結果

問題 No.310 2文字しりとり
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-03-28 17:06:20
言語 D
(dmd 2.106.1)
結果
AC  
実行時間 2,972 ms / 6,000 ms
コード長 9,086 bytes
コンパイル時間 4,666 ms
コンパイル使用メモリ 153,456 KB
実行使用メモリ 38,684 KB
最終ジャッジ日時 2023-09-04 22:47:53
合計ジャッジ時間 21,465 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge14
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 1 ms
4,376 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 2 ms
4,380 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 2 ms
4,376 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 2 ms
4,380 KB
testcase_08 AC 2 ms
4,380 KB
testcase_09 AC 1 ms
4,380 KB
testcase_10 AC 1 ms
4,380 KB
testcase_11 AC 1 ms
4,376 KB
testcase_12 AC 1 ms
4,380 KB
testcase_13 AC 1 ms
4,376 KB
testcase_14 AC 1 ms
4,376 KB
testcase_15 AC 1 ms
4,376 KB
testcase_16 AC 1 ms
4,380 KB
testcase_17 AC 2 ms
4,380 KB
testcase_18 AC 4 ms
4,376 KB
testcase_19 AC 16 ms
4,392 KB
testcase_20 AC 21 ms
4,500 KB
testcase_21 AC 2,351 ms
38,152 KB
testcase_22 AC 2,972 ms
38,576 KB
testcase_23 AC 2,950 ms
38,524 KB
testcase_24 AC 2,958 ms
38,608 KB
testcase_25 AC 2,953 ms
38,684 KB
testcase_26 AC 617 ms
11,108 KB
testcase_27 AC 889 ms
12,400 KB
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ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }

uint xrand() {
  static uint x = 314159265, y = 358979323, z = 846264338, w = 327950288;
  uint t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;
}

int root(int[] uf, int u) {
  return (uf[u] < 0) ? u : (uf[u] = uf.root(uf[u]));
}
bool connect(int[] uf, int u, int v) {
  u = uf.root(u);
  v = uf.root(v);
  if (u == v) return false;
  if (uf[u] > uf[v]) swap(u, v);
  uf[u] += uf[v];
  uf[v] = u;
  return true;
}

F[] findLinearRecurrence(F)(F[] as) {
  import std.algorithm : min;
  const n = cast(int)(as.length);
  int d, m;
  auto cs = new F[n + 1], bs = new F[n + 1];
  cs[0] = bs[0] = 1;
  F invBef = 1;
  foreach (i; 0 .. n) {
    ++m;
    F dif = as[i];
    foreach (j; 1 .. d + 1) dif += cs[j] * as[i - j];
    if (dif.x != 0) {
      auto csDup = cs.dup;
      const r = dif * invBef;
      foreach (j; m .. n) cs[j] -= r * bs[j - m];
      if (2 * d <= i) {
        d = i + 1 - d;
        m = 0;
        bs = csDup;
        invBef = dif.inv;
      }
    }
  }
  return cs[0 .. d + 1];
}

struct ModInt(int M_) {
  import std.conv : to;
  alias M = M_;
  int x;
  this(ModInt a) { x = a.x; }
  this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }
  ref ModInt opAssign(long a) { return (this = ModInt(a)); }
  ref ModInt opOpAssign(string op)(ModInt a) {
    static if (op == "+") { x += a.x; if (x >= M) x -= M; }
    else static if (op == "-") { x -= a.x; if (x < 0) x += M; }
    else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }
    else static if (op == "/") { this *= a.inv(); }
    else static assert(false);
    return this;
  }
  ref ModInt opOpAssign(string op)(long a) {
    static if (op == "^^") {
      if (a < 0) return (this = inv()^^(-a));
      ModInt t2 = this, te = ModInt(1);
      for (long e = a; e > 0; e >>= 1) {
        if (e & 1) te *= t2;
        t2 *= t2;
      }
      x = cast(int)(te.x);
      return this;
    } else return mixin("this " ~ op ~ "= ModInt(a)");
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  ModInt opUnary(string op: "-")() const { return ModInt(-x); }
  ModInt opBinary(string op, T)(T a) const {
    return mixin("ModInt(this) " ~ op ~ "= a");
  }
  ModInt opBinaryRight(string op)(long a) const {
    return mixin("ModInt(a) " ~ op ~ "= this");
  }
  bool opCast(T: bool)() const { return (x != 0); }
  string toString() const { return x.to!string; }
}

enum MO = 1000000007;
alias Mint = ModInt!MO;

void main() {
  try {
    for (; ; ) {
      debug {
        writeln("========");
      }
      
      const N = readInt();
      const M = readInt();
      auto A = new int[M];
      auto B = new int[M];
      foreach (k; 0 .. M) {
        A[k] = readInt() - 1;
        B[k] = readInt() - 1;
      }
      
      auto adj = new bool[][](N, N);
      foreach (u; 0 .. N) foreach (v; 0 .. N) {
        adj[u][v] = true;
      }
      foreach (k; 0 .. M) {
        adj[A[k]][B[k]] = false;
      }
      auto used = new bool[N];
      auto deg = new int[N];
      auto uf = new int[N];
      uf[] = -1;
      foreach (u; 0 .. N) foreach (v; 0 .. N) {
        if (adj[u][v]) {
          ++deg[u];
          --deg[v];
          used[u] = used[v] = true;
          uf.connect(u, v);
        }
      }
      int[] us;
      foreach (u; 0 .. N) {
        if (used[u]) {
          us ~= u;
        }
      }
      if (us.empty) {
        writeln(1);
        continue;
      }
      
      bool ok = true;
      int s = -1, t = -1;
      foreach (u; us) {
        switch (deg[u]) {
          case +1: {
            ok = ok && (s == -1);
            s = u;
          } break;
          case 0: {
            //
          } break;
          case -1: {
            ok = ok && (t == -1);
            t = u;
          } break;
          default: {
            ok = false;
          }
        }
      }
      foreach (u; us) {
        ok = ok && (uf.root(us[0]) == uf.root(u));
      }
      if (!ok) {
        writeln(0);
        continue;
      }
      debug {
        writeln("adj = ", adj);
        writeln("us = ", us);
        writeln("s = ", s, ", t = ", t);
      }
      
      const usLen = cast(int)(us.length);
      auto outdeg = new int[usLen];
      foreach (i; 0 .. usLen) foreach (j; 0 .. usLen) {
        if (adj[us[i]][us[j]]) {
          ++outdeg[i];
        }
      }
      int[] as, bs, cs;
      foreach (k; 0 .. M) {
        if (used[A[k]] && used[B[k]]) {
          as ~= us.lowerBound(A[k]);
          bs ~= us.lowerBound(B[k]);
          cs ~= +1;
        }
      }
      if (s != -1) {
        // add (t, s)
        s = us.lowerBound(s);
        t = us.lowerBound(t);
        ++outdeg[t];
        as ~= t;
        bs ~= s;
        cs ~= -1;
      }
      const n = usLen - 1;
      const m = cast(int)(as.length);
      debug {
        writeln("outdeg = ", outdeg);
        writeln("as = ", as);
        writeln("bs = ", bs);
        writeln("cs = ", cs);
      }
      
      debug {
        // O(N^3)
        auto a = new Mint[][](n, n);
        foreach (i; 0 .. n) foreach (j; 0 .. n) {
          if (adj[us[i]][us[j]]) {
            a[i][j] -= 1;
          }
        }
        if (s != -1) {
          if (s < n && t < n) {
            a[t][s] -= 1;
          }
        }
        foreach (i; 0 .. n) {
          a[i][i] += outdeg[i];
        }
        Mint brt = 1;
        foreach (h; 0 .. n) {
          foreach (i; h .. n) {
            if (a[i][h]) {
              if (h != i) {
                brt *= -1;
              }
              swap(a[h], a[i]);
              break;
            }
          }
          brt *= a[h][h];
          if (!a[h][h]) {
            break;
          }
          const ahhInv = a[h][h].inv;
          foreach (i; h + 1 .. n) {
            const coef = a[i][h] * ahhInv;
            foreach (j; h .. n) {
              a[i][j] -= coef * a[h][j];
            }
          }
        }
        writeln("brt det = ", brt);
        foreach (i; 0 .. usLen) {
          foreach (d; 1 .. outdeg[i]) {
            brt *= d;
          }
        }
        if (s == -1) {
          brt *= (N^^2 - M);
        }
        writeln("brt = ", brt);
      }
      
      Mint ans;
      for (; ; ) {
        auto dots = new Mint[2 * n];
        auto coef = new Mint[n];
        foreach (i; 0 .. n) {
          coef[i] = xrand();
        }
        auto diag = new Mint[n];
        foreach (i; 0 .. n) {
          diag[i] = 1 + xrand() % (MO - 1);
        }
        auto vec = new Mint[n];
        foreach (i; 0 .. n) {
          vec[i] = xrand();
        }
        foreach (h; 0 .. 2 * n) {
          // dot
          foreach (i; 0 .. n) {
            dots[h] += coef[i] * vec[i];
          }
          // mul diag
          vec[] *= diag[];
          // mul Laplacian
          auto vecNext = new Mint[n];
          vecNext[] = -vec.sum;
          foreach (i; 0 .. n) {
            vecNext[i] += outdeg[i] * vec[i];
          }
          foreach (k; 0 .. m) {
            if (as[k] < n && bs[k] < n) {
              vecNext[as[k]] += cs[k] * vec[bs[k]];
            }
          }
          vec = vecNext;
        }
        const res = findLinearRecurrence(dots);
        if (res.length == n + 1) {
          ans = (-1)^^(n & 1) * res[n];
          foreach (i; 0 .. n) {
            ans /= diag[i];
          }
          debug {
            writeln("det = ", ans);
          }
          break;
        }
      }
      foreach (i; 0 .. usLen) {
        foreach (d; 1 .. outdeg[i]) {
          ans *= d;
        }
      }
      if (s == -1) {
        ans *= (N^^2 - M);
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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