結果
問題 | No.1039 Project Euler でやれ |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 18 |
ソースコード
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 primereturn 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)); }}