結果
問題 | No.1322 Totient Bound |
ユーザー |
|
提出日時 | 2020-12-19 01:09:15 |
言語 | Java (openjdk 23) |
結果 |
WA
|
実行時間 | - |
コード長 | 14,037 bytes |
コンパイル時間 | 5,001 ms |
コンパイル使用メモリ | 92,936 KB |
実行使用メモリ | 55,140 KB |
最終ジャッジ日時 | 2024-09-21 09:35:16 |
合計ジャッジ時間 | 41,524 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 23 WA * 13 |
ソースコード
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 += (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=nint[] 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 1public 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)); }}