結果

問題 No.2507 Yet Another Subgraph Counting
ユーザー torisasami4torisasami4
提出日時 2023-10-12 11:31:59
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 195 ms / 2,000 ms
コード長 9,029 bytes
コンパイル時間 3,008 ms
コンパイル使用メモリ 244,872 KB
最終ジャッジ日時 2025-02-17 06:47:09
ジャッジサーバーID
(参考情報)
judge4 / judge1
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ファイルパターン 結果
other AC * 52
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ソースコード

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// #define _GLIBCXX_DEBUG
#pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--)
#define each(e, v) for (auto& e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
template <typename T> void print(const vector<T>& v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T> bool chmax(T& x, const T& y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T> bool chmin(T& x, const T& y) {
return (x > y) ? (x = y, true) : false;
}
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using maxheap = std::priority_queue<T>;
template <typename T> int lb(const vector<T>& v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> int ub(const vector<T>& v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> void rearrange(vector<T>& v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
// __int128_t gcd(__int128_t a, __int128_t b) {
// if (a == 0)
// return b;
// if (b == 0)
// return a;
// __int128_t cnt = a % b;
// while (cnt != 0) {
// a = b;
// b = cnt;
// cnt = a % b;
// }
// return b;
// }
struct Union_Find_Tree {
vector<int> data;
const int n;
int cnt;
Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}
int root(int x) {
if (data[x] < 0) return x;
return data[x] = root(data[x]);
}
int operator[](int i) { return root(i); }
bool unite(int x, int y) {
x = root(x), y = root(y);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y], data[y] = x;
cnt--;
return true;
}
int size(int x) { return -data[root(x)]; }
int count() { return cnt; };
bool same(int x, int y) { return root(x) == root(y); }
void clear() {
cnt = n;
fill(begin(data), end(data), -1);
}
};
template <int mod> struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int& operator+=(const Mod_Int& p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int& operator-=(const Mod_Int& p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int& operator*=(const Mod_Int& p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int& operator/=(const Mod_Int& p) {
*this *= p.inverse();
return *this;
}
Mod_Int& operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int& operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int& p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int& p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int& p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int& p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int& p) const { return x == p.x; }
bool operator!=(const Mod_Int& p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream& operator<<(ostream& os, const Mod_Int& p) {
return os << p.x;
}
friend istream& operator>>(istream& is, Mod_Int& p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
ll mpow2(ll x, ll n, ll mod) {
ll ans = 1;
x %= mod;
while (n != 0) {
if (n & 1) ans = ans * x % mod;
x = x * x % mod;
n = n >> 1;
}
ans %= mod;
return ans;
}
template <typename T> T modinv(T a, const T& m) {
T b = m, u = 1, v = 0;
while (b > 0) {
T t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return u >= 0 ? u % m : (m - (-u) % m) % m;
}
ll divide_int(ll a, ll b) {
if (b < 0) a = -a, b = -b;
return (a >= 0 ? a / b : (a - b + 1) / b);
}
// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;
// ----- library -------
template <typename T>
void fast_zeta_transform(vector<T> &a, bool upper) {
int n = a.size();
assert((n & (n - 1)) == 0);
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if (!(j & i)) {
if (upper) {
a[j] += a[j | i];
} else {
a[j | i] += a[j];
}
}
}
}
}
template <typename T>
void fast_mobius_transform(vector<T> &a, bool upper) {
int n = a.size();
assert((n & (n - 1)) == 0);
for (int i = 1; i < n; i <<= 1) {
for (int j = 0; j < n; j++) {
if (!(j & i)) {
if (upper) {
a[j] -= a[j | i];
} else {
a[j | i] -= a[j];
}
}
}
}
}
template <typename T>
vector<T> subset_convolve(const vector<T> &a, const vector<T> &b) {
int n = a.size();
assert((int)b.size() == n && (n & (n - 1)) == 0);
int k = __builtin_ctz(n);
vector<vector<T>> A(k + 1, vector<T>(n, 0)), B(k + 1, vector<T>(n, 0)), C(k + 1, vector<T>(n, 0));
for (int i = 0; i < n; i++) {
int t = __builtin_popcount(i);
A[t][i] = a[i], B[t][i] = b[i];
}
for (int i = 0; i <= k; i++) fast_zeta_transform(A[i], false), fast_zeta_transform(B[i], false);
for (int i = 0; i <= k; i++) {
for (int j = 0; j <= k - i; j++) {
for (int l = 0; l < n; l++) C[i + j][l] += A[i][l] * B[j][l];
}
}
for (int i = 0; i <= k; i++) fast_mobius_transform(C[i], false);
vector<T> c(n);
for (int i = 0; i < n; i++) c[i] = C[__builtin_popcount(i)][i];
return c;
}
template <typename T>
vector<T> exp_of_set_power_series(const vector<T> &a) {
int n = a.size();
assert((n & (n - 1)) == 0 && a[0] == 0);
vector<T> ret(n, 0);
ret[0] = 1;
for (int i = 1; i < n; i <<= 1) {
vector<T> f(begin(a) + i, begin(a) + (i << 1));
vector<T> g(begin(ret), begin(ret) + i);
auto h = subset_convolve(f, g);
copy(begin(h), end(h), begin(ret) + i);
}
return ret;
}
// ----- library -------
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(15);
int n, m;
cin >> n >> m;
vector<vector<int>> g(n, vector<int>(n, 0));
rep(i, m) {
int u, v;
cin >> u >> v;
u--, v--;
g[u][v] = 1, g[v][u] = 1;
}
vector<vector<ll>> dp(1 << n, vector<ll>(n, 0));
rep(i, n) dp[1 << i][i] = 1;
rep2(i, 1, 1 << n) {
int s = __builtin_ctz(i);
rep(j, n) rep2(k, s + 1, n) if (!(i & (1 << k)) && g[j][k]) dp[i | (1 << k)][k] += dp[i][j];
}
vector<ll> c(1 << n);
rep2(i, 1, 1 << n) {
int k = __builtin_popcount(i);
if (k == 1) {
c[i] = 1;
continue;
}
if (k == 2) {
c[i] = 0;
continue;
}
c[i] = 0;
int s = __builtin_ctz(i);
rep(j, n) c[i] += dp[i][j] * g[s][j];
c[i] /= 2;
}
vector<ll> E(1 << n, 0);
rep(i, 1 << n) rep(j, n) rep2(k, j + 1, n) if ((i & (1 << j)) && (i & (1 << k))) E[i] += g[j][k];
vector<ll> f(1 << n, 0);
rep2(C, 1, 1 << n) {
int m = 1;
while (m <= C) m *= 2;
int D = (m - 1) & ~C;
vector<ll> g;
for (int T = D;; T = (T - 1) & D) {
g.eb(f[T] * (E[T | C] - E[T] - E[C]));
if (T == 0)
break;
}
reverse(all(g));
auto h = exp_of_set_power_series(g);
f[C] += c[C];
for (int T = D, idx = sz(h) - 1; idx > 0; T = (T - 1) & D, idx--) f[C | T] += c[C] * h[idx];
}
cout << exp_of_set_power_series(f).back() << endl;
}
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