#63810 (Java21) No.310 2文字しりとり

提出ソース
結果

問題	No.310 2文字しりとり
ユーザー	uwi
提出日時	2015-12-08 02:52:05
言語	Java21 (openjdk 21)
結果	AC
実行時間	2,248 ms / 6,000 ms
コード長	14,343 bytes
コンパイル時間	4,668 ms
コンパイル使用メモリ	88,424 KB
実行使用メモリ	180,932 KB
最終ジャッジ日時	2023-10-12 20:45:40
合計ジャッジ時間	19,757 ms
ジャッジサーバーID （参考情報）	judge15 / judge11
このコードへのチャレンジ
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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	43 ms 49,584 KB
testcase_01	AC	42 ms 49,612 KB
testcase_02	AC	43 ms 49,416 KB
testcase_03	AC	43 ms 49,552 KB
testcase_04	AC	43 ms 49,580 KB
testcase_05	AC	43 ms 49,676 KB
testcase_06	AC	43 ms 49,648 KB
testcase_07	AC	43 ms 49,264 KB
testcase_08	AC	42 ms 49,264 KB
testcase_09	AC	42 ms 49,784 KB
testcase_10	AC	42 ms 49,512 KB
testcase_11	AC	43 ms 49,500 KB
testcase_12	AC	45 ms 49,316 KB
testcase_13	AC	44 ms 49,536 KB
testcase_14	AC	42 ms 49,552 KB
testcase_15	AC	44 ms 50,020 KB
testcase_16	AC	45 ms 50,020 KB
testcase_17	AC	43 ms 49,460 KB
testcase_18	AC	77 ms 51,428 KB
testcase_19	AC	67 ms 51,272 KB
testcase_20	AC	80 ms 51,784 KB
testcase_21	AC	2,100 ms 180,564 KB
testcase_22	AC	2,248 ms 180,632 KB
testcase_23	AC	2,243 ms 180,600 KB
testcase_24	AC	2,234 ms 180,932 KB
testcase_25	AC	2,137 ms 180,600 KB
testcase_26	AC	666 ms 75,224 KB
testcase_27	AC	769 ms 91,276 KB
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ソースコード

raw source code
package q8xx;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Random;

public class Q874_5 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
//	String INPUT = "10 0";
//	String INPUT = "4 7 1 2 2 1 2 3 3 2 2 4 4 2 2 2";
	
	boolean[][] shrink(boolean[][] ng)
	{
		int n = ng.length;
		int[] outdeg = new int[n];
		int[] indeg = new int[n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(!ng[i][j]){
					outdeg[i]++;
					indeg[j]++;
				}
			}
		}
		int[] map = new int[n];
		Arrays.fill(map, -1);
		int p = 0;
		for(int i = 0;i < n;i++){
			if(!(outdeg[i] == 0 && indeg[i] == 0)){
				map[i] = p++;
			}
		}
		boolean[][] nng = new boolean[p][p];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(ng[i][j] && map[i] != -1 && map[j] != -1){
					nng[map[i]][map[j]] = true;
				}
			}
		}
		return nng;
	}
	
	long S,G;
	int mod = 1000000007;
	
	void solve()
	{
		int n = ni(), m = ni();
		if(n*n == m){
			out.println(1);
			return;
		}
		int on = n;
		boolean[][] ng = new boolean[n][n];
		for(int i = 0;i < m;i++){
			int f = ni()-1, t = ni()-1;
			ng[f][t] = true;
		}
		ng = shrink(ng);
		n = ng.length;
		int[] outdeg = new int[n];
		int[] indeg = new int[n];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(!ng[i][j]){
					outdeg[i]++;
					indeg[j]++;
				}
			}
		}
		
		// connectivity
		DJSet ds = new DJSet(n);
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(!ng[i][j]){
					ds.union(i, j);
				}
			}
		}
		for(int i = 0;i < n;i++){
			for(int j = i+1;j < n;j++){
				if(
						(outdeg[i] >= 1 || indeg[i] >= 1) &&
						(outdeg[j] >= 1 || indeg[j] >= 1)
						){
					if(!ds.equiv(i, j)){
						out.println(0);
						return;
					}
				}
			}
		}
		
		int src = -1, sink = -1;
		for(int i = 0;i < n;i++){
			if(outdeg[i] == indeg[i])continue;
			if(outdeg[i] == indeg[i]+1 && src == -1){
				src = i;
				continue;
			}
			if(outdeg[i] == indeg[i]-1 && sink == -1){
				sink = i;
				continue;
			}
			out.println(0);
			return;
		}
		
		int[][] MM = new int[n+1][n+1];
		for(int i = 0;i < n;i++){
			for(int j = 0;j < n;j++){
				if(i == j){
					MM[i+1][i+1]++;
				}else if(!ng[i][j]){
					MM[i+1][j+1] = 0;
					MM[i+1][i+1]++;
				}else{
					MM[i+1][j+1] = 1;
				}
			}
		}
		MM[0][0] = 1;
		for(int i = 1;i < n+1;i++)MM[0][i] = mod-1;
		for(int i = 1;i < n+1;i++)MM[i][0] = mod-1;
		
		if(src == -1){
			out.println(numEulerianCircuit(MM, outdeg, indeg) * (on*on-m) % mod);
		}else{
//			int u = MM[sink+1][src+1] == 0 ? 2 : 1;
			if(--MM[sink+1][src+1] < 0)MM[sink+1][src+1] += mod;
			MM[sink+1][sink+1]++;
			outdeg[sink]++;
			indeg[src]++;
			long nec = numEulerianCircuit(MM, outdeg, indeg);
			out.println(nec);
		}
	}
	
	long numEulerianCircuit(int[][] M, int[] outdeg, int[] indeg)
	{
		int n = M.length;
		long[] F = new long[n+2];
		F[0] = 1;
		for(int i = 1;i <= n;i++)F[i] = F[i-1] * i % mod;
		
		long ec = 1;
		for(int i = 0;i < outdeg.length;i++){
			ec = ec * F[outdeg[i]-1] % mod;
		}
		
		long[][][] QQ = denseToSparse(M, n-1);
		Random gen = new Random(0);
		long det = det(QQ, mod, gen);
		return ec * det % mod;
	}
	
	public long det(long[][][] A, int mod, Random gen)
	{
		int n = A.length;
		long div = 1L;
		long[] diag = new long[n];
		for(int i = 0;i < n;i++){
			diag[i] = gen.nextInt(mod-1)+1;
			div = div * diag[i] % mod;
		}
		for(int i = 0;i < n;i++){
			for(long[] e : A[i]){
				e[1] = e[1] * diag[(int)e[0]] % mod;
			}
		}
		
		long[] u = new long[n];
		for(int i = 0;i < n;i++)u[i] = gen.nextInt(mod);
		long[] v = new long[n];
		for(int i = 0;i < n;i++)v[i] = gen.nextInt(mod);
		long[] f = minPolynomialSparse(A, v, u, mod);
		
		if(n % 2 == 1)f[0] = mod-f[0];
		return f[0] * invl(div, mod) % mod;
	}
	
	public static long[][][] denseToSparse(int[][] A, int n)
	{
		long[][][] ret = new long[n][][];
		for(int i = 0;i < n;i++){
			int nz = 0;
			for(int j = 0;j < n;j++)if(A[i][j] != 0)nz++;
			ret[i] = new long[nz][];
			nz = 0;
			for(int j = 0;j < n;j++){
				if(A[i][j] != 0){
					ret[i][nz++] = new long[]{j, A[i][j]};
				}
			}
		}
		return ret;
	}
	
	
//	public static long[] minPolynomial(long[][] M, long[] v, long[] u, int mod)
//	{
//		int n = M.length;
//		long[] co = new long[2*n];
//		long[] w = Arrays.copyOf(v, n);
//		long big = 8L*mod*mod;
//		for(int i = 0;i < 2*n;i++){
//			co[i] = 0L;
//			for(int j = 0;j < n;j++){
//				co[i] += w[j] * u[j];
//				if(co[i] >= big)co[i] -= big;
//			}
//			co[i] %= mod;
//			w = mul(M, w, mod);
//		}
//		
//		return modifiedBerlekampMassey(co, mod);
//	}
	
	public static long[] minPolynomialSparse(long[][][] M, long[] v, long[] u, int mod)
	{
		int n = M.length;
//		U -= System.nanoTime();
		long[] co = new long[2*n];
		long[] w = Arrays.copyOf(v, n);
		long big = 8L*mod*mod;
		for(int i = 0;i < 2*n;i++){
			co[i] = 0L;
			for(int j = 0;j < n;j++){
				co[i] += w[j] * u[j];
				if(co[i] >= big)co[i] -= big;
			}
			co[i] %= mod;
			w = mulSparse(M, w, mod);
		}
//		U += System.nanoTime();
//		tr("U", U);
//		long S = System.nanoTime();
		long[] res = modifiedBerlekampMassey(co, mod); // 0.53/1.18
//		long G = System.nanoTime();
//		tr(G-S);
		return res;
	}
	
	public static long[] minPolynomialSparse(long[][][] M, long[] v, long[] u, int mod, int step)
	{
		int n = M.length;
		long[] co = new long[step];
		long[] w = Arrays.copyOf(v, n);
		long big = 8L*mod*mod;
		for(int i = 0;i < step;i++){
			co[i] = 0L;
			for(int j = 0;j < n;j++){
				co[i] += w[j] * u[j];
				if(co[i] >= big)co[i] -= big;
			}
			co[i] %= mod;
			w = mulSparse(M, w, mod);
		}
		return modifiedBerlekampMassey(co, mod);
	}
	
	public static long pow(long[][] M, long[] v, long[] u, long e, long[] minp, int mod)
	{
		int n = M.length;
		int q = minp.length-1;
		if(q == 0)return 0L;
		long[] rminp = new long[q];
		for(int i = 0;i < q;i++)rminp[i] = mod-minp[i];
		// x^e mod minp
		long[] coo = lrx(rminp, e, mod);
		
		long[] w = Arrays.copyOf(v, n);
		long ret = 0;
		for(int i = 0;i < q;i++){
			long lret = 0;
			for(int j = 0;j < n;j++){
				lret += w[j] * u[j];
				lret %= mod;
			}
			ret += lret * coo[i];
			ret %= mod;
			w = mul(M, w, mod);
		}
		return ret;
	}
	
	static long[] mul(long[][] M, long[] v, int mod)
	{
		int n = v.length;
		long[] w = new long[n];
		for(int i = 0;i < n;i++){
			long sum = 0;
			for(int j = 0;j < n;j++){
				sum += M[i][j] * v[j];
				sum %= mod;
			}
			w[i] = sum;
		}
		return w;
	}
	
	static long[] mulSparse(long[][][] M, long[] v, int mod)
	{
		int n = v.length;
		long[] w = new long[n];
		long big = 8L*mod*mod;
		for(int i = 0;i < n;i++){
			long sum = 0;
			for(long[] e : M[i]){
				sum += e[1] * v[(int)e[0]];
				if(sum >= big)sum -= big;
			}
			w[i] = sum % mod;
		}
		return w;
	}
	
	static int ct = 0;
	
	public static long[] modifiedBerlekampMassey(long[] a, int mod)
	{
		assert a.length % 2 == 0;
		int n = a.length/2;
		int m = 2*n-1;
		long[] R0 = new long[2*n+1]; R0[2*n] = 1;
		long[] R1 = new long[2*n];
		for(int i = 0;i < 2*n;i++)R1[i] = a[m-i];
		R1 = strip(R1);
		long[] v0 = {0L};
		long[] v1 = {1L};
		
		// TODO メモリを使い回す
		while(n <= R1.length-1){
			long[][] QR = divmod(R0, R1, mod); // 0.34s?
			long[] v = sub(v0, mul(QR[0], v1, mod), mod);
			v0 = v1; v1 = v; R0 = R1; R1 = QR[1];
		}
		// normalize
		long z = invl(v1[v1.length-1], mod);
		for(int i = 0;i < v1.length;i++){
			v1[i] = v1[i] * z % mod;
		}
		return strip(v1);
	}
	
	static long U = 0;
	
	public static long[] mul(long[] a, long[] b, int mod)
	{
		long[] c = new long[a.length+b.length-1];
		long big = 8L*mod*mod;
		for(int i = 0;i < a.length;i++){
			for(int j = 0;j < b.length;j++){
				c[i+j] += a[i] * b[j];
				if(c[i+j] >= big)c[i+j] -= big;
			}
		}
		for(int i = 0;i < c.length;i++)c[i] %= mod;
		return strip(c);
	}
	
	public static long[] sub(long[] a, long[] b, int mod)
	{
		long[] c = Arrays.copyOf(a, Math.max(a.length, b.length));
		for(int i = 0;i < c.length;i++){
			c[i] -= b[i];
			if(c[i] < 0)c[i] += mod;
		}
		return strip(c);
	}
	
	public static long[] strip(long[] a)
	{
		int i;
		for(i = a.length-1;i > 0 && a[i] == 0;i--);
		if(i + 1 == a.length)return a;
		return Arrays.copyOf(a, i+1);
	}

	public static long[][] divmod(long[] A, long[] B, int mod)
	{
		assert B[B.length-1] != 0;
		long[] R = A;
		long[] Q = new long[Math.max(1, A.length-B.length+1)];
		long ib = invl(B[B.length-1], mod);
		long big = 8L*mod*mod;
		for(int i = A.length-1, t = Q.length-1;i >= B.length-1;i--,t--){
			R[i] %= mod;
			if(R[i] < 0)R[i] += mod;
			long m = R[i] * ib % mod;
			Q[t] = m;
			for(int j = 0, k = i-B.length+1+j;j < B.length-1;j++,k++){
				R[k] -= B[j] * m;
//				R[k] %= mod;
//				if(R[k] < 0)R[k] += mod;
				if(R[k] < -big)R[k] += big;
			}
//			R[i] %= mod;
			R[i] = 0;
//			assert R[i] == 0;
		}
		for(int i = B.length-2;i >= 0;i--){
			R[i] %= mod;
			if(R[i] < 0)R[i] += mod;
		}
//		tr("A", A);
//		tr("B", B);
//		tr("Q", Q);
//		tr("R", R);
		return new long[][]{Q, strip(R)};
	}
	
	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[] lrx(long[] co, long n, long mod)
	{
		long BIG = (Long.MAX_VALUE - 2L*mod*mod)/mod*mod;
		int m = co.length;
		if(m == 1){
			long ret = 1;
			long mul = co[0];
			for(;n > 0;n >>>= 1){
				if((n&1)==1){
					ret = ret * mul % mod;
				}
				mul = mul * mul % mod;
			}
			return new long[]{ret};
		}
		
		long[][] m2 = new long[m-1][m];
		for(int j = 0;j < m;j++){
			m2[0][j] = co[j];
		}
		for(int i = 1;i < m-1;i++){
			for(int j = 0;j < m;j++){
				long x = m2[i-1][m-1] * co[j];
				if(j-1 >= 0)x += m2[i-1][j-1];
				m2[i][j] = x % mod;
			}
		}
		
		long[] ret = new long[m];
		ret[0] = 1;
		long[] temp = new long[2*m];
		for(int l = 62;l >= 0;l--){
			if(n<<~l<0){
				for(int i = 0;i < m;i++)temp[i] = ret[m-1] * co[i];
				for(int i = 1;i < m;i++)temp[i] += ret[i-1];
				for(int i = 0;i < m;i++)ret[i] = temp[i] % mod;
			}
			if(l > 0){
				Arrays.fill(temp, 0L);
				for(int i = 0;i < m;i++){
					for(int j = 0;j < m;j++){
						temp[i+j] += ret[i] * ret[j];
						if(temp[i+j] >= BIG)temp[i+j] -= BIG;
					}
				}
				for(int i = 0;i < 2*m-1;i++)temp[i] %= mod;
				for(int i = 0;i < m;i++){
					long s = temp[i];
					for(int j = m;j < 2*m-1;j++){
						s += temp[j] * m2[j-m][i];
						if(s >= BIG)s -= BIG;
					}
					ret[i] = s % mod;
				}
			}
		}
		return ret;
	}

	
	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;
	}

	
	void run() throws Exception
	{
//		int n = 4000, m = 99999;
//		Random gen = new Random(0);
//		StringBuilder sb = new StringBuilder();
//		sb.append(n+ " ");
//		sb.append(1 + " ");
//		for(int i = 0;i < 1;i++){
//			sb.append(gen.nextInt(n)+1 + " ");
//			sb.append(gen.nextInt(n)+1 + " ");
//		}
//		INPUT = sb.toString();
		
		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 Q874_5().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)); }
}
yukicoder

結果

テストケース

ソースコード
