結果

問題 No.1116 Cycles of Dense Graph
ユーザー uwiuwi
提出日時 2020-07-17 21:59:36
言語 Java
(openjdk 23)
結果
AC  
実行時間 742 ms / 2,000 ms
コード長 7,131 bytes
コンパイル時間 4,671 ms
コンパイル使用メモリ 84,484 KB
実行使用メモリ 59,328 KB
最終ジャッジ日時 2024-11-29 23:45:35
合計ジャッジ時間 13,492 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 38
権限があれば一括ダウンロードができます

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.ArrayDeque;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.Queue;
import java.util.Set;

public class D {
	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;
			}
			
			Set<Integer> line = new HashSet<>();
			Queue<Integer> q = new ArrayDeque<>();
			for(int k : deg.keySet()){
				if(deg.get(k).equals(1)){
					q.add(k);
					line.add(k);
				}
			}
			while(!q.isEmpty()){
				int cur = q.poll();
				for(int j = 0;j < m;j++){
					if(i<<~j<0 && (es[j][0] == cur || es[j][1] == cur)){
						int to = es[j][0]^es[j][1]^cur;
						if(!line.contains(to)){
							line.add(to);
							q.add(to);
						}
					}
				}
			}
			if(line.size() < deg.size()){
				// it has cycle
				Set<Integer> cycle = new HashSet<>();
				for(int k : deg.keySet()){
					q.add(k);
					cycle.add(k);
					break;
				}
				while(!q.isEmpty()){
					int cur = q.poll();
					for(int j = 0;j < m;j++){
						if(i<<~j<0 && (es[j][0] == cur || es[j][1] == cur)){
							int to = es[j][0]^es[j][1]^cur;
							if(!cycle.contains(to)){
								cycle.add(to);
								q.add(to);
							}
						}
					}
				}
				if(line.size() > 0 && cycle.size() > 0){
					continue outer;
				}
				if(line.size() == 0 && cycle.size() != deg.size())continue outer;
				
				ans += (Integer.bitCount(i) % 2 == 1 ? mod-1 : 1) * 1;
				ans %= mod;
				continue outer;
			}
			
			int one = 0;
			int zero = n-deg.size();
			for(int v : deg.values()){
				if(v == 1)one++;
			}
			int con = one/2;
			long code = (long)zero<<32|con;
			
			if(!cache.containsKey(code)){
				long w = 0;
				for(int k = 0;k <= zero;k++){
					w += C(zero, k, mod, fif) * fif[0][con-1+k];
					w %= mod;
				}
				cache.put(code, w);
			}
			
			long ww = cache.get(code);
			if(Integer.bitCount(i) == 1){
				ww += mod - fif[0][con-1];
			}
			
			ans += (Integer.bitCount(i) % 2 == 1 ? mod-1 : 1) * 
					(pow(2, con-1, mod) % mod * ww % mod);
			ans %= mod;
		}
		out.println(ans);
	}
	
	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 D().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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