結果
| 問題 |
No.1498 Factorization from -1 to 1
|
| ユーザー |
 ゆうき
|
| 提出日時 | 2023-10-11 01:14:37 |
| 言語 | Java (openjdk 23) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 13,721 bytes |
| コンパイル時間 | 3,580 ms |
| コンパイル使用メモリ | 100,056 KB |
| 実行使用メモリ | 114,588 KB |
| 最終ジャッジ日時 | 2024-09-13 01:30:51 |
| 合計ジャッジ時間 | 12,628 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 -- * 3 |
| other | AC * 1 TLE * 1 -- * 15 |
ソースコード
import static java.lang.Math.*;
import static java.util.Arrays.*;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.function.*;
import java.util.stream.IntStream;
class Solver{
long st = System.currentTimeMillis();
long elapsed(){ return System.currentTimeMillis() -st; }
void reset(){ st = System.currentTimeMillis(); }
final static int infI = (1 <<30) -1;
final static long infL = 1L <<60;
// final static long mod = (int) 1e9 +7;
final static long mod = 998244353;
final static String yes = "Yes";
final static String no = "No";
MyReader in = new MyReader(System.in);
MyWriter out = new MyWriter(System.out);
MyWriter log = new MyWriter(System.err){
@Override
void println(Object obj){ super.println(obj == null ? "null" : obj); };
@Override
protected void ln(){
super.ln();
flush();
};
};
Object solve(){
Prime pm = new Prime();
int Q = in.it();
while (Q-- > 0) {
long n = in.lg();
out.println(pm.factorize(n *n +1).stream().mapToLong(a -> a).toArray());
}
return null;
}
int bSearchI(int o,int n,Predicate<Integer> judge){
if (!judge.test(o))
return o -(n -o) /abs(n -o);
for (int c = 0;1 < abs(n -o);)
if (judge.test(c = o +n >>1))
o = c;
else
n = c;
return o;
}
}
class Prime{
BitSet primes;
int[] spf;
BigInteger[] A;
Prime(){ this(10_000_000); }
Prime(int n){
primes = new BitSet();
primes.set(2,n +1);
spf = Util.arrI(n +1,i -> i);
for (int p = 2;p *p <= n;p++)
if (primes.get(p))
for (int nn = p *p;nn <= n;primes.clear(nn),nn += p)
spf[nn] = p;
A = IntStream.of(2,325,9375,28178,450775,9780504,1795265022).mapToObj(BigInteger::valueOf)
.toArray(nn -> new BigInteger[nn]);
}
boolean isPrime(long n){
if (n < spf.length)
return primes.get((int) n);
if ((n &1) == 0)
return false;
if (n < 3e9) {
long lsb = Long.lowestOneBit(n -1);
long m = (n -1) /lsb;
a:for (var ba:A) {
long z = pow(ba.longValue(),m,n);
if (z <= 1)
continue;
for (long k = 1;k <= lsb;k <<= 1) {
if (z == n -1)
continue a;
z = pow(z,2,n);
}
return false;
}
} else {
BigInteger bn = BigInteger.valueOf(n);
long lsb = Long.lowestOneBit(n -1);
BigInteger m = BigInteger.valueOf((n -1) /lsb);
a:for (var ba:A) {
BigInteger z = ba.modPow(m,bn);
if (z.longValue() <= 1)
continue;
for (long k = 1;k <= lsb;k <<= 1) {
if (z.longValue() == n -1)
continue a;
z = z.modPow(BigInteger.TWO,bn);
}
return false;
}
}
return true;
}
long pow(long x,long n,long mod){
x %= mod;
long ret = 1;
do {
if ((n &1) == 1)
ret = ret *x %mod;
x = x *x %mod;
} while (0 < (n >>= 1));
return ret;
}
List<Long> factorize(long n){
if (n < 2)
return List.of();
List<Long> ret = new ArrayList<>();
long[] stk = new long[100];
int s = 0;
stk[++s] = n;
while (0 < s) {
long cur = stk[s--];
if (isPrime(cur))
ret.add(cur);
else {
var p = pollard(cur);
stk[++s] = p;
stk[++s] = cur /p;
}
}
Collections.sort(ret);
return ret;
}
// long[] divisors(long n){
// List<long[]> facts = factorize(n);
// int l = 1;
// for (var f:factorize(n))
// l *= f[1] +1;
//
// long[] ret = new long[l];
// int id = 1;
// ret[0] = 1;
// for (var f:facts) {
// long p = f[0];
// for (;f[1]-- > 0;p *= f[0])
// for (int j = 0;ret[j] != f[0];j++)
// ret[id++] = ret[j] *p;
// }
//
// return ret;
// }
long gcd(long a,long b){
while (0 < b) {
long t = a;
a = b;
b = t %b;
}
return a;
}
long pollard(long n){
if (n < spf.length)
return spf[(int) n];
BigInteger bn = BigInteger.valueOf(n);
LongUnaryOperator f = x -> x < Solver.infI ? x *x %n
: BigInteger.valueOf(x).modPow(BigInteger.TWO,bn).longValue();
long step = 0;
while (true) {
long x = ++step,y = f.applyAsLong(x);
while (true) {
long p = gcd(y -x +n,n);
if (p == 0 || p == n)
break;
if (p != 1)
return p;
x = f.applyAsLong(x);
y = f.applyAsLong(f.applyAsLong(y));
}
}
}
}
class Combin{
int n = 2;
long[] fac,finv,inv;
long mod = Solver.mod;
Combin(){ fac = finv = inv = new long[]{1, 1}; }
void grow(int n){
fac = copyOf(fac,n);
finv = copyOf(finv,n);
inv = copyOf(inv,n);
for (int i = this.n;i < n;i++) {
fac[i] = fac[i -1] *i %mod;
inv[i] = mod -inv[(int) (mod %i)] *(mod /i) %mod;
finv[i] = finv[i -1] *inv[i] %mod;
}
this.n = n;
}
long nHr(int n,int r){ return r < 0 ? 0 : nCr(n +r -1,r); }
long nCr(int n,int r){
if (r < 0 || n -r < 0)
return 0;
if (this.n <= n)
grow(n <<1);
return fac[n] *(finv[r] *finv[n -r] %mod) %mod;
}
}
class Sum{
long[] sum;
public Sum(long[] A){
sum = new long[A.length +1];
for (int i = 0;i < A.length;i++)
sum[i +1] = (sum[i] +A[i]) %Solver.mod;
}
long get(int l,int r){ return sum[r] -sum[l]; }
}
abstract class SegmentTree<V, F> extends Seg<V, F>{
SegmentTree(int n,V e){ this(n,e,i -> e); }
SegmentTree(int n,V e,IntFunction<V> sup){ super(n,e,sup); }
@Override
protected F comp(F f0,F f1){ return null; }
@Override
protected void upd(int i,F f){
super.upd(i,f);
up(i,i +1);
}
}
abstract class DualSegmentTree<V, F> extends Seg<V, F>{
DualSegmentTree(int n,V e){ this(n,e,i -> e); }
DualSegmentTree(int n,V e,IntFunction<V> sup){ super(n,e,sup); }
@Override
V agg(V v0,V v1){ return null; }
@Override
protected void rangeMap(int i){}
@Override
protected void upd(int i,F f){ upd(i,i +1,f); }
@Override
protected void upd(int l,int r,F f){
down(l,r);
super.upd(l,r,f);
}
@Override
protected V get(int i){
down(i,i +1);
return super.get(i);
}
}
abstract class LazySegmentTree<V, F> extends Seg<V, F>{
LazySegmentTree(int n,V e){ this(n,e,i -> e); }
LazySegmentTree(int n,V e,IntFunction<V> sup){ super(n,e,sup); }
@Override
protected void upd(int i,F f){ upd(i,i +1,f); }
@Override
protected void upd(int l,int r,F f){
down(l,r);
super.upd(l,r,f);
up(l,r);
}
@Override
protected V get(int i){ return get(i,i +1); }
@Override
protected V get(int l,int r){
down(l,r);
return super.get(l,r);
}
}
abstract class Seg<V, F> {
protected int n;
private V e;
private V[] val;
private F[] lazy;
private int[] l,r,stk;
@SuppressWarnings("unchecked")
Seg(int n,V e,IntFunction<V> sup){
this.n = n;
this.e = e;
val = (V[]) new Object[n <<1];
lazy = (F[]) new Object[n];
l = new int[n <<1];
r = new int[n <<1];
stk = new int[100];
for (int i = -1;++i < n;l[i +n] = i,r[i +n] = i +1)
val[i +n] = sup.apply(i);
for (int i = n;--i > 0;l[i] = l[i <<1],r[i] = r[i <<1 |1])
merge(i);
}
abstract V agg(V v0,V v1);
abstract V map(V v,F f,int l,int r);
abstract F comp(F f0,F f1);
private void merge(int i){ val[i] = agg(eval(i <<1),eval(i <<1 |1)); }
protected void rangeMap(int i){ val[i] = map(val[i],lazy[i],l[i],r[i]); }
protected V eval(int i){
if (i < n && lazy[i] != null) {
rangeMap(i);
prop(i <<1,lazy[i]);
prop(i <<1 |1,lazy[i]);
lazy[i] = null;
}
return val[i];
}
protected void prop(int i,F f){
if (i < n)
lazy[i] = lazy[i] == null ? f : comp(lazy[i],f);
else
val[i] = map(val[i],f,l[i],r[i]);
}
protected void up(int l,int r){
l = oddPart(l +n);
r = oddPart(r +n);
while (1 < l)
merge(l >>= 1);
while (1 < r)
merge(r >>= 1);
}
protected void down(int l,int r){
int s = 0;
stk[++s] = l = oddPart(l +n);
stk[++s] = r = oddPart(r +n);
while (1 < l)
stk[++s] = l >>= 1;
while (1 < r)
stk[++s] = r >>= 1;
while (0 < s)
eval(stk[s--]);
}
private int oddPart(int i){ return i /(i &-i); }
protected void upd(int i,F f){ prop(i +n,f); }
protected void upd(int l,int r,F f){
l += n;
r += n;
do {
if ((l &1) == 1)
prop(l++,f);
if ((r &1) == 1)
prop(--r,f);
} while ((l >>= 1) < (r >>= 1));
}
protected V get(int i){ return val[i +n]; }
protected V get(int l,int r){
l += n;
r += n;
V vl = e;
V vr = e;
do {
if ((l &1) == 1)
vl = agg(vl,eval(l++));
if ((r &1) == 1)
vr = agg(eval(--r),vr);
} while ((l >>= 1) < (r >>= 1));
return agg(vl,vr);
}
}
class Util{
static int[] arrI(int N,IntUnaryOperator f){
int[] ret = new int[N];
setAll(ret,f);
return ret;
}
static long[] arrL(int N,IntToLongFunction f){
long[] ret = new long[N];
setAll(ret,f);
return ret;
}
static double[] arrD(int N,IntToDoubleFunction f){
double[] ret = new double[N];
setAll(ret,f);
return ret;
}
static <T> T[] arr(T[] arr,IntFunction<T> f){
setAll(arr,f);
return arr;
}
}
class MyReader{
byte[] buf = new byte[1 <<16];
int ptr = 0;
int tail = 0;
InputStream in;
MyReader(InputStream in){ this.in = in; }
byte read(){
if (ptr == tail)
try {
tail = in.read(buf);
ptr = 0;
} catch (IOException e) {}
return buf[ptr++];
}
boolean isPrintable(byte c){ return 32 < c && c < 127; }
boolean isNum(byte c){ return 47 < c && c < 58; }
byte nextPrintable(){
byte ret = read();
while (!isPrintable(ret))
ret = read();
return ret;
}
int it(){ return toIntExact(lg()); }
int[] it(int N){ return Util.arrI(N,i -> it()); }
int[][] it(int H,int W){ return Util.arr(new int[H][],i -> it(W)); }
int idx(){ return it() -1; }
int[] idx(int N){ return Util.arrI(N,i -> idx()); }
int[][] idx(int H,int W){ return Util.arr(new int[H][],i -> idx(W)); }
long lg(){
byte i = nextPrintable();
boolean negative = i == 45;
long n = negative ? 0 : i -'0';
while (isPrintable(i = read()))
n = 10 *n +i -'0';
return negative ? -n : n;
}
long[] lg(int N){ return Util.arrL(N,i -> lg()); }
long[][] lg(int H,int W){ return Util.arr(new long[H][],i -> lg(W)); }
double dbl(){ return Double.parseDouble(str()); }
double[] dbl(int N){ return Util.arrD(N,i -> dbl()); }
double[][] dbl(int H,int W){ return Util.arr(new double[H][],i -> dbl(W)); }
char[] ch(){ return str().toCharArray(); }
char[][] ch(int H){ return Util.arr(new char[H][],i -> ch()); }
String line(){
StringBuilder sb = new StringBuilder();
for (byte c;(c = read()) != '\n';)
sb.append((char) c);
return sb.toString();
}
String str(){
StringBuilder sb = new StringBuilder();
sb.append((char) nextPrintable());
for (byte c;isPrintable(c = read());)
sb.append((char) c);
return sb.toString();
}
String[] str(int N){ return Util.arr(new String[N],i -> str()); }
}
class MyWriter{
OutputStream out;
byte[] buf = new byte[1 <<16];
byte[] ibuf = new byte[20];
int tail = 0;
MyWriter(OutputStream out){ this.out = out; }
void flush(){
try {
out.write(buf,0,tail);
tail = 0;
} catch (IOException e) {
e.printStackTrace();
}
}
protected void ln(){ write((byte) '\n'); }
private void write(byte b){
buf[tail++] = b;
if (tail == buf.length)
flush();
}
private void write(byte[] b,int off,int len){
for (int i = off;i < off +len;i++)
write(b[i]);
}
private void write(long n){
if (n < 0) {
n = -n;
write((byte) '-');
}
int i = ibuf.length;
do {
ibuf[--i] = (byte) (n %10 +'0');
n /= 10;
} while (n > 0);
write(ibuf,i,ibuf.length -i);
}
private void print(Object obj){
if (obj instanceof Boolean)
print((boolean) obj ? Solver.yes : Solver.no);
else if (obj instanceof Character)
write((byte) (char) obj);
else if (obj instanceof Integer)
write((int) obj);
else if (obj instanceof Long)
write((long) obj);
else if (obj instanceof char[])
for (char b:(char[]) obj)
write((byte) b);
else if (obj.getClass().isArray()) {
int l = Array.getLength(obj);
for (int i = 0;i < l;i++) {
print(Array.get(obj,i));
if (i +1 < l)
write((byte) ' ');
}
} else
for (char b:Objects.toString(obj).toCharArray())
write((byte) b);
}
void printlns(Object... o){
print(Util.arr(new Object[o.length],i -> o[i]));
ln();
}
void println(Object obj){
if (obj == null)
return;
if (obj instanceof Collection<?>)
for (Object e:(Collection<?>) obj)
println(e);
else if (obj.getClass().isArray() && Array.getLength(obj) > 0 && !(Array.get(obj,0) instanceof char[])
&& Array.get(obj,0).getClass().isArray()) {
int l = Array.getLength(obj);
for (int i = 0;i < l;i++)
println(Array.get(obj,i));
} else {
print(obj);
ln();
}
}
}
class Main{
public static void main(String[] args) throws Exception{
Solver solver = new Solver();
solver.out.println(solver.solve());
solver.out.flush();
solver.log.println(solver.elapsed());
}
}