#61900 (Java21) No.308 素数は通れません

• 問題: No.308 素数は通れません
• ユーザー: uwi
• 提出日時: 2015-12-01 22:24:22
• 言語: Java21 (openjdk 21)
• 結果: AC
• 実行時間: 145 ms / 1,000 ms
• コード長: 6,786 bytes
• コンパイル時間: 3,853 ms
• コンパイル使用メモリ: 89,456 KB
• 実行使用メモリ: 57,884 KB
• 最終ジャッジ日時: 2023-08-18 13:08:02
• 合計ジャッジ時間: 16,216 ms
• ジャッジサーバーID （参考情報）: judge13 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	43 ms; 49,240 KB
testcase_01	AC	43 ms; 49,256 KB
testcase_02	AC	44 ms; 49,464 KB
testcase_03	AC	44 ms; 49,868 KB
testcase_04	AC	44 ms; 49,376 KB
testcase_05	AC	43 ms; 49,300 KB
testcase_06	AC	44 ms; 49,384 KB
testcase_07	AC	43 ms; 49,256 KB
testcase_08	AC	44 ms; 49,456 KB
testcase_09	AC	43 ms; 49,404 KB
testcase_10	AC	43 ms; 49,356 KB
testcase_11	AC	43 ms; 49,220 KB
testcase_12	AC	43 ms; 49,424 KB
testcase_13	AC	42 ms; 49,368 KB
testcase_14	AC	42 ms; 47,724 KB
testcase_15	AC	44 ms; 49,440 KB
testcase_16	AC	44 ms; 49,288 KB
testcase_17	AC	44 ms; 49,388 KB
testcase_18	AC	43 ms; 49,408 KB
testcase_19	AC	43 ms; 49,508 KB
testcase_20	AC	44 ms; 49,524 KB
testcase_21	AC	43 ms; 49,412 KB
testcase_22	AC	43 ms; 49,392 KB
testcase_23	AC	44 ms; 49,276 KB
testcase_24	AC	48 ms; 49,248 KB
testcase_25	AC	43 ms; 49,284 KB
testcase_26	AC	45 ms; 49,388 KB
testcase_27	AC	44 ms; 49,484 KB
testcase_28	AC	44 ms; 49,256 KB
testcase_29	AC	45 ms; 49,388 KB
testcase_30	AC	43 ms; 49,416 KB
testcase_31	AC	43 ms; 49,600 KB
testcase_32	AC	45 ms; 49,288 KB
testcase_33	AC	43 ms; 49,380 KB
testcase_34	AC	44 ms; 49,460 KB
testcase_35	AC	44 ms; 49,264 KB
testcase_36	AC	78 ms; 52,008 KB
testcase_37	AC	105 ms; 52,984 KB
testcase_38	AC	108 ms; 52,700 KB
testcase_39	AC	121 ms; 53,592 KB
testcase_40	AC	129 ms; 57,884 KB
testcase_41	AC	71 ms; 51,224 KB
testcase_42	AC	105 ms; 53,556 KB
testcase_43	AC	113 ms; 53,048 KB
testcase_44	AC	120 ms; 53,672 KB
testcase_45	AC	130 ms; 56,180 KB
testcase_46	AC	110 ms; 53,004 KB
testcase_47	AC	52 ms; 50,404 KB
testcase_48	AC	70 ms; 51,632 KB
testcase_49	AC	126 ms; 55,468 KB
testcase_50	AC	113 ms; 53,196 KB
testcase_51	AC	125 ms; 53,520 KB
testcase_52	AC	74 ms; 51,852 KB
testcase_53	AC	100 ms; 52,820 KB
testcase_54	AC	127 ms; 55,276 KB
testcase_55	AC	124 ms; 55,156 KB
testcase_56	AC	77 ms; 52,036 KB
testcase_57	AC	125 ms; 53,448 KB
testcase_58	AC	73 ms; 51,880 KB
testcase_59	AC	113 ms; 53,700 KB
testcase_60	AC	108 ms; 54,016 KB
testcase_61	AC	97 ms; 53,448 KB
testcase_62	AC	109 ms; 53,632 KB
testcase_63	AC	137 ms; 54,196 KB
testcase_64	AC	132 ms; 53,332 KB
testcase_65	AC	62 ms; 51,704 KB
testcase_66	AC	121 ms; 53,576 KB
testcase_67	AC	109 ms; 54,028 KB
testcase_68	AC	75 ms; 50,800 KB
testcase_69	AC	121 ms; 54,204 KB
testcase_70	AC	145 ms; 54,600 KB
testcase_71	AC	122 ms; 54,144 KB
testcase_72	AC	99 ms; 53,600 KB
testcase_73	AC	118 ms; 54,004 KB
testcase_74	AC	92 ms; 53,136 KB
testcase_75	AC	114 ms; 54,452 KB
testcase_76	AC	122 ms; 53,644 KB
testcase_77	AC	76 ms; 51,676 KB
testcase_78	AC	121 ms; 53,612 KB
testcase_79	AC	75 ms; 51,208 KB
testcase_80	AC	110 ms; 54,168 KB
testcase_81	AC	132 ms; 53,752 KB
testcase_82	AC	129 ms; 53,656 KB
testcase_83	AC	106 ms; 53,644 KB
testcase_84	AC	72 ms; 50,936 KB
testcase_85	AC	120 ms; 53,868 KB
testcase_86	AC	108 ms; 53,544 KB
testcase_87	AC	91 ms; 52,752 KB
testcase_88	AC	102 ms; 53,504 KB
testcase_89	AC	60 ms; 51,880 KB
testcase_90	AC	103 ms; 53,836 KB
testcase_91	AC	132 ms; 53,700 KB
testcase_92	AC	112 ms; 53,424 KB
testcase_93	AC	136 ms; 53,932 KB
testcase_94	AC	136 ms; 53,964 KB
testcase_95	AC	65 ms; 52,096 KB
testcase_96	AC	128 ms; 53,844 KB
testcase_97	AC	111 ms; 54,148 KB
testcase_98	AC	102 ms; 53,224 KB
testcase_99	AC	48 ms; 50,360 KB
testcase_100	AC	89 ms; 52,672 KB
testcase_101	AC	134 ms; 54,036 KB
testcase_102	AC	103 ms; 53,684 KB
testcase_103	AC	142 ms; 54,080 KB
testcase_104	AC	130 ms; 54,216 KB
testcase_105	AC	85 ms; 52,680 KB
testcase_106	AC	110 ms; 54,312 KB

ソースコード

package q8xx;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Q840_2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		String N = ns();
		if(N.length() <= 2){
			int n = Integer.parseInt(N);
			if(n == 4 || n == 6 || n == 12 || n == 14 || n == 20 || n == 24){
				out.println(n-1);
				return;
			}
			if(n == 21 || n == 25){
				out.println(n-2);
				return;
			}
		}
		
		if(N.length() <= 3){
			int n = Integer.parseInt(N);
			long[] isp = isp(1005);
			for(int w = 1;w <= n;w++){
				if(check(n, w, isp)){
					out.println(w);
					return;
				}
			}
		}
		
		// 8*3*5*7
		int Z = 840;
		BigInteger bn = new BigInteger(N);
		int mt = bn.mod(BigInteger.valueOf(Z)).intValue();
		if(mt == 0)mt += Z;
		BigInteger base = bn.divide(BigInteger.valueOf(Z)).multiply(BigInteger.valueOf(Z));
		if(mt == Z)base = base.subtract(BigInteger.valueOf(Z));
		
		boolean[] ok = new boolean[Z+1];
		for(int num = 1;num <= Z;num++){
			if(num > mt){
				ok[num] = false;
			}else if(num == mt){
				ok[num] = true;
			}else if(num % 3 == 0 || num % 5 == 0 || num % 2 == 0 || num % 7 == 0){
				ok[num] = true;
			}else{
				BigInteger x = base.add(BigInteger.valueOf(num));
				if(x.isProbablePrime(30)){
					ok[num] = false;
				}else{
					ok[num] = true;
				}
			}
		}
		out.println(check(mt, 8, ok) ? 8 : 14);
	}
	
	static boolean check(int n, int w, boolean[] ok)
	{
		DJSet ds = new DJSet(n+1);
		for(int j = 1;j <= n;j++){
			if(j+1 <= n && j%w != 0 && ok[j] && ok[j+1]){
				ds.union(j, j+1);
			}
			if(j+w <= n && ok[j] && ok[j+w]){
				ds.union(j, j+w);
			}
		}
		for(int i = 1;i <= w;i++){
			if(ok[i] && ds.equiv(i, n))return true;
		}
		return false;
	}
	
	static boolean check(int n, int w, long[] isp)
	{
		DJSet ds = new DJSet(n+1);
		for(int j = 1;j <= n;j++){
			if(j+1 <= n && j%w != 0 && isp[j>>>6]<<~j>=0 && isp[j+1>>>6]<<~(j+1)>=0){
				ds.union(j, j+1);
			}
			if(j+w <= n && isp[j>>>6]<<~j>=0 && isp[j+w>>>6]<<~(j+w)>=0){
				ds.union(j, j+w);
			}
		}
		return ds.equiv(1, n);
	}
	public static long[] isp(int n)
	{
		int[] tprimes = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61};
		if(n <= 64){
			long ptn = 0;
			for(int p : tprimes)if(p <= n)ptn |= 1L<<p;
			return new long[]{ptn};
		}
		
		long[] isnp = new long[(n+1)/64+1];
		int sup = (n+1)/64+1;
		
		isnp[0] |= 1<<1;
		for(int tp : tprimes){
			long[] ptn = new long[tp];
			for(int i = 0;i < tp<<6;i+=tp)ptn[i>>>6] |= 1L<<i;
			for(int j = 0;j < sup;j += tp){
				for(int i = 0;i < tp && i+j < sup;i++){
					isnp[j+i] |= ptn[i];
				}
			}
		}
		
		final int[] magic = {0, 1, 2, 53, 3, 7, 54, 27, 4, 38, 41, 8, 34, 55, 48, 28, 62, 5, 39, 46, 44, 42, 22, 9, 24, 35, 59, 56, 49, 18, 29, 11, 63, 52, 6, 26, 37, 40, 33, 47, 61, 45, 43, 21, 23, 58, 17, 10, 51, 25, 36, 32,
	              60, 20, 57, 16, 50, 31, 19, 15, 30, 14, 13, 12};
		out:
		for(int i = 0;i < sup;i++){
			for(long j = ~isnp[i];j != 0;j &= j-1){
				int p = i<<6|magic[(int)((j&-j)*0x022fdd63cc95386dL>>>58)];
				if((long)p*p > n)break out;
				for(int q = p*p;q <= n;q += p)isnp[q>>6] |= 1L<<q;
			}
		}
		
		for(int i = 0;i < isnp.length;i++)isnp[i] = ~isnp[i];
		for(int tp : tprimes)isnp[0] |= 1L<<tp;
		isnp[isnp.length-1] &= (1L<<n+1)-1;
		
		return isnp;
	}

	
	public static class DJSet {
		public int[] upper;

		public DJSet(int n) {
			upper = new int[n];
			Arrays.fill(upper, -1);
		}

		public int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}

		public boolean equiv(int x, int y) {
			return root(x) == root(y);
		}

		public boolean union(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[y] < upper[x]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[x] += upper[y];
				upper[y] = x;
			}
			return x == y;
		}

		public int count() {
			int ct = 0;
			for (int u : upper)
				if (u < 0)
					ct++;
			return ct;
		}
	}
	
	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 Q840_2().run(); }
	
	private byte[] inbuf = new byte[1024];
	private 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)); }
}