#595167 (Java21) No.1322 Totient Bound

提出ソース

結果

問題	No.1322 Totient Bound
ユーザー	uwi
提出日時	2020-12-19 01:10:09
言語	Java21 (openjdk 21)
結果	AC
実行時間	2,342 ms / 5,000 ms
コード長	14,049 bytes
コンパイル時間	4,906 ms
コンパイル使用メモリ	92,696 KB
実行使用メモリ	55,060 KB
最終ジャッジ日時	2024-09-21 09:36:31
合計ジャッジ時間	44,543 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

このコードへのチャレンジ
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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	81 ms 38,104 KB
testcase_01	AC	93 ms 38,160 KB
testcase_02	AC	88 ms 38,564 KB
testcase_03	AC	84 ms 38,328 KB
testcase_04	AC	83 ms 38,040 KB
testcase_05	AC	83 ms 38,104 KB
testcase_06	AC	86 ms 38,124 KB
testcase_07	AC	82 ms 37,832 KB
testcase_08	AC	84 ms 38,092 KB
testcase_09	AC	82 ms 37,796 KB
testcase_10	AC	87 ms 38,272 KB
testcase_11	AC	83 ms 38,404 KB
testcase_12	AC	83 ms 38,112 KB
testcase_13	AC	180 ms 42,528 KB
testcase_14	AC	187 ms 42,148 KB
testcase_15	AC	156 ms 41,432 KB
testcase_16	AC	171 ms 41,756 KB
testcase_17	AC	160 ms 41,280 KB
testcase_18	AC	865 ms 52,060 KB
testcase_19	AC	1,009 ms 52,672 KB
testcase_20	AC	2,049 ms 53,504 KB
testcase_21	AC	2,063 ms 54,500 KB
testcase_22	AC	1,898 ms 54,440 KB
testcase_23	AC	2,062 ms 54,052 KB
testcase_24	AC	2,093 ms 54,036 KB
testcase_25	AC	1,994 ms 53,940 KB
testcase_26	AC	2,084 ms 54,780 KB
testcase_27	AC	2,135 ms 53,988 KB
testcase_28	AC	2,120 ms 53,920 KB
testcase_29	AC	1,994 ms 53,992 KB
testcase_30	AC	81 ms 37,960 KB
testcase_31	AC	79 ms 37,984 KB
testcase_32	AC	81 ms 38,208 KB
testcase_33	AC	2,286 ms 55,060 KB
testcase_34	AC	2,278 ms 54,616 KB
testcase_35	AC	2,033 ms 53,528 KB
testcase_36	AC	2,342 ms 54,628 KB
testcase_37	AC	2,226 ms 54,688 KB
testcase_38	AC	2,220 ms 54,784 KB

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ソースコード

raw source code

package adv2020;

import java.io.*;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.LongUnaryOperator;

public class Day19_2 {
	InputStream is;
	FastWriter out;

	String INPUT = "";

	long[][] pr;
	long N;
	int[] primes = sieveEratosthenes(120000);

	long f(long n, long div, int pid)
	{
		if(pid >= primes.length || n < primes[pid]-1){
			return 1L;
		}
		long ans = 0;
		int x = pid;
		for(;n >= (long)(primes[x]-1)*(primes[x]-1);x++) {
			int p = primes[x];
			long m = n / (p-1);
			long nd = div * (p-1);
			while (m > 0) {
				ans += f(m, nd, x + 1);
				m /= p;
				nd *= p;
			}
		}
		ans += ((double)div*div <= N && div*div <= N ? pr[1][(int)div] : pr[0][(int)n]) - x + 1;
//		tr(n,div, x,  primes[x], (div*div <= N+1 ? pr[1][(int)div] : pr[0][(int)n]) - x, ans, pr[0] ,pr[1]);

		return ans;
	}

	public void solve()
	{
		long n = nl();
		N = n;
		pr = countsPrime(n);
		int[] primes = sieveEratosthenes(pr[0].length+1);
		for(int i = 1;i < pr[0].length;i++){
			if(Arrays.binarySearch(primes, i+1) >= 0){
				pr[0][i]++;
			}
		}
		for(int i = 1;i < pr[1].length;i++){
			if(BigInteger.valueOf(n/i+1).isProbablePrime(20)){
				pr[1][i]++;
			}
		}
		// 2*10^12ぐらい
		// phi(x)<=n
		// phi(3x) = 2phi(x)
		// f(n,p)=f(n,np) + f(n/(p-1),np) + f(n/p(p-1),np) + ...
		// f(n,p)=1 if n<p-1
		// big p
		// n/(p-1) < np-1
		// n/(p-1) < p-1
		// n < (p-1)^2
		//
		// f(n,p)=f(n,np) + f(n/(p-1),np) = f(n,np)+1
		// f(n,p)=f(n,nnp) + 2
		// f(n,p)=pi(n)-pi(p) + 1?
		out.println(f(n, 1, 0));
	}

	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);
	}


	public static long[][] countsPrime(long n)
	{
		return sumsOnPrimes(n, x -> 1, x -> x);
	}

	public static long[][] sumsOnPrimes(long n, LongUnaryOperator f, LongUnaryOperator S)
	{
		int B = (int)Math.sqrt(n);
		int[] primes = sieveEratosthenes(B);
		long[] low = new long[B+1];
		long[] high = new long[B+1];
		for(int i = 1;i <= B;i++) {
			low[i] = S.applyAsLong(i);
			high[i] = S.applyAsLong(n/i);
		}
		for(int p : primes) {
			long fp = f.applyAsLong(p);
			int isup = (int)Math.min(n/p/p, B);
			for(int i = 1;i <= isup;i++) {
				if((long)i*p <= B) {
					high[i] -= fp * (high[i*p] - low[p-1]);
				}else {
					high[i] -= fp * (low[(int)(n/i/p)] - low[p-1]);
				}
			}
			for(int i = B;i >= (long)p*p;i--) {
				low[i] -= fp * (low[i/p] - low[p-1]);
			}
		}
		for(int i = 1;i <= B;i++) {
			low[i]--;
			high[i]--;
		}
		return new long[][] {low, high};
	}

	public static void main(String[] args) {
		new Day19_2().run();
	}

	public void run()
	{
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);

		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
		//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
		//			@Override
		//			public void run() {
		//				long s = System.currentTimeMillis();
		//				solve();
		//				out.flush();
		//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
		//			}
		//		};
		//		t.start();
		//		t.join();
	}

	private boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;

		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}

	private final byte[] inbuf = new byte[1024];
	public 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 boolean isSpaceChar(int c) { return !(c >= 32 && 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))){
			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 long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		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();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public static void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public static void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public static void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public static void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}

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結果

テストケース

ソースコード