結果

問題 No.310 2文字しりとり
ユーザー uwi
提出日時 2015-12-03 03:27:43
言語 Java
(openjdk 23)
結果
TLE  
実行時間 -
コード長 7,673 bytes
コンパイル時間 5,643 ms
コンパイル使用メモリ 84,028 KB
実行使用メモリ 202,092 KB
最終ジャッジ日時 2024-09-14 08:18:10
合計ジャッジ時間 14,199 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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
other AC * 21 TLE * 1 -- * 6
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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;
// O(N^3)
public class Q874 {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    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;
    }
    
    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[][] M = new int[n][n];
        for(int i = 0;i < n;i++){
            for(int j = 0;j < n;j++){
                if(!ng[i][j]){
                    if(i != j){
                        M[i][j] = mod-1;
                        M[i][i]++;
                    }
                }
            }
        }
        if(src == -1){
            out.println(numEulerianCircuit(M, outdeg, indeg) * (on*on-m) % mod);
        }else{
            if(--M[sink][src] < 0)M[sink][src] += mod;
            M[sink][sink]++;
            outdeg[sink]++;
            indeg[src]++;
            long nec = numEulerianCircuit(M, outdeg, indeg);
            out.println(nec * invl(mod-M[sink][src], mod) % mod);
        }
    }
    
    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 < n;i++){
            ec = ec * F[outdeg[i]-1] % mod;
        }
        
        int[][] Q = new int[n-1][n-1];
        for(int i = 0;i < n-1;i++){
            for(int j = 0;j < n-1;j++){
                Q[i][j] = M[i][j];
            }
        }
        
        long det = det(Q, mod, 1);
        return ec * det % mod;
    }
    
    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 det(int[][] a, int p, int e)
    {
        int n = a.length;
        long ret = 1;
        int mod = 1;
        for(int i = 1;i <= e;i++)mod *= p;
        
        for(int i = 0;i < n;i++){
            int pivot = -1;
            int mine = 99;
            for(int j = i;j < n;j++){
                if(a[j][i] == 0)continue;
                int le = 0;
                int w = a[j][i];
                while(w % p == 0){
                    w /= p;
                    le++;
                }
                if(le < mine){
                    mine = le;
                    pivot = j;
                }
            }
            if(pivot == -1)return 0L;
            // swap rows
            if(i != pivot){
                {int[] d = a[i]; a[i] = a[pivot]; a[pivot] = d;}
                ret = mod-ret;
            }
            
            // p^f*x
            // p^g*y=p^f*(p^(g-f)*y*x^-1
            // y/x*p^(g-f)
            // p^mine
            long pmine = 1;
            for(int j = 1;j <= mine;j++)pmine *= p;
            long inv = invl(a[i][i]/pmine, mod);
            for(int r = i+1;r < n;r++){
                if(a[r][i] != 0){
                    long mul = -a[r][i]/pmine * inv % mod;
                    if(mul < 0)mul += mod;
                    for(int c = i+1;c < n;c++){
                        a[r][c] = (int)((a[r][c] + a[i][c] * mul) % mod);
                    }
                }
            }
            ret = ret * a[i][i] % mod;
        }
        if(ret < 0)ret += 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
    {
        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().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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