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 Java
(openjdk 23)
結果
AC  
実行時間 2,326 ms / 6,000 ms
コード長 14,343 bytes
コンパイル時間 4,683 ms
コンパイル使用メモリ 90,424 KB
実行使用メモリ 166,228 KB
最終ジャッジ日時 2024-09-14 19:05:35
合計ジャッジ時間 19,961 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
other AC * 28
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ソースコード

diff #
プレゼンテーションモードにする

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)); }
}
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