結果

問題 No.1039 Project Euler でやれ
ユーザー uwiuwi
提出日時 2020-04-24 23:06:02
言語 Java21
(openjdk 21)
結果
AC  
実行時間 106 ms / 2,000 ms
コード長 5,931 bytes
コンパイル時間 3,588 ms
コンパイル使用メモリ 82,888 KB
実行使用メモリ 55,240 KB
最終ジャッジ日時 2023-08-07 21:34:52
合計ジャッジ時間 5,840 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge15
このコードへのチャレンジ（β）

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 65 ms
51,864 KB
testcase_01 AC 106 ms
54,588 KB
testcase_02 AC 87 ms
53,452 KB
testcase_03 AC 89 ms
55,216 KB
testcase_04 AC 91 ms
55,240 KB
testcase_05 AC 92 ms
53,524 KB
testcase_06 AC 75 ms
53,164 KB
testcase_07 AC 50 ms
49,344 KB
testcase_08 AC 67 ms
50,976 KB
testcase_09 AC 75 ms
53,196 KB
testcase_10 AC 50 ms
49,152 KB
testcase_11 AC 81 ms
53,264 KB
testcase_12 AC 62 ms
50,764 KB
testcase_13 AC 41 ms
49,360 KB
testcase_14 AC 74 ms
53,132 KB
testcase_15 AC 79 ms
53,136 KB
testcase_16 AC 40 ms
49,664 KB
testcase_17 AC 42 ms
49,260 KB
testcase_18 AC 40 ms
49,348 KB
testcase_19 AC 40 ms
49,228 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

package contest200424;
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 G {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		/*
\# Aut(C_{p^n}^k)=p^{(n-1)k^2}\prod_{j=0}^{k-1} (p^{k}-p^{j})
		 * 
		 */
		int n = ni();
		int[] lpf = enumLowestPrimeFactors(n);
		int mod = 1000000007;
		int[][] f = factorFast(n, lpf);
		
		long ans = 1;
		for(int i = 0;i < f.length;i++){
			int P = f[i][0], E = f[i][1];
			ans = ans * aut(P, E, mod) % mod;
		}
		for(int i = 1;i <= n;i++){
			ans = ans * i % mod;
		}
		out.println(ans);
	}
	
	long aut(int P, int E, int mod)
	{
		ans = 0;
		dfs(P, E, 1, E, mod, new int[E+1]);
		int q = (int)Math.pow(P, E);
		ans %= mod;
//		for(int i = 1;i <= q;i++){
//			ans = ans * i % mod;
//		}
		return ans;
	}
	
	long ans = 0;
	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}


	
	void dfs(int P, int rem, int e, int E, int mod, int[] es)
	{
		if(e == E+1){
			if(rem > 0)return;
			long ret = 1;
			long pe = 0;
			for(int i = 1;i <= E;i++){
				pe += (i-1)*es[i]*es[i];
				for(int j = 0;j < es[i];j++){
					ret = ret * (pow(P, es[i], mod) - pow(P, j, mod) + mod) % mod;
				}
				long lpe = 0;
				for(int j = 1;j <= E;j++){
					if(i != j){
						lpe += Math.min(i, j) * es[j];
					}
				}
				pe += lpe * es[i];
			}
			ret = ret * pow(P, pe, mod) % mod;
			ans += invl(ret, mod);
			return;
		}
		
		for(int i = 0;i*e <= rem;i++){
			es[e] = i;
			dfs(P, rem-i*e, e+1, E, mod, es);
			es[e] = 0;
		}
	}
	
	public static int[] enumDivisorsFast(int n, int[] lpf)
	{
		int[] divs = {1};
		while(lpf[n] > 0){
			int p = lpf[n];
			int e = 0;
			for(;p == lpf[n];e++, n /= p);
			int olen = divs.length;
			divs = Arrays.copyOf(divs, olen*(e+1));
			for(int i = olen;i < divs.length;i++)divs[i] = divs[i-olen] * p;
		}
		return divs;
	}
	

	
	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 int[][] factorFast(int n, int[] lpf)
	{
		int[][] f = new int[9][];
		int q = 0;
		while(lpf[n] > 0){
			int p = lpf[n];
			if(q == 0 || p != f[q-1][0]){
				f[q++] = new int[]{p, 1};
			}else{
				f[q-1][1]++;
			}
			n /= p;
		}
		if(n > 1){
			// big prime
			return new int[][]{{n, 1}};
		}
		return Arrays.copyOf(f, q);
	}

	
	public static int[] enumLowestPrimeFactors(int n) {
		int tot = 0;
		int[] lpf = new int[n + 1];
		int u = n + 32;
		double lu = Math.log(u);
		int[] primes = new int[(int) (u / lu + u / lu / lu * 1.5)];
		for (int i = 2; i <= n; i++)
			lpf[i] = i;
		for (int p = 2; p <= n; p++) {
			if (lpf[p] == p)
				primes[tot++] = p;
			int tmp;
			for (int i = 0; i < tot && primes[i] <= lpf[p] && (tmp = primes[i] * p) <= n; i++) {
				lpf[tmp] = primes[i];
			}
		}
		return lpf;
	}

	
	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");
//		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();
	}
	
	public static void main(String[] args) throws Exception { new G().run(); }
	
	private 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 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 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 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[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	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)); }
}
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