; c < 200; ++c) {
			long x = 2;
			long y = (x * x + c) % n;
			for (int t = 0; t < Lim; ++t) {
				long g = gcd(n, Math.abs(x - y));
				if (g != 1 && g != n)
					return g;
				if (g == n)
					break;
				x = (mul_mod(x, x, n) + c) % n;
				y = (mul_mod(y, y, n) + c) % n;
				y = (mul_mod(y, y, n) + c) % n;
			}
		}
		tr(n);
		throw new AssertionError();
	}

	boolean isPrime(long n) {
		if (n == 1)
			return false;
		if (n < 1000) {
			for (int i = 2; i * i <= n; ++i) {
				if (n % i == 0)
					return false;
			}
			return true;
		}
		if (n % 2 == 0)
			return false;

		long m = n - 1;
		int c = 0;
		while (m % 2 == 0) {
			m /= 2;
			++c;
		}
		for (int i = 0; i < 20; ++i) {
			long a = (long) (Math.random() * (n - 1)) + 1;
			a = pow(a, m, n);
			boolean f = a == 1 || (c > 0 && a == n - 1);
			for (int j = 0; j < c - 1; ++j) {
				a = mul_mod(a, a, n);
				f |= a == n - 1;
			}
			if (!f)
				return false;
		}
		return true;
	}

	long pow(long a, long n, long mod) {
		long ret = 1;
		for (; n > 0; n >>= 1, a = mul_mod(a, a, mod)) {
			if (n % 2 == 1) {
				ret = mul_mod(ret, a, mod);
			}
		}
		return ret;
	}

	long gcd(long a, long b) {
		if (a > b) {
			return gcd(b, a);
		}
		if (a == 0)
			return b;
		return gcd(b % a, a);
	}

	long mul_mod(long a, long b, long mod) {
		long ret = 0;
		while (b > 0) {
			if (b % 2 == 0) {
				a = 2 * a % mod;
				b /= 2;
				// a*b=2*a*b/2
			} else {
				// a*b=a*(2b'+1)
				ret = (ret + a) % mod;
				a = 2 * a % mod;
				b /= 2;
			}
		}
		return ret;
	}

	void run() {
		Scanner sc = new Scanner();
		int Q = sc.nextInt();
		PrintWriter pw = new PrintWriter(System.out);
		while (Q-- > 0) {
			long n = sc.nextLong();
			pw.println(check(n) ? "Yes" : "No");
		}
		pw.close();
	}

	class Scanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;

		private boolean hasNextByte() {
			if (ptr < buflen) {
				return true;
			} else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) {
					return false;
				}
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[ptr++];
			else
				return -1;
		}

		private boolean isPrintableChar(int c) {
			return 33 <= c && c <= 126;
		}

		private void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr]))
				ptr++;
		}

		public boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

		public int nextInt() {
			return (int) nextLong();
		}
	}

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}
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