結果

問題 No.1039 Project Euler でやれ
ユーザー uwi
提出日時 2020-04-24 23:06:02
言語 Java
(openjdk 23)
結果
AC  
実行時間 125 ms / 2,000 ms
コード長 5,931 bytes
コンパイル時間 4,132 ms
コンパイル使用メモリ 83,112 KB
実行使用メモリ 42,816 KB
最終ジャッジ日時 2024-11-08 02:59:05
合計ジャッジ時間 6,674 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 18
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 #
プレゼンテーションモードにする

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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