結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー 👑 hos.lyrichos.lyric
提出日時 2023-10-27 16:33:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 11,280 bytes
コンパイル時間 1,292 ms
コンパイル使用メモリ 122,080 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-25 13:04:28
合計ジャッジ時間 3,586 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
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ファイルパターン 結果
other AC * 44 WA * 8
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ソースコード

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プレゼンテーションモードにする

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i
    >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
// as * bs
// ZT: T[2^n][n+1]
template <class T, class ZT>
vector<T> setMul(int n, const vector<T> &as, const vector<T> &bs, ZT zas, ZT zbs) {
assert(static_cast<int>(as.size()) == 1 << n);
assert(static_cast<int>(bs.size()) == 1 << n);
// ranked
for (int h = 0; h < 1 << n; ++h) {
memset(zas[h], 0, (n + 1) * sizeof(T));
zas[h][__builtin_popcount(h)] = as[h];
}
for (int h = 0; h < 1 << n; ++h) {
memset(zbs[h], 0, (n + 1) * sizeof(T));
zbs[h][__builtin_popcount(h)] = bs[h];
}
// zeta
for (int w = 1; w < 1 << n; w <<= 1) {
for (int h0 = 0; h0 < 1 << n; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= n; ++k) zas[h + w][k] += zas[h][k];
}
}
for (int w = 1; w < 1 << n; w <<= 1) {
for (int h0 = 0; h0 < 1 << n; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= n; ++k) zbs[h + w][k] += zbs[h][k];
}
}
// product
for (int h = 0; h < 1 << n; ++h) {
for (int k = n; k >= 0; --k) {
T t = 0;
for (int l = 0; l <= k; ++l) t += zas[h][l] * zbs[h][k - l];
zas[h][k] = t;
}
}
// moebius
for (int w = 1; w < 1 << n; w <<= 1) {
for (int h0 = 0; h0 < 1 << n; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= n; ++k) zas[h + w][k] -= zas[h][k];
}
}
// unrank
vector<T> cs(1 << n);
for (int h = 0; h < 1 << n; ++h) cs[h] = zas[h][__builtin_popcount(h)];
return cs;
}
// exp(as)
// assume as[0] == 0
// exp(a0 + a1 X) = exp(a0) + exp(a0) a1 X
// ZT1: T[2^(n-1)][n]
// ZT: T[2^n][n+1]
template <class T, class ZT1, class ZT>
vector<T> setExp(int n, const vector<T> &as, ZT1 zas, ZT zbs) {
assert(static_cast<int>(as.size()) == 1 << n);
assert(as[0] == 0);
zbs[0][0] = 1;
for (int m = 0; m < n; ++m) {
// ranked a[2^m, 2^(m+1))
for (int h = 0; h < 1 << m; ++h) {
memset(zas[h], 0, (m + 1) * sizeof(T));
zas[h][__builtin_popcount(h)] = as[(1 << m) + h];
}
// zeta
for (int w = 1; w < 1 << m; w <<= 1) {
for (int h0 = 0; h0 < 1 << m; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= m; ++k) zas[h + w][k] += zas[h][k];
}
}
for (int h = 0; h < 1 << m; ++h) {
// zeta
zbs[h][m + 1] = 0;
memcpy(zbs[(1 << m) + h], zbs[h], ((m + 1) + 1) * sizeof(T));
// product
for (int k = 0; k <= m; ++k) for (int l = 0; l <= m - k; ++l) {
zbs[(1 << m) + h][k + l + 1] += zbs[h][k] * zas[h][l];
}
}
}
// moebius
for (int w = 1; w < 1 << n; w <<= 1) {
for (int h0 = 0; h0 < 1 << n; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= n; ++k) zbs[h + w][k] -= zbs[h][k];
}
}
// unrank
vector<T> bs(1 << n);
for (int h = 0; h < 1 << n; ++h) bs[h] = zbs[h][__builtin_popcount(h)];
return bs;
}
// \sum[0<=i<=n] fs[i] as^i/i!
// assume as[0] == 0
// f(a0 + a1 X) + f(a0) + f'(a0) a1 X
// ZT1: T[2^(n-1)][n]
// ZT: T[2^(n+1)][n+1]
template <class T, class ZT1, class ZT>
vector<T> setCom(int n, const vector<T> &fs, const vector<T> &as, ZT1 zas, ZT zbs) {
assert(static_cast<int>(fs.size()) == n + 1);
assert(static_cast<int>(as.size()) == 1 << n);
assert(as[0] == 0);
// zbs[2^(n-i), 2^(n-i+1)): composite f^(i)
for (int i = 0; i <= n; ++i) zbs[1<<(n-i)][0] = fs[i];
for (int m = 0; m < n; ++m) {
// ranked a[2^m, 2^(m+1))
for (int h = 0; h < 1 << m; ++h) {
memset(zas[h], 0, (m + 1) * sizeof(T));
zas[h][__builtin_popcount(h)] = as[(1 << m) + h];
}
// zeta
for (int w = 1; w < 1 << m; w <<= 1) {
for (int h0 = 0; h0 < 1 << m; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= m; ++k) zas[h + w][k] += zas[h][k];
}
}
for (int i = 0; i < n - m; ++i) {
for (int h = 0; h < 1 << m; ++h) {
// zeta
zbs[(1<<(n-i)) + h][m + 1] = 0;
memcpy(zbs[(1<<(n-i)) + (1 << m) + h], zbs[(1<<(n-i)) + h], ((m + 1) + 1) * sizeof(T));
// product
for (int k = 0; k <= m; ++k) for (int l = 0; l <= m - k; ++l) {
zbs[(1<<(n-i)) + (1 << m) + h][k + l + 1] += zbs[(1<<(n-(i+1))) + h][k] * zas[h][l];
}
}
}
}
// moebius
for (int w = 1; w < 1 << n; w <<= 1) {
for (int h0 = 0; h0 < 1 << n; h0 += w << 1) for (int h = h0; h < h0 + w; ++h) {
for (int k = 0; k <= n; ++k) zbs[(1<<n) + h + w][k] -= zbs[(1<<n) + h][k];
}
}
// unrank
vector<T> bs(1 << n);
for (int h = 0; h < 1 << n; ++h) bs[h] = zbs[(1<<n) + h][__builtin_popcount(h)];
return bs;
}
// \sum[i] fs[i] as^i
// not necessarily as[0] == 0
// ZT1: T[2^(n-1)][n]
// ZT: T[2^(n+1)][n+1]
template <class T, class ZT1, class ZT>
vector<T> setComPoly(int n, vector<T> fs, vector<T> as, ZT1 zas, ZT zbs) {
assert(static_cast<int>(as.size()) == 1 << n);
const int fsLen = fs.size();
if (fsLen == 0) return vector<T>(1 << n, 0);
vector<T> gs(n + 1);
for (int i = 0; i <= n; ++i) {
T t = 0;
for (int j = fsLen; --j >= 0; ) (t *= as[0]) += fs[j];
gs[i] = t;
for (int j = 1; j < fsLen; ++j) fs[j - 1] = j * fs[j];
fs[fsLen - 1] = 0;
}
as[0] = 0;
return setCom(n, gs, as, zas, zbs);
}
////////////////////////////////////////////////////////////////////////////////
constexpr int MAX_N = 13;
Mint zas[1 << (MAX_N + 1)][MAX_N + 1];
Mint zbs[1 << (MAX_N + 1)][MAX_N + 1];
int N, M;
vector<int> A, B;
Mint dp[1 << MAX_N][MAX_N];
int main() {
for (; ~scanf("%d%d", &N, &M); ) {
A.resize(M);
B.resize(M);
for (int i = 0; i < M; ++i) {
scanf("%d%d", &A[i], &B[i]);
--A[i];
--B[i];
if (A[i] > B[i]) {
swap(A[i], B[i]);
}
}
vector<int> adj(N, 0);
for (int i = 0; i < M; ++i) {
adj[A[i]] |= 1 << B[i];
adj[B[i]] |= 1 << A[i];
}
// cycle
vector<Mint> cs(1 << N, 0);
memset(dp, 0, sizeof(dp));
for (int r = 0; r < N; ++r) {
dp[1 << r][r] = 1;
for (int p = 1 << r; p < 1 << (r + 1); ++p) {
for (int u = 0; u <= r; ++u) if (p & 1 << u) {
for (int v = 0; v < r; ++v) if (!(p & 1 << v)) {
if (adj[u] >> v & 1) {
dp[p | 1 << v][v] += dp[p][u];
}
}
if (adj[u] >> r & 1) {
cs[p] += dp[p][u];
}
}
}
}
const Mint INV2 = Mint(2).inv();
for (int i = 0; i < M; ++i) cs[1 << A[i] | 1 << B[i]] -= 1;
for (int p = 0; p < 1 << N; ++p) cs[p] *= INV2;
// cerr<<"cs = "<<cs<<endl;
for (int u = 0; u < N; ++u) cs[1 << u] += 1;
fill(adj.begin(), adj.end(), 0);
for (int i = 0; i < M; ++i) {
adj[B[i]] |= 1 << A[i];
}
for (int r = 1; r < N; ++r) {
/*
cs[p]:
before: connected graph on p, allow bridge (u, v) s.t. u < v < r
after : connected graph on p, allow bridge (u, v) s.t. u < v <= r
*/
vector<Mint> ds(1 << (N - 1)), es(1 << (N - 1));
for (int p = 0; p < 1 << r; ++p) for (int q = 0; q < 1 << (N-1-r); ++q) {
ds[p | q << r] = cs[p | 1 << r | q << (r + 1)];
es[p | q << r] = __builtin_popcount(p & adj[r]) * cs[p | q << (r + 1)];
}
es = setExp(N - 1, es, zas, zbs);
ds = setMul(N - 1, ds, es, zas, zbs);
for (int p = 0; p < 1 << r; ++p) for (int q = 0; q < 1 << (N-1-r); ++q) {
cs[p | 1 << r | q << (r + 1)] = ds[p | q << r];
}
// cerr<<"cs = "<<cs<<endl;
}
cs = setExp(N, cs, zas, zbs);
printf("%u\n", cs.back().x);
}
return 0;
}
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