結果

問題 No.1784 Not a star yet...
ユーザー 👑 hos.lyric
提出日時 2021-12-13 01:07:30
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 191 ms / 2,000 ms
コード長 7,192 bytes
コンパイル時間 2,087 ms
コンパイル使用メモリ 159,596 KB
実行使用メモリ 23,484 KB
最終ジャッジ日時 2024-06-22 13:39:06
合計ジャッジ時間 8,445 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 3
other AC * 61
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 # 

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)); }

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

enum MO = 998244353;
alias Mint = ModInt!MO;

enum LIM = 2 * 260^^2 + 10;
Mint[] inv, fac, invFac;
void prepare() {
  inv = new Mint[LIM];
  fac = new Mint[LIM];
  invFac = new Mint[LIM];
  inv[1] = 1;
  foreach (i; 2 .. LIM) {
    inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]);
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(long n, long k) {
  if (n < 0) {
    if (k >= 0) {
      return (-1)^^(k & 1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (-1)^^((n - k) & 1) * binom(-k - 1, n - k);
    } else {
      return Mint(0);
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM);
      return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];
    } else {
      return Mint(0);
    }
  }
}


void main() {
  prepare;
  
  try {
    for (; ; ) {
      const N = readInt();
      auto U = new int[N - 1];
      auto V = new int[N - 1];
      auto L = new int[N - 1];
      foreach (i; 0 .. N - 1) {
        U[i] = readInt - 1;
        V[i] = readInt - 1;
        L[i] = readInt;
      }
      
      const D = N * (N - 1) / 2 - (N - 2);
      const A = cast(int)(L.count(1));
      const B = cast(int)(L.count(2));
      auto as = new int[N];
      auto bs = new int[N];
      foreach (i; 0 .. N - 1) {
        if (L[i] == 1) { ++as[U[i]]; ++as[V[i]]; }
        if (L[i] == 2) { ++bs[U[i]]; ++bs[V[i]]; }
      }
      debug {
        writeln("D = ", D);
        writeln("A = ", A, ", B = ", B);
        writeln("as = ", as);
        writeln("bs = ", bs);
      }
      
      auto f = new Mint[][][](A + 1, B + 1, B + 1);
      auto g = new Mint[][](B, B + 1);
      foreach (b; 1 .. B + 1) {
        f[0][b][b - 1] = 1;
      }
      foreach (a; 0 .. A + 1) foreach (b; 0 .. B + 1) {
        if (a == A && b == B) {
          continue;
        }
        auto tmp = new Mint[B + 1];
        tmp[B] = 1;
        if (a > 0) {
          const prob = (Mint(a) / Mint(A + 2 * B)) * (1 - Mint((N - 1) - (a - 1) - b) / Mint(D));
          foreach (j; 0 .. B + 1) {
            tmp[j] -= prob * (f[a - 1][b][j] - f[a][b][j]);
          }
        }
        if (b > 0) {
          const prob = (Mint(2 * b) / Mint(A + 2 * B)) * (1 - Mint((N - 1) - a - (b - 1)) / Mint(D));
          foreach (j; 0 .. B + 1) {
            tmp[j] -= prob * (f[a][b - 1][j] - f[a][b][j]);
          }
        }
        if (b < B) {
          const prob = (Mint(2 * (B - b)) / Mint(A + 2 * B)) * (Mint((N - 1) - a - b) / Mint(D));
          foreach (j; 0 .. B + 1) {
            tmp[j] -= prob * (f[a][b + 1][j] - f[a][b][j]);
          }
        }
        if (a < A) {
          const prob = (Mint(A - a) / Mint(A + 2 * B)) * (Mint((N - 1) - a - b) / Mint(D));
          foreach (j; 0 .. B + 1) {
            tmp[j] -= prob * (/*f[a + 1][b][j]*/ - f[a][b][j]);
          }
          tmp[] *= prob.inv;
          f[a + 1][b][] = tmp[];
        } else {
          g[b][] = tmp[];
          g[b][B] *= -1;
        }
      }
      
      foreach (h; 0 .. B) {
        foreach (i; h .. B) {
          if (g[i][h]) {
            break;
          }
        }
        assert(g[h][h]);
        const s = g[h][h].inv;
        foreach (j; h + 1 .. B + 1) {
          g[h][j] *= s;
        }
        foreach (i; h + 1 .. B) {
          const t = g[i][h];
          foreach (j; h + 1 .. B + 1) {
            g[i][j] -= t * g[h][j];
          }
        }
      }
      foreach_reverse (i; 0 .. B) {
        foreach (j; i + 1 .. B) {
          g[i][B] -= g[i][j] * g[j][B];
        }
      }
      
      auto pot = new Mint[][](A + 1, B + 1);
      foreach (a; 0 .. A + 1) foreach (b; 0 .. B + 1) {
        pot[a][b] = f[a][b][B];
        foreach (j; 0 .. B) {
          pot[a][b] += f[a][b][j] * g[j][B];
        }
      }
      Mint start, goal;
      foreach (u; 0 .. N) {
        start += pot[as[u]][bs[u]];
      }
      if (A > 0) goal += A * pot[1][0];
      if (B > 0) goal += B * pot[0][1];
      goal += pot[A][B];
      const ans = (goal - start) / N;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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