結果

問題 No.1116 Cycles of Dense Graph
ユーザー uwiuwi
提出日時 2020-07-18 17:59:13
言語 Java21
(openjdk 21)
結果
AC  
実行時間 475 ms / 2,000 ms
コード長 7,016 bytes
コンパイル時間 3,919 ms
コンパイル使用メモリ 89,484 KB
実行使用メモリ 54,452 KB
最終ジャッジ日時 2024-11-30 22:19:09
合計ジャッジ時間 10,809 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 55 ms
37,568 KB
testcase_01 AC 415 ms
54,452 KB
testcase_02 AC 92 ms
39,040 KB
testcase_03 AC 70 ms
37,672 KB
testcase_04 AC 59 ms
37,552 KB
testcase_05 AC 109 ms
40,012 KB
testcase_06 AC 191 ms
46,192 KB
testcase_07 AC 95 ms
39,008 KB
testcase_08 AC 58 ms
37,164 KB
testcase_09 AC 67 ms
37,440 KB
testcase_10 AC 74 ms
38,084 KB
testcase_11 AC 157 ms
44,496 KB
testcase_12 AC 109 ms
39,888 KB
testcase_13 AC 56 ms
37,444 KB
testcase_14 AC 70 ms
38,000 KB
testcase_15 AC 56 ms
37,384 KB
testcase_16 AC 103 ms
40,256 KB
testcase_17 AC 58 ms
37,068 KB
testcase_18 AC 82 ms
38,412 KB
testcase_19 AC 128 ms
42,104 KB
testcase_20 AC 76 ms
38,596 KB
testcase_21 AC 72 ms
37,816 KB
testcase_22 AC 153 ms
44,016 KB
testcase_23 AC 58 ms
37,172 KB
testcase_24 AC 452 ms
53,344 KB
testcase_25 AC 55 ms
37,296 KB
testcase_26 AC 438 ms
53,264 KB
testcase_27 AC 54 ms
37,616 KB
testcase_28 AC 67 ms
38,080 KB
testcase_29 AC 55 ms
37,604 KB
testcase_30 AC 53 ms
37,308 KB
testcase_31 AC 47 ms
36,776 KB
testcase_32 AC 56 ms
37,572 KB
testcase_33 AC 46 ms
36,928 KB
testcase_34 AC 45 ms
37,004 KB
testcase_35 AC 54 ms
37,536 KB
testcase_36 AC 455 ms
53,416 KB
testcase_37 AC 221 ms
46,968 KB
testcase_38 AC 226 ms
48,900 KB
testcase_39 AC 470 ms
52,880 KB
testcase_40 AC 475 ms
54,088 KB
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ソースコード

diff # 

package contest200717;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;

public class D2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int mod = 998244353;
		long all = 0;
		int[][] fif = enumFIF(n, mod);
		for(int i = 3;i <= n;i++){
			// C(n,i)*(i-1)!
			all += C(n, i, mod, fif) * fif[0][i-1];
			all %= mod;
		}
		all = all * invl(2, mod) % mod;
		
		int m = ni();
		int[][] es = new int[m][];
		for(int i = 0;i < m;i++){
			es[i] = new int[]{ni()-1, ni()-1};
		}
		long ans = all;
		
		Map<Long, Long> cache = new HashMap<>();
		
		outer:
		for(int i = 1;i < 1<<m;i++){
			Map<Integer, Integer> deg = new HashMap<>();
			for(int j = 0;j < m;j++){
				if(i<<~j<0){
					inc(es[j][0], deg);
					inc(es[j][1], deg);
				}
			}
			for(int v : deg.values()){
				if(v >= 3)continue outer;
			}
			
			int[] map = new int[deg.size()];
			int p = 0;
			for(int k : deg.keySet()){
				map[p++] = k;
			}
			Arrays.sort(map);
			
			DJSet ds = new DJSet(deg.size());
			for(int j = 0;j < m;j++){
				if(i<<~j<0){
					ds.union(
							Arrays.binarySearch(map, es[j][0]),
							Arrays.binarySearch(map, es[j][1])
							);
				}
			}
			int C = ds.count();
			
			int one = 0;
			for(int v : deg.values()){
				if(v == 1)one++;
			}
			
			if(C*2 > one){
				// has cycle(s)
				if(C > 1){
				}else{
					ans += (Integer.bitCount(i) % 2 == 1 ? mod-1 : 1) * 1;
					ans %= mod;
				}
				continue outer;
			}
			
			int zero = n-deg.size();
			long code = (long)zero<<32|C;
			
			cache.computeIfAbsent(code, z -> {
				long w = 0;
				for(int k = 0;k <= zero;k++){
					w += C(zero, k, mod, fif) * fif[0][C-1+k];
					w %= mod;
				}
				return w;
			});
			
			long ww = cache.get(code);
			if(Integer.bitCount(i) == 1){
				ww += mod - fif[0][C-1];
			}
			
			ans += (Integer.bitCount(i) % 2 == 1 ? mod-1 : 1) * 
					(pow(2, C-1, mod) % mod * ww % mod);
			ans %= mod;
		}
		out.println(ans);
	}
	
	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;
		}
	}

	
	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;
	}

	
	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 <T> void inc(T key, Map<T, Integer> map){inc(key, 1, map);}
	public static <T> void inc(T key, int inc, Map<T, Integer> map){map.put(key, map.getOrDefault(key, 0) + inc);}
	public static <T> void inc(T key, long inc, Map<T, Long> map){map.put(key, map.getOrDefault(key, 0L) + inc);}
	
	public static long C(int n, int r, int mod, int[][] fif) {
		if (n < 0 || r < 0 || r > n)
			return 0;
		return (long) fif[0][n] * fif[1][r] % mod * fif[1][n - r] % mod;
	}

	
	public static int[][] enumFIF(int n, int mod) {
		int[] f = new int[n + 1];
		int[] invf = new int[n + 1];
		f[0] = 1;
		for (int i = 1; i <= n; i++) {
			f[i] = (int) ((long) f[i - 1] * i % mod);
		}
		long a = f[n];
		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;
		}
		invf[n] = (int) (p < 0 ? p + mod : p);
		for (int i = n - 1; i >= 0; i--) {
			invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
		}
		return new int[][] { f, invf };
	}

	
	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 D2().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)); }
}
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