#586636 (D) No.1303 Inconvenient Kingdom

提出ソース

結果

問題	No.1303 Inconvenient Kingdom
ユーザー	👑 hos.lyric
提出日時	2020-11-28 20:24:19
言語	D (dmd 2.106.1)
結果	WA
実行時間	-
コード長	6,060 bytes
コンパイル時間	1,757 ms
コンパイル使用メモリ	162,896 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-22 10:07:59
合計ジャッジ時間	2,989 ms
ジャッジサーバーID （参考情報）	judge5 / judge3

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 6,812 KB
testcase_01	AC	1 ms 6,944 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	3 ms 6,944 KB
testcase_05	WA	-
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
testcase_10	WA	-
testcase_11	WA	-
testcase_12	AC	17 ms 6,940 KB
testcase_13	WA	-
testcase_14	AC	18 ms 6,944 KB
testcase_15	WA	-
testcase_16	AC	19 ms 6,940 KB
testcase_17	AC	19 ms 6,940 KB
testcase_18	AC	6 ms 6,944 KB
testcase_19	AC	5 ms 6,944 KB
testcase_20	AC	6 ms 6,940 KB
testcase_21	AC	9 ms 6,944 KB
testcase_22	AC	13 ms 6,944 KB
testcase_23	AC	16 ms 6,944 KB
testcase_24	AC	18 ms 6,944 KB
testcase_25	AC	19 ms 6,944 KB
testcase_26	AC	4 ms 6,940 KB
testcase_27	AC	4 ms 6,944 KB
testcase_28	AC	3 ms 6,940 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	4 ms 6,944 KB
testcase_31	AC	5 ms 6,944 KB
testcase_32	AC	5 ms 6,940 KB
testcase_33	AC	5 ms 6,940 KB
testcase_34	AC	1 ms 6,940 KB
testcase_35	AC	1 ms 6,940 KB
testcase_36	AC	5 ms 6,940 KB
testcase_37	AC	6 ms 6,940 KB

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ソースコード

raw source code

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;
}


// det(x I + a)
// O(n^3)
T[] charPoly(T)(const(T[][]) a) {
  import std.algorithm.mutation : swap;
  const n = cast(int)(a.length);
  auto b = new T[][](n, n);
  foreach (i; 0 .. n) b[i][] = a[i][];
  // upper Hessenberg
  foreach (j; 0 .. n - 2) {
    foreach (i; j + 1 .. n) {
      if (b[i][j]) {
        swap(b[j + 1], b[i]);
        break;
      }
    }
    if (b[j + 1][j]) {
      const r = 1 / b[j + 1][j];
      foreach (i; j + 2 .. n) {
        const s = r * b[i][j];
        foreach (jj; j .. n) b[i][jj] -= s * b[j + 1][jj];
        foreach (ii; 0 .. n) b[ii][j + 1] += s * b[ii][i];
      }
    }
  }
  // fss[i] := det(x I_i + b[0..i][0..i])
  auto fss = new T[][n + 1];
  fss[0] = [T(1)];
  foreach (i; 0 .. n) {
    fss[i + 1] = new T[i + 2];
    foreach (k; 0 .. i + 1) fss[i + 1][k + 1] = fss[i][k];
    foreach (k; 0 .. i + 1) fss[i + 1][k] += b[i][i] * fss[i][k];
    T prod = 1;
    foreach_reverse (j; 0 .. i) {
      prod *= -b[j + 1][j];
      const s = prod * b[j][i];
      foreach (k; 0 .. j + 1) fss[i + 1][k] += s * fss[j][k];
    }
  }
  return fss[n];
}


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 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;
      
      int id;
      auto ids = new int[N];
      foreach (r; 0 .. N) {
        if (uf[r] < 0) {
          foreach (u; 0 .. N) {
            if (uf.root(u) == r) {
              ids[u] = id++;
            }
          }
        }
      }
      auto lap = new Mint[][](N, N);
      foreach (i; 0 .. M) {
        const x = ids[A[i]];
        const y = ids[B[i]];
        lap[x][x] += 1;
        lap[x][y] -= 1;
        lap[y][x] -= 1;
        lap[y][y] += 1;
      }
      const fs = charPoly(lap);
      debug {
        writeln("fs = ", fs);
      }
      Mint ans;
      if (szs.length >= 2) {
        int cnt;
        foreach (x; 0 .. szs.length) foreach (y; x + 1 .. szs.length) {
          if (szs[0] * szs[1] == szs[x] * szs[y]) {
            ++cnt;
          }
        }
        ans = fs[szs.length];
        foreach (sz; szs) {
          ans /= sz;
        }
        ans *= cnt;
        ans *= szs[0] * szs[1];
      } else {
        // (N - 1) double counts
        ans = fs[1] / N * (1 - (N - 1)) + fs[2];
      }
      
      writeln(cost);
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}

yukicoder

結果

テストケース

ソースコード