結果

問題 No.2134 $\sigma$-algebra over Finite Set
ユーザー kaikey
提出日時 2022-11-25 21:56:23
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 144 ms / 2,000 ms
コード長 9,708 bytes
コンパイル時間 2,964 ms
コンパイル使用メモリ 228,532 KB
最終ジャッジ日時 2025-02-09 00:11:06
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 17
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include "bits/stdc++.h"
#include <random>
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define SZ(x) ((lint)(x).size())
#define FOR(i, begin, end) for(lint i=(begin),i##_end_=(end);i<i##_end_;++i)
#define IFOR(i, begin, end) for(lint i=(end)-1,i##_begin_=(begin);i>=i##_begin_;--i)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
#define endk '\n'
using namespace std; typedef unsigned long long _ulong; typedef long long int lint; typedef long double ld; typedef pair<lint, lint> plint; typedef pair<ld, ld> pld;
struct fast_ios { fast_ios() { cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(10); }; } fast_ios_;
template<class T> auto add = [](T a, T b) -> T { return a + b; };
template<class T> auto mul = [](T a, T b) -> T { return a * b; };
template<class T> auto f_max = [](T a, T b) -> T { return max(a, b); };
template<class T> auto f_min = [](T a, T b) -> T { return min(a, b); };
template<class T> using V = vector<T>;
using Vl = V<lint>; using VVl = V<Vl>; using VVVl = V<V<Vl>>;
template< typename T > ostream& operator<<(ostream& os, const vector< T >& v) {
	for (int i = 0; i < (int)v.size(); i++) os << v[i] << (i + 1 != v.size() ? " " : "");
	return os;
}
template< typename T >istream& operator>>(istream& is, vector< T >& v) {
	for (T& in : v) is >> in;
	return is;
}
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; }
template <class T>
T div_floor(T a, T b) {
	if (b < 0) a *= -1, b *= -1;
	return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T div_ceil(T a, T b) {
	if (b < 0) a *= -1, b *= -1;
	return a > 0 ? (a - 1) / b + 1 : a / b;
}
template <class F> struct rec {
	F f;
	rec(F&& f_) : f(std::forward<F>(f_)) {}
	template <class... Args> auto operator()(Args &&... args) const {
		return f(*this, std::forward<Args>(args)...);
	}
};
//lint gcd(lint a, lint b) { if (b == 0) return a; else return gcd(b, a % b); }
lint digit(lint a) { return (lint)log10(a); }
lint e_dist(plint a, plint b) { return abs(a.first - b.first) * abs(a.first - b.first) + abs(a.second - b.second) * abs(a.second - b.second); }
lint m_dist(plint a, plint b) { return abs(a.first - b.first) + abs(a.second - b.second); }
bool check_overflow(lint a, lint b, lint limit) { if (b == 0) return false; return a >= limit / b; } // a * b > c => true
void Worshall_Floyd(VVl& g) { REP(k, SZ(g)) REP(i, SZ(g)) REP(j, SZ(g)) chmin(g[i][j], g[i][k] + g[k][j]); }
const lint MOD1000000007 = 1000000007, MOD998244353 = 998244353, INF = 1e18;
lint dx[8] = { 0, 1, 0, -1, 1, -1, 1, -1 }, dy[8] = { 1, 0, -1, 0, -1, -1, 1, 1 };
bool YN(bool flag) { cout << (flag ? "YES" : "NO") << endk; return flag; } bool yn(bool flag) { cout << (flag ? "Yes" : "No") << endk; return flag; }
struct Edge {
	lint from, to;
	lint cost;
	Edge() {

	}
	Edge(lint u, lint v, lint c) {
		cost = c;
		from = u;
		to = v;
	}
	bool operator<(const Edge& e) const {
		return cost < e.cost;
	}
};
struct WeightedEdge {
	lint to;
	lint cost;
	WeightedEdge(lint v, lint c) {
		to = v;
		cost = c;
	}
	bool operator<(const WeightedEdge& e) const {
		return cost < e.cost;
	}
};
using WeightedGraph = V<V<WeightedEdge>>;
typedef pair<plint, lint> tlint;
typedef pair<ld, ld> pld;
typedef pair<plint, plint> qlint;
typedef pair<char, lint> vstr;
typedef pair<lint, Vl> valv;


template <std::int_fast64_t Modulus>
class modint
{
	using u64 = std::int_fast64_t;

public:
	u64 a;
	constexpr modint(const u64 x = 0) noexcept : a(x% Modulus) {}
	constexpr u64& value() noexcept { return a; }
	constexpr const u64& value() const noexcept { return a; }
	constexpr modint operator+(const modint rhs) const noexcept
	{
		return modint(*this) += rhs;
	}
	constexpr modint operator-(const modint rhs) const noexcept
	{
		return modint(*this) -= rhs;
	}
	constexpr modint operator*(const modint rhs) const noexcept
	{
		return modint(*this) *= rhs;
	}
	constexpr modint operator/(const modint rhs) const noexcept
	{
		return modint(*this) /= rhs;
	}
	constexpr modint& operator+=(const modint rhs) noexcept
	{
		a += rhs.a;
		if (a >= Modulus)
		{
			a -= Modulus;
		}
		return *this;
	}
	constexpr modint& operator-=(const modint rhs) noexcept
	{
		if (a < rhs.a)
		{
			a += Modulus;
		}
		a -= rhs.a;
		return *this;
	}
	constexpr modint& operator*=(const modint rhs) noexcept
	{
		a = a * rhs.a % Modulus;
		return *this;
	}
	constexpr modint& operator/=(modint rhs) noexcept
	{
		u64 exp = Modulus - 2;
		while (exp)
		{
			if (exp % 2)
			{
				*this *= rhs;
			}
			rhs *= rhs;
			exp /= 2;
		}
		return *this;
	}
};
typedef modint<MOD998244353> ModInt;

ModInt mod_pow(ModInt x, lint n) {
	ModInt ret = 1;
	while (n > 0) {
		if (n & 1) (ret *= x);
		(x *= x);
		n >>= 1;
	}
	return ret;
}

ModInt func[200000];
void funcinit(int N)
{
	func[0] = 1;
	for (int i = 1; i <= N; i++)
	{
		func[i] = func[i - 1] * i;
	}
}
ModInt comb(ModInt n, ModInt r)
{
	if (n.a <= 0 || n.a < r.a)
	{
		return 1;
	}
	return func[n.a] / (func[r.a] * func[(n - r).a]);
}

struct UnionFind {
public:
	UnionFind() : _n(0) {}
	UnionFind(int n) : _n(n), parent_or_size(n, -1) {}

	int merge(int a, int b) {
		assert(0 <= a && a < _n);
		assert(0 <= b && b < _n);
		int x = leader(a), y = leader(b);
		if (x == y) return x;
		if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
		if (used_count) {
			if (count_in_set[x].size() < count_in_set[y].size()) {
				std::swap(count_in_set[x], count_in_set[y]);
			}
			for (auto p : count_in_set[y]) {
				count_in_set[x][p.first] += p.second;
			}
		}
		if (set_operate) {
			root_values[x] = f(root_values[y], root_values[x]);
		}
		parent_or_size[x] += parent_or_size[y];
		parent_or_size[y] = x;

		return x;
	}

	bool same(int a, int b) {
		assert(0 <= a && a < _n);
		assert(0 <= b && b < _n);
		return leader(a) == leader(b);
	}

	int leader(int a) {
		assert(0 <= a && a < _n);
		if (parent_or_size[a] < 0) return a;
		return parent_or_size[a] = leader(parent_or_size[a]);
	}

	int size(int a) {
		assert(0 <= a && a < _n);
		return -parent_or_size[leader(a)];
	}

	std::vector<std::vector<int>> groups() {
		std::vector<int> leader_buf(_n), group_size(_n);
		for (int i = 0; i < _n; i++) {
			leader_buf[i] = leader(i);
			group_size[leader_buf[i]]++;
		}
		std::vector<std::vector<int>> result(_n);
		for (int i = 0; i < _n; i++) {
			result[i].reserve(group_size[i]);
		}
		for (int i = 0; i < _n; i++) {
			result[leader_buf[i]].push_back(i);
		}
		result.erase(
			std::remove_if(result.begin(), result.end(),
				[&](const std::vector<int>& v) { return v.empty(); }),
			result.end());
		return result;
	}
	//update root calc
	//set by set operations
	void set_operate_and_value(std::vector<lint> array, function<lint(lint, lint)> _f) {
		f = _f;
		root_values = array;
		set_operate = true;
	}
	lint get_set_value(int a) {
		return root_values[leader(a)];
	}

	//regist count
	void regist_count(int a, int label) {
		if (!used_count) {
			used_count = true;
			count_in_set.assign(_n, std::map<int, int>());
		}
		count_in_set[leader(a)][label]++;
	}

	int get_count(int a, int label) {
		if (!used_count) return -1;
		return count_in_set[leader(a)][label];
	}

private:
	int _n;
	std::vector<int> parent_or_size;
	std::vector<std::map<int, int>> count_in_set;
	bool used_count = false;
	std::vector<lint> root_values;
	function<lint(lint, lint)> f;
	bool set_operate = false;
};

struct RollingHash {
	const _ulong MASK30 = (1ULL << 30) - 1;
	const _ulong MASK31 = (1ULL << 31) - 1;
	const _ulong MOD = (1ULL << 61) - 1;
	const _ulong MASK61 = MOD;

	vector<_ulong> hashed, power;

	RollingHash(const string& s, _ulong base) {
		int sz = SZ(s);
		hashed.assign(sz + 1, 0);
		power.assign(sz + 1, 0);
		power[0] = 1;
		for (int i = 0; i < sz; i++) {
			power[i + 1] = mul(power[i], base);
			hashed[i + 1] = mul(hashed[i], base) + s[i];
			if (hashed[i + 1] >= MOD) hashed[i + 1] -= MOD;
		}
	}

	//乱数生成、main関数にコピペする
	void generate_base() {
		_ulong base;
		{
			//乱数生成
			random_device seed_gen;
			mt19937 engine(seed_gen());
			uniform_real_distribution<> dist1(129, INT_MAX);
			base = dist1(engine);
		}
	}

	_ulong get(int l, int r) const {
		_ulong ret = hashed[r] + MOD - mul(hashed[l], power[r - l]);
		if (ret >= MOD) ret -= MOD;
		return ret;
	}

	//a*b mod 2^61-1を返す関数
	inline _ulong mul(_ulong a, _ulong b) const {
		_ulong u_a = a >> 31;//aの31bit以降
		_ulong d_a = a & MASK31;//aの31bit未満
		_ulong u_b = b >> 31;
		_ulong d_b = b & MASK31;

		_ulong mid = d_a * u_b + u_a * d_b;
		_ulong u_mid = mid >> 30;
		_ulong d_mid = mid & MASK30;
		return CalcMod(u_a * u_b * 2 + u_mid + (d_mid << 31) + d_a * d_b);
	}

	//mod 2^61-1を返す関数
	inline _ulong CalcMod(_ulong x) const {
		_ulong u_x = x >> 61;
		_ulong d_x = x & MASK61;
		_ulong res = u_x + d_x;
		if (res >= MOD) res -= MOD;
		return res;
	}
};

int main() {
	lint N, M;
	cin >> N >> M;
	VVl arr(M), mat(M, Vl(N));
	REP(i, M) {
		lint L;
		cin >> L;
		arr[i].assign(L, 0);
		cin >> arr[i];
		REP(j, L) {
			mat[i][arr[i][j] - 1] = 1;
		}
	}
	V<RollingHash> rhs;
	_ulong base;
	{
		//乱数生成
		random_device seed_gen;
		mt19937 engine(seed_gen());
		uniform_real_distribution<> dist1(129, INT_MAX);
		base = dist1(engine);
	}
	REP(i, N) {
		string s = "";
		REP(j, M) {
			s += (char)('0' + mat[j][i]);
		}
		rhs.push_back(RollingHash(s, base));
	}
	UnionFind tree(N);
	REP(i, N) {
		REP(j, N) {
			if (rhs[i].get(0, M) == rhs[j].get(0, M)) tree.merge(i, j);
		}
	}
	set<lint> st;
	REP(i, N) st.insert(tree.leader(i));
	cout << mod_pow(2, SZ(st)).a << endk;
}
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