結果

問題 No.2605 Pickup Parentheses
ユーザー tokusakuraitokusakurai
提出日時 2024-01-12 22:33:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 328 ms / 2,000 ms
コード長 11,883 bytes
コンパイル時間 2,244 ms
コンパイル使用メモリ 214,888 KB
実行使用メモリ 10,940 KB
最終ジャッジ日時 2024-09-30 06:27:34
合計ジャッジ時間 10,722 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 1 ms
5,248 KB
testcase_03 AC 3 ms
5,248 KB
testcase_04 AC 3 ms
5,248 KB
testcase_05 AC 4 ms
5,248 KB
testcase_06 AC 5 ms
5,248 KB
testcase_07 AC 4 ms
5,248 KB
testcase_08 AC 5 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 4 ms
5,248 KB
testcase_11 AC 3 ms
5,248 KB
testcase_12 AC 2 ms
5,248 KB
testcase_13 AC 2 ms
5,248 KB
testcase_14 AC 3 ms
5,248 KB
testcase_15 AC 4 ms
5,248 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 3 ms
5,248 KB
testcase_18 AC 193 ms
9,260 KB
testcase_19 AC 95 ms
6,512 KB
testcase_20 AC 19 ms
5,248 KB
testcase_21 AC 11 ms
5,248 KB
testcase_22 AC 6 ms
5,248 KB
testcase_23 AC 202 ms
8,824 KB
testcase_24 AC 19 ms
5,248 KB
testcase_25 AC 231 ms
9,140 KB
testcase_26 AC 238 ms
9,256 KB
testcase_27 AC 192 ms
9,132 KB
testcase_28 AC 236 ms
9,332 KB
testcase_29 AC 48 ms
5,248 KB
testcase_30 AC 114 ms
7,120 KB
testcase_31 AC 106 ms
6,312 KB
testcase_32 AC 47 ms
5,248 KB
testcase_33 AC 239 ms
10,236 KB
testcase_34 AC 231 ms
9,728 KB
testcase_35 AC 173 ms
8,088 KB
testcase_36 AC 215 ms
9,252 KB
testcase_37 AC 217 ms
8,796 KB
testcase_38 AC 47 ms
6,260 KB
testcase_39 AC 15 ms
5,248 KB
testcase_40 AC 115 ms
8,044 KB
testcase_41 AC 103 ms
9,436 KB
testcase_42 AC 148 ms
9,616 KB
testcase_43 AC 28 ms
5,248 KB
testcase_44 AC 27 ms
5,376 KB
testcase_45 AC 4 ms
5,248 KB
testcase_46 AC 11 ms
5,248 KB
testcase_47 AC 2 ms
5,248 KB
testcase_48 AC 68 ms
8,936 KB
testcase_49 AC 163 ms
9,056 KB
testcase_50 AC 68 ms
6,440 KB
testcase_51 AC 131 ms
9,264 KB
testcase_52 AC 83 ms
7,004 KB
testcase_53 AC 131 ms
9,352 KB
testcase_54 AC 70 ms
6,692 KB
testcase_55 AC 124 ms
9,552 KB
testcase_56 AC 26 ms
5,248 KB
testcase_57 AC 144 ms
9,556 KB
testcase_58 AC 272 ms
10,940 KB
testcase_59 AC 214 ms
9,628 KB
testcase_60 AC 266 ms
9,868 KB
testcase_61 AC 250 ms
9,756 KB
testcase_62 AC 267 ms
9,596 KB
testcase_63 AC 261 ms
9,976 KB
testcase_64 AC 281 ms
9,964 KB
testcase_65 AC 219 ms
9,896 KB
testcase_66 AC 328 ms
10,208 KB
testcase_67 AC 251 ms
9,960 KB
testcase_68 AC 7 ms
6,400 KB
testcase_69 AC 1 ms
5,248 KB
testcase_70 AC 2 ms
5,248 KB
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>
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;
}

int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

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 T>
void reorder(vector<T> &a, const vector<int> &ord) {
    int n = a.size();
    vector<T> b(n);
    for (int i = 0; i < n; i++) b[i] = a[ord[i]];
    swap(a, b);
}

template <typename T>
T floor(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? x / y : (x - y + 1) / y);
}

template <typename T>
T ceil(T x, T y) {
    assert(y != 0);
    if (y < 0) x = -x, y = -y;
    return (x >= 0 ? (x + y - 1) / y : x / y);
}

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);
        cerr << fixed << setprecision(15);
    }
} io_setup;

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

template <typename T>
struct Combination {
    static vector<T> _fac, _ifac;

    Combination() {}

    static void init(int n) {
        _fac.resize(n + 1), _ifac.resize(n + 1);
        _fac[0] = 1;
        for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
        _ifac[n] = _fac[n].inverse();
        for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
    }

    static T fac(int k) { return _fac[k]; }

    static T ifac(int k) { return _ifac[k]; }

    static T inv(int k) { return fac(k - 1) * ifac(k); }

    static T P(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac(n) * ifac(n - k);
    }

    static T C(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac(n) * ifac(n - k) * ifac(k);
    }

    // n 個の区別できる箱に、k 個の区別できない玉を入れる場合の数
    static T H(int n, int k) {
        if (n < 0 || k < 0) return 0;
        return k == 0 ? 1 : C(n + k - 1, k);
    }

    // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数
    static T second_stirling_number(int n, int k) {
        T ret = 0;
        for (int i = 0; i <= k; i++) {
            T tmp = C(k, i) * T(i).pow(n);
            ret += ((k - i) & 1) ? -tmp : tmp;
        }
        return ret * ifac(k);
    }

    // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数
    static T bell_number(int n, int k) {
        if (n == 0) return 1;
        k = min(k, n);
        vector<T> pref(k + 1);
        pref[0] = 1;
        for (int i = 1; i <= k; i++) {
            if (i & 1) {
                pref[i] = pref[i - 1] - ifac(i);
            } else {
                pref[i] = pref[i - 1] + ifac(i);
            }
        }
        T ret = 0;
        for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
        return ret;
    }
};

template <typename T>
vector<T> Combination<T>::_fac = vector<T>();

template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();

using comb = Combination<mint>;

template <typename T>
struct Number_Theoretic_Transform {
    static int max_base;
    static T root;
    static vector<T> r, ir;

    Number_Theoretic_Transform() {}

    static void init() {
        if (!r.empty()) return;
        int mod = T::get_mod();
        int tmp = mod - 1;
        root = 2;
        while (root.pow(tmp >> 1) == 1) root++;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        r.resize(max_base), ir.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]  := 1 の 2^(i+2) 乗根
            ir[i] = r[i].inverse();                 // ir[i] := 1/r[i]
        }
    }

    static void ntt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = n; k >>= 1;) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = w * a[j];
                    a[i] = x + y, a[j] = x - y;
                }
                w *= r[__builtin_ctz(++t)];
            }
        }
    }

    static void intt(vector<T> &a) {
        init();
        int n = a.size();
        assert((n & (n - 1)) == 0);
        assert(n <= (1 << max_base));
        for (int k = 1; k < n; k <<= 1) {
            T w = 1;
            for (int s = 0, t = 0; s < n; s += 2 * k) {
                for (int i = s, j = s + k; i < s + k; i++, j++) {
                    T x = a[i], y = a[j];
                    a[i] = x + y, a[j] = w * (x - y);
                }
                w *= ir[__builtin_ctz(++t)];
            }
        }
        T inv = T(n).inverse();
        for (auto &e : a) e *= inv;
    }

    static vector<T> convolve(vector<T> a, vector<T> b) {
        if (a.empty() || b.empty()) return {};
        if (min(a.size(), b.size()) < 40) {
            int n = a.size(), m = b.size();
            vector<T> c(n + m - 1, 0);
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j];
            }
            return c;
        }
        int k = (int)a.size() + (int)b.size() - 1, n = 1;
        while (n < k) n <<= 1;
        a.resize(n, 0), b.resize(n, 0);
        ntt(a), ntt(b);
        for (int i = 0; i < n; i++) a[i] *= b[i];
        intt(a), a.resize(k);
        return a;
    }
};

template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;

template <typename T>
T Number_Theoretic_Transform<T>::root = T();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();

template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();

using NTT = Number_Theoretic_Transform<mint>;

void solve() {
    int N, M;
    cin >> N >> M;

    comb::init(N * 2);

    vector<int> l(M), r(M), d(M);
    rep(i, M) {
        cin >> l[i] >> r[i];
        l[i]--;
        d[i] = r[i] - l[i];
    }

    auto catalan = [&](int n) -> mint {
        if (n % 2 != 0) return 0;
        return comb::C(n, n / 2) / (n / 2 + 1);
    };

    if (M == 0) {
        cout << catalan(N) << '\n';
        return;
    }

    // vector<vector<mint>> f(M);
    // rep(i, M) {
    //     f[i].assign(d[i] + 1, 0);
    //     f[i][0] = 1;
    //     f[i][d[i]] = -catalan(d[i]);
    // }

    auto get = [&](int i) {
        vector<mint> f(d[i] + 1, 0);
        f[0] = 1;
        f[d[i]] = -catalan(d[i]);
        return f;
    };

    auto rec = [&](auto &&rec, int L, int R) -> vector<mint> {
        if (R == L + 1) return get(L);
        int m = (L + R) / 2;
        return NTT::convolve(rec(rec, L, m), rec(rec, m, R));
    };

    auto g = rec(rec, 0, M);

    mint ans = 0;

    rep(i, min(N + 1, sz(g))) {
        ans += catalan(N - i) * g[i]; //
    }

    cout << ans << '\n';
}

int main() {
    int T = 1;
    // cin >> T;
    while (T--) solve();
}
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