結果
問題 | No.2507 Yet Another Subgraph Counting |
ユーザー |
👑 |
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 |
ソースコード
#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);// rankedfor (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];}// zetafor (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];}}// productfor (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;}}// moebiusfor (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];}}// unrankvector<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];}// zetafor (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) {// zetazbs[h][m + 1] = 0;memcpy(zbs[(1 << m) + h], zbs[h], ((m + 1) + 1) * sizeof(T));// productfor (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];}}}// moebiusfor (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];}}// unrankvector<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];}// zetafor (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) {// zetazbs[(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));// productfor (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];}}}}// moebiusfor (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];}}// unrankvector<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];}// cyclevector<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 < rafter : 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;}