結果

問題 No.1303 Inconvenient Kingdom
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-11-27 22:30:47
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 287 ms / 3,000 ms
コード長 7,794 bytes
コンパイル時間 1,893 ms
コンパイル使用メモリ 162,704 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-06-22 10:05:57
合計ジャッジ時間 5,612 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
sample AC * 4
other AC * 34
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(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 = 998244353;
alias Mint = ModInt!MO;


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;
}


Mint det(Mint[][] a) {
  const n = cast(int)(a.length);
  Mint ret = 1;
  foreach (h; 0 .. n) {
    if (!a[h][h]) {
      foreach (i; h + 1 .. n) {
        if (a[i][h]) {
          swap(a[h], a[i]);
          ret += 1;
          goto found;
        }
      }
      ret = 0;
      break;
     found:
    }
    ret *= a[h][h];
    const r = a[h][h].inv;
    foreach (i; h + 1 .. n) {
      const s = r * a[i][h];
      foreach (j; h + 1 .. n) {
        a[i][j] -= s * a[h][j];
      }
    }
  }
  return ret;
}

Mint[] charPoly(Mint[][] a) {
  const n = cast(int)(a.length);
  auto ps = new Mint[n + 1];
  ps[n] = 1;
  for (int h = n - 1; h >= 0; --h) {
    // closed walks at h with repetition allowed from 0, ..., h - 1
    auto sub = new Mint[][](n, h + 1);
    for (int i = n; i >= 1; --i) {
      sub[i - 1][h] += ps[i];
    }
    for (int i = n - 1; i >= 1; --i) for (int u = 0; u <= h; ++u) {
      for (int v = 0; v < h; ++v) {
        sub[i - 1][v] -= sub[i][u] * a[u][v];
      }
    }
    for (int i = n - 1; i >= 0; --i) for (int u = 0; u <= h; ++u) {
      ps[i] += sub[i][u] * a[u][h];
    }
  }
  for (int i = n - 1; i >= 0; i -= 2) {
    ps[i] *= -1;
  }
  return ps;
}

void main() {
  try {
    for (; ; ) {
      const N = readInt();
      const M = readInt();
      auto A = new int[M];
      auto B = new int[M];
      foreach (i; 0 .. M) {
        A[i] = readInt() - 1;
        B[i] = readInt() - 1;
      }
      
      auto adj = new bool[][](N, N);
      foreach (i; 0 .. M) {
        adj[A[i]][B[i]] = true;
        adj[B[i]][A[i]] = true;
      }
      
      auto uf = new int[N];
      uf[] = -1;
      foreach (i; 0 .. M) {
        uf.connect(A[i], B[i]);
      }
      int[] szs;
      foreach (r; 0 .. N) {
        if (uf[r] < 0) {
          szs ~= -uf[r];
        }
      }
      szs.sort.reverse;
      int cost = N * (N - 1) / 2;
      foreach (s; szs) {
        cost -= s * (s - 1) / 2;
      }
      if (szs.length >= 2) {
        cost -= szs[0] * szs[1];
      }
      cost *= 2;
      
      auto uss = new int[][N];
      foreach (u; 0 .. N) {
        uss[uf.root(u)] ~= u;
      }
      
      Mint ans;
      if (szs.length >= 2) {
        if (szs[0] == szs[1]) {
          const cnt = cast(int)(szs.count(szs[0]));
          ans = cnt * (cnt - 1) / 2;
        } else {
          const cnt = cast(int)(szs.count(szs[1]));
          ans = cnt;
        }
        ans *= szs[0] * szs[1];
        foreach (r; 0 .. N) {
          if (uf[r] < 0) {
            const n = -uf[r];
            auto a = new Mint[][](n - 1, n - 1);
            foreach (x; 0 .. n) foreach (y; 0 .. n) {
              if (adj[uss[r][x]][uss[r][y]]) {
                if (x < n - 1) {
                  a[x][x] += 1;
                }
                if (x < n - 1 && y < n - 1) {
                  a[x][y] -= 1;
                }
              }
            }
            debug {
              writeln("a = ", a);
            }
            ans *= det(a);
          }
        }
      } else {
        {
          auto a = new Mint[][](N - 1, N - 1);
          foreach (u; 0 .. N) foreach (v; 0 .. N) {
            if (adj[u][v]) {
              if (u < N - 1) {
                a[u][u] += 1;
              }
              if (u < N - 1 && v < N - 1) {
                a[u][v] -= 1;
              }
            }
          }
          // ans += det(a);
          const d = det(a);
          ans += d;
          ans -= d * (N - 1);
        }
        /*
        foreach (p; 0 .. N) foreach (q; p + 1 .. N) {
          if (!adj[p][q]) {
            int[] us;
            foreach (u; 0 .. N) {
              if (u != p && u != q) {
                us ~= u;
              }
            }
            const n = cast(int)(us.length);
            auto a = new Mint[][](n, n);
            foreach (x; 0 .. n) foreach (y; 0 .. n) {
              if (adj[us[x]][us[y]]) {
                a[x][x] += 1;
                a[x][y] -= 1;
              }
            }
            foreach (x; 0 .. n) {
              if (adj[p][us[x]]) a[x][x] += 1;
              if (adj[q][us[x]]) a[x][x] += 1;
            }
            ans += det(a);
          }
        }
        */
        {
          auto a = new Mint[][](N, N);
          foreach (u; 0 .. N) foreach (v; 0 .. N) {
            if (adj[u][v]) {
              a[u][u] += 1;
              a[u][v] -= 1;
            }
          }
          const fs = charPoly(a);
          debug {
            writeln("fs = ", fs);
          }
          ans += (-1)^^((N - 2) & 1) * fs[2];
        }
      }
      
      
      writeln(cost);
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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