#18865 (Java21) No.181 A↑↑N mod M

提出ソース

結果

問題	No.181 A↑↑N mod M
ユーザー	uwi
提出日時	2015-04-06 01:56:55
言語	Java21 (openjdk 21)
結果	AC
実行時間	45 ms / 5,000 ms
コード長	5,269 bytes
コンパイル時間	4,196 ms
コンパイル使用メモリ	77,972 KB
実行使用メモリ	49,620 KB
最終ジャッジ日時	2023-08-15 18:55:24
合計ジャッジ時間	7,716 ms
ジャッジサーバーID （参考情報）	judge14 / judge13

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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	42 ms 49,048 KB
testcase_01	AC	43 ms 49,148 KB
testcase_02	AC	43 ms 49,204 KB
testcase_03	AC	42 ms 49,200 KB
testcase_04	AC	42 ms 48,948 KB
testcase_05	AC	42 ms 49,320 KB
testcase_06	AC	43 ms 49,104 KB
testcase_07	AC	43 ms 49,092 KB
testcase_08	AC	43 ms 49,116 KB
testcase_09	AC	42 ms 49,276 KB
testcase_10	AC	43 ms 49,204 KB
testcase_11	AC	43 ms 49,156 KB
testcase_12	AC	43 ms 49,168 KB
testcase_13	AC	43 ms 49,192 KB
testcase_14	AC	42 ms 49,620 KB
testcase_15	AC	42 ms 49,168 KB
testcase_16	AC	43 ms 49,036 KB
testcase_17	AC	42 ms 49,012 KB
testcase_18	AC	42 ms 49,424 KB
testcase_19	AC	42 ms 49,108 KB
testcase_20	AC	45 ms 49,080 KB
testcase_21	AC	42 ms 49,032 KB
testcase_22	AC	43 ms 49,024 KB
testcase_23	AC	44 ms 49,504 KB
testcase_24	AC	43 ms 49,264 KB
testcase_25	AC	43 ms 49,024 KB
testcase_26	AC	43 ms 49,144 KB
testcase_27	AC	43 ms 49,448 KB
testcase_28	AC	44 ms 49,232 KB
testcase_29	AC	43 ms 49,228 KB
testcase_30	AC	44 ms 49,120 KB
testcase_31	AC	43 ms 49,100 KB
testcase_32	AC	43 ms 48,968 KB
testcase_33	AC	43 ms 49,344 KB
testcase_34	AC	44 ms 49,216 KB
testcase_35	AC	43 ms 49,196 KB
testcase_36	AC	43 ms 49,096 KB
testcase_37	AC	43 ms 49,036 KB
testcase_38	AC	43 ms 49,056 KB
testcase_39	AC	43 ms 49,456 KB
testcase_40	AC	44 ms 49,212 KB
testcase_41	AC	44 ms 49,088 KB
testcase_42	AC	42 ms 49,152 KB

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ソースコード

raw source code

package q4xx;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Q472 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	int[] primes = sieveEratosthenes(2000);
	
	void solve()
	{
		long a = nl(), n = nl();
		int m = ni();
		out.println(dfs(a, n, m));
	}
	
	long dfs(long a, long n, int m)
	{
		if(n == 0){
			return 1 % m;
		}
		if(m == 1){
			return 0;
		}
		if(a == 1){
			return 1 % m;
		}
		
		int t = (int)totient(m, primes);
		long e = dfs(a, n-1, t);
		
		if(n-1 > 0){
			double x = a;
			if(x > t){
				e += t;
			}else{
				for(long u = n-1;u > 0;u--){
					x = Math.pow(a, x);
					if(Double.isInfinite(x) || x > t){
						e += t;
						break;
					}
				}
			}
		}
		
		return pow(a, e, m);
	}
	
	public static long pow(long a, long n, long mod) {
		//		a %= mod;
		long ret = 1;
		int x = 63 - Long.numberOfLeadingZeros(n);
		for (; x >= 0; x--) {
			ret = ret * ret % mod;
			if (n << 63 - x < 0)
				ret = ret * a % mod;
		}
		return ret;
	}
	
	public static long totient(long n, int[] primes)
	{
		long ret = n;
		for(int p : primes){
			if((long)p * p > n)break;
			if(n % p == 0){
				ret /= p;
				ret *= p - 1;
			}
			while(n % p == 0)n /= p;
		}
		if(n != 1){
			ret /= n;
			ret *= n - 1;
		}
		return ret;
	}

	public static int[] sieveEratosthenes(int n) {
		if (n <= 32) {
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for (int i = 0; i < primes.length; i++) {
				if (n < primes[i]) {
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isnp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for (int tp : tprimes) {
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for (int i = (tp - 3) / 2; i < tp << 5; i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for (int j = 0; j < sup; j += tp) {
				for (int i = 0; i < tp && i + j < sup; i++) {
					isnp[j + i] |= ptn[i];
				}
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4,
				13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for (int i = 0; i < sup; i++) {
			for (int j = ~isnp[i]; j != 0; j &= j - 1) {
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if (p > n)
					break;
				ret[pos++] = p;
				if ((long) p * p > n)
					continue;
				for (int q = (p * p - 3) / 2; q <= h; q += p)
					isnp[q >> 5] |= 1 << q;
			}
		}

		return Arrays.copyOf(ret, pos);
	}
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new Q472().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}

yukicoder

結果

テストケース

ソースコード