結果

問題 No.1116 Cycles of Dense Graph
ユーザー 👑 hos.lyrichos.lyric
提出日時 2020-07-17 22:03:47
言語 D
(dmd 2.106.1)
結果
RE  
実行時間 -
コード長 6,550 bytes
コンパイル時間 1,840 ms
コンパイル使用メモリ 166,036 KB
実行使用メモリ 13,760 KB
最終ジャッジ日時 2024-06-22 07:40:44
合計ジャッジ時間 3,810 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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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 8 ms
6,812 KB
testcase_01 AC 129 ms
13,040 KB
testcase_02 AC 9 ms
6,940 KB
testcase_03 AC 7 ms
6,944 KB
testcase_04 AC 8 ms
7,180 KB
testcase_05 AC 11 ms
6,976 KB
testcase_06 AC 42 ms
13,188 KB
testcase_07 AC 9 ms
6,940 KB
testcase_08 AC 8 ms
6,940 KB
testcase_09 AC 7 ms
6,940 KB
testcase_10 AC 7 ms
6,944 KB
testcase_11 AC 23 ms
11,116 KB
testcase_12 AC 12 ms
7,072 KB
testcase_13 AC 7 ms
6,940 KB
testcase_14 AC 8 ms
6,944 KB
testcase_15 AC 7 ms
6,944 KB
testcase_16 AC 11 ms
6,940 KB
testcase_17 AC 7 ms
6,940 KB
testcase_18 AC 9 ms
7,340 KB
testcase_19 AC 16 ms
10,340 KB
testcase_20 AC 9 ms
7,132 KB
testcase_21 AC 8 ms
7,064 KB
testcase_22 AC 25 ms
11,472 KB
testcase_23 AC 7 ms
6,944 KB
testcase_24 AC 158 ms
13,244 KB
testcase_25 AC 8 ms
6,944 KB
testcase_26 AC 156 ms
13,188 KB
testcase_27 AC 8 ms
6,940 KB
testcase_28 AC 9 ms
6,940 KB
testcase_29 AC 8 ms
6,940 KB
testcase_30 AC 8 ms
6,940 KB
testcase_31 AC 7 ms
6,944 KB
testcase_32 AC 8 ms
6,944 KB
testcase_33 AC 8 ms
6,940 KB
testcase_34 AC 8 ms
6,944 KB
testcase_35 AC 7 ms
6,944 KB
testcase_36 AC 164 ms
13,760 KB
testcase_37 RE -
testcase_38 RE -
testcase_39 AC 159 ms
13,356 KB
testcase_40 AC 154 ms
13,424 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)); }


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;


enum LIM = 2 * 10^^5 + 100;
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 (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);
  }
}


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;
}


void main() {
  prepare;
  auto two = new Mint[LIM];
  two[0] = 1;
  foreach (i; 1 .. LIM) {
    two[i] = two[i - 1] * 2;
  }
  
  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;
      }
      
      int[] us = A.dup ~ B.dup;
      us = us.sort.uniq.array;
      const usLen = cast(int)(us.length);
      foreach (i; 0 .. M) {
        A[i] = us.lowerBound(A[i]);
        B[i] = us.lowerBound(B[i]);
      }
      
      Mint ans;
      
      // 0
      foreach (k; 3 .. N + 1) {
        ans += binom(N, k) * fac[k - 1] * inv[2];
      }
      
      // 1
      foreach (j; 1 .. (N - 2) + 1) {
        ans -= M * (binom(N - 2, j) * fac[j]);
        debug {
          writeln(j, ": ", binom(N - 2, j) * fac[j]);
        }
      }
      
      auto mem = new bool[][](2 * M + 1, 2 * M + 1);
      auto cache = new Mint[][](2 * M + 1, 2 * M + 1);
      Mint calc(int x, int y) {
        Mint ret;
        if (!mem[x][y]) {
          foreach (j; 0 .. (N - y) + 1) {
            ret += binom(N - y, j) * two[x - 1] * fac[x + j - 1];
          }
          debug {
            writefln("calc %s %s = %s", x, y, ret);
          }
          mem[x][y] = true;
          cache[x][y] = ret;
        } else {
          ret = cache[x][y];
        }
        return ret;
      }
      
      foreach (p; 0 .. 1 << M) {
        if (popcnt(p) >= 2) {
          auto uf = new int[usLen];
          uf[] = -1;
          auto deg = new int[usLen];
          foreach (i; 0 .. M) {
            if (p & 1 << i) {
              uf.connect(A[i], B[i]);
              ++deg[A[i]];
              ++deg[B[i]];
            }
          }
          auto uss = new int[][usLen];
          foreach (u; 0 .. usLen) {
            uss[uf.root(u)] ~= u;
          }
          int numComps, numVertices;
          int numCycles;
          foreach (r; 0 .. usLen) {
            if (uss[r].length >= 2) {
              numComps += 1;
              numVertices += uss[r].length;
              if (uss[r].any!(u => (deg[u] >= 3))) {
                goto failed;
              }
              if (uss[r].all!(u => (deg[u] == 2))) {
                ++numCycles;
              }
            }
          }
          {
            Mint num;
            switch (numCycles) {
              case 0: {
                num = calc(numComps, numVertices);
              } break;
              case 1: {
                num = 1;
              } break;
              default: {
import core.stdc.stdlib;exit(1);
              }
            }
            ans += (-1)^^(popcnt(p) & 1) * num;
          }
         failed:
        }
      }
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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