結果
| 問題 |
No.1955 Not Prime
|
| コンテスト | |
| ユーザー |
 uwi
|
| 提出日時 | 2022-05-20 23:15:54 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 459 ms / 2,000 ms |
| コード長 | 16,242 bytes |
| コンパイル時間 | 5,148 ms |
| コンパイル使用メモリ | 92,788 KB |
| 実行使用メモリ | 85,164 KB |
| 最終ジャッジ日時 | 2024-09-20 09:40:08 |
| 合計ジャッジ時間 | 12,554 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 26 |
ソースコード
package contest220520;
import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;
public class O {
InputStream is;
FastWriter out;
String INPUT = "";
public void solve()
{
int n = ni();
int[] lpf = enumLowestPrimeFactors(999999);
String[] a = new String[n];
String[] b = new String[n];
for(int i = 0;i < n;i++){
a[i] = ns();
b[i] = ns();
}
TwoSatisfiability ts = new TwoSatisfiability(n);
for(int i = 0;i < 2*n;i++){
for(int j = 0;j < 2*n;j++){
String x = i < n ? a[i] : b[i-n];
String y = j < n ? a[j] : b[j-n];
int num = Integer.parseInt(x+y);
if(num == lpf[num]){
// !(x in s and y in t)
// x in t or y in s
ts.or(i % n, i < n ? false : true, j % n, j < n ? true : false);
}
}
}
out.println(ts.isSatisfied() ? "Yes" : "No");
}
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;
}
public static class TwoSatisfiability {
public int[] from, to;
public int p;
public int n;
public TwoSatisfiability(int n) {
this.n = n;
from = new int[2];
to = new int[2];
p = 0;
}
private void addEdge(int x, int y)
{
if(p == from.length){
from = Arrays.copyOf(from, p*3/2);
to = Arrays.copyOf(to, p*3/2);
}
from[p] = x;
to[p] = y;
p++;
}
public boolean isSatisfied()
{
int[][] g = packD(2*n, from, to, p);
int[] clus = decomposeToSCC(g);
for(int i = 0;i < n;i++){
if(clus[i] == clus[i+n])return false;
}
return true;
}
public int[] restore()
{
int[][] g = packD(2*n, from, to, p);
int[] clus = decomposeToSCC(g);
int[] ret = new int[n];
for(int i = 0;i < n;i++){
if(clus[i] == clus[i+n])return null; // unsatisfied
ret[i] = clus[i] > clus[i+n] ? -1 : 1;
}
return ret;
}
// x or y
// ~x->y, ~y->x
public void or(int x, int y)
{
addEdge(x+n, y);
addEdge(y+n, x);
}
public void or(int x, boolean positivex, int y, boolean positivey)
{
addEdge(x+(positivex ? n : 0), y+(positivey ? 0 : n));
addEdge(y+(positivey ? n : 0), x+(positivex ? 0 : n));
}
// x = y
// ~x -> ~y, ~y -> ~x
// x -> y, y -> x
public void eq(int x, int y)
{
addEdge(x, y);
addEdge(y, x);
addEdge(x+n, y+n);
addEdge(y+n, x+n);
}
public void eq(int x, boolean positivex, int y, boolean positivey)
{
addEdge(x+(positivex ? 0 : n), y+(positivey ? 0 : n));
addEdge(y+(positivey ? 0 : n), x+(positivex ? 0 : n));
addEdge(x+(positivex ? n : 0), y+(positivey ? n : 0));
addEdge(y+(positivey ? n : 0), x+(positivex ? n : 0));
}
// x xor y
// ~x -> y, y -> ~x
// x -> ~y, ~y -> x
public void xor(int x, int y)
{
addEdge(x+n, y);
addEdge(y, x+n);
addEdge(x, y+n);
addEdge(y+n, x);
}
// always true
public void t(int x)
{
addEdge(x+n, x);
}
// always false
public void f(int x)
{
addEdge(x, x+n);
}
////// inner utility
public static int[][] packD(int n, int[] from, int[] to, int sup)
{
int[][] g = new int[n][];
int[] p = new int[n];
for(int i = 0;i < sup;i++)p[from[i]]++;
for(int i = 0;i < n;i++)g[i] = new int[p[i]];
for(int i = 0;i < sup;i++){
g[from[i]][--p[from[i]]] = to[i];
}
return g;
}
public static int[] decomposeToSCC(int[][] g)
{
int n = g.length;
int[] stack = new int[n+1];
int[] ind = new int[n+1];
int[] ord = new int[n];
Arrays.fill(ord, -1);
int[] low = new int[n];
Arrays.fill(low, -1);
int sp = 0;
int id = 0; // preorder
int[] clus = new int[n];
int cid = 0;
int[] cstack = new int[n+1];
int csp = 0;
boolean[] incstack = new boolean[n];
for(int i = 0;i < n;i++){
if(ord[i] == -1){
ind[sp] = 0;
cstack[csp++] = i;
stack[sp++] = i;
incstack[i] = true;
while(sp > 0){
int cur = stack[sp-1];
if(ind[sp-1] == 0){
ord[cur] = low[cur] = id++;
}
if(ind[sp-1] < g[cur].length){
int nex = g[cur][ind[sp-1]];
if(ord[nex] == -1){
ind[sp-1]++;
ind[sp] = 0;
incstack[nex] = true;
cstack[csp++] = nex;
stack[sp++] = nex;
}else{
// shortcut
// U.tr(cur, nex, incstack[nex], low[nex], stack);
if(incstack[nex])low[cur] = Math.min(low[cur], low[nex]);
ind[sp-1]++;
}
}else{
if(ord[cur] == low[cur]){
while(csp > 0){
incstack[cstack[csp-1]] = false;
clus[cstack[--csp]] = cid;
if(cstack[csp] == cur)break;
}
cid++;
}
if(--sp >= 1)low[stack[sp-1]] = Math.min(low[stack[sp-1]], low[stack[sp]]);
}
}
}
}
return clus;
}
}
public static void main(String[] args) {
new O().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 write(IntUnaryOperator f, int... xs)
{
boolean first = true;
for(int x : xs) {
if (!first) write(' ');
first = false;
write(f.applyAsInt(x));
}
return this;
}
public FastWriter write(LongUnaryOperator f, long... xs)
{
boolean first = true;
for(long x : xs) {
if (!first) write(' ');
first = false;
write(f.applyAsLong(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(IntUnaryOperator f, int... xs) { return write(f, xs).writeln(); }
public FastWriter writeln(LongUnaryOperator f, long... xs) { return write(f, 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 print(IntUnaryOperator f, int... xs) { return write(f, xs); }
public FastWriter print(LongUnaryOperator f, long... xs) { return write(f, xs); }
public FastWriter println(int... xs) { return writeln(xs); }
public FastWriter println(long... xs) { return writeln(xs); }
public FastWriter println(IntUnaryOperator f, int... xs) { return writeln(f, xs); }
public FastWriter println(LongUnaryOperator f, long... xs) { return writeln(f, 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 1
public 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)); }
}