#819649 (C++17) No.2134 $\sigma$-algebra over Finite Set

• 問題: No.2134 $\sigma$-algebra over Finite Set
• ユーザー: tokusakurai
• 提出日時: 2022-11-25 22:07:18
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 101 ms / 2,000 ms
• コード長: 8,286 bytes
• コンパイル時間: 2,316 ms
• コンパイル使用メモリ: 207,364 KB
• 最終ジャッジ日時: 2025-02-09 00:17:34
• ジャッジサーバーID （参考情報）: judge2 / judge2

ファイルパターン	結果
sample	AC * 2
other	AC * 17

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); 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()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

template <typename T>
using maxheap = priority_queue<T>;

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 <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

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';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

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));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

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;
    }
};

using mint = Mod_Int<MOD>;

struct Random_Number_Generator {
    mt19937_64 mt;

    Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}

    int64_t operator()(int64_t l, int64_t r) {
        uniform_int_distribution<int64_t> dist(l, r - 1);
        return dist(mt);
    }

    int64_t operator()(int64_t r) { return (*this)(0, r); }
} rng;

using ull = unsigned long long;
const ull mod = (1ULL << 61) - 1;

ull hash_mod(ull x) {
    ull ret = (x >> 61) + (x & mod);
    return ret - (ret >= mod ? mod : 0);
}

ull hash_mul(ull x, ull y) {
    x = hash_mod(x), y = hash_mod(y);
    ull x1 = x >> 31, x2 = x & ((1ULL << 31) - 1), y1 = y >> 31, y2 = y & ((1ULL << 31) - 1);
    ull z = x1 * y2 + x2 * y1, z1 = z >> 30, z2 = z & ((1ULL << 30) - 1);
    return hash_mod(x1 * y1 * 2 + x2 * y2 + z1 + (z2 << 31));
}

ull hash_pow(ull x, ull n) {
    ull ret = 1;
    for (; n > 0; n >>= 1, x = hash_mul(x, x)) {
        if (n & 1) ret = hash_mul(ret, x);
    }
    return ret;
}

// m 以上の base を乱択で生成する
ull generate_base(ull m = (1ULL << 50)) {
    while (true) {
        ull k = rng(mod);
        if (gcd(mod - 1, k) != 1) continue;
        ull base = hash_pow(3, k);
        if (base >= m) return base;
    }
    return 0;
}

// 0 が含まれないように
template <typename T = string>
struct Rolling_Hash {
    const int n;
    const ull base; // 基数
    vector<ull> hashed, pw;

    Rolling_Hash(const T &s, ull base) : n(s.size()), base(base) {
        hashed.assign(n + 1, 0), pw.assign(n + 1, 1);
        for (int i = 0; i < n; i++) {
            pw[i + 1] = hash_mul(pw[i], base);
            hashed[i + 1] = hash_mul(hashed[i], base) + s[i];
            if (hashed[i + 1] >= mod) hashed[i + 1] -= mod;
        }
    }

    // 文字列の [l,r) の部分のハッシュ値
    ull get_hash(int l, int r) const {
        ull ret = hashed[r] + mod - hash_mul(hashed[l], pw[r - l]);
        return ret - (ret >= mod ? mod : 0);
    }

    ull get_all_hash() const { return hashed[n]; }
};

template <typename T>
struct Fixed_Size_Hash {
    const int n;
    const ull base;
    vector<T> v;
    ull hashed;
    vector<ull> pw;

    Fixed_Size_Hash(const vector<T> &v, ull base) : n(v.size()), base(base), v(v) {
        hashed = 0;
        pw.assign(n + 1, 1);
        for (int i = 0; i < n; i++) {
            pw[i + 1] = hash_mul(pw[i], base);
            hashed = hash_mul(hashed, base) + v[i];
            if (hashed >= mod) hashed -= mod;
        }
    }

    Fixed_Size_Hash(int m, const T &x, ull base) : Fixed_Size_Hash(vector<T>(m, x), base) {}

    ull add(int i, const T &x) {
        hashed += hash_mul(pw[n - 1 - i], mod + x);
        if (hashed >= mod) hashed -= mod;
        v[i] += x;
        return hashed;
    }

    ull change(int i, const T &x) { return add(i, x - v[i]); }

    ull get_hash() const { return hashed; }
};

int main() {
    int N, M;
    cin >> N >> M;

    ull base = generate_base();

    vector<vector<int>> a(N, vector<int>(M, 0));

    rep(i, M) {
        int K;
        cin >> K;

        while (K--) {
            int j;
            cin >> j;
            j--;
            a[j][i] = 1;
        }
    }

    set<ull> s;

    rep(i, N) {
        ull x = Fixed_Size_Hash<int>(a[i], base).get_hash();
        s.emplace(x);
    }

    cout << mint(2).pow(sz(s)) << '\n';
}