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#471941#8721. 括号序列Andyqian7TL 1691ms18004kbC++209.6kb2024-07-11 11:46:152024-07-11 11:46:16

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  • [2024-07-11 11:46:16]
  • 评测
  • 测评结果：TL
  • 用时：1691ms
  • 内存：18004kb
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  • [2024-07-11 11:46:15]
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answer

#include <vector>
#include <iostream>
#include <cassert>
#include <functional>
using namespace std;

constexpr int P = 998244353;
using i64 = long long;
// assume -P <= x < 2P
int norm(int x)
{
    if (x < 0)
    {
        x += P;
    }
    if (x >= P)
    {
        x -= P;
    }
    return x;
}
template <class T>
T power(T a, int b)
{
    T res = 1;
    for (; b; b /= 2, a *= a)
    {
        if (b % 2)
        {
            res *= a;
        }
    }
    return res;
}
struct Z
{
    int x;
    Z(int x = 0) : x(norm(x)) {}
    int val() const
    {
        return x;
    }
    Z operator-() const
    {
        return Z(norm(P - x));
    }
    Z inv() const
    {
        assert(x != 0);
        return power(*this, P - 2);
    }
    Z &operator*=(const Z &rhs)
    {
        x = i64(x) * rhs.x % P;
        return *this;
    }
    Z &operator+=(const Z &rhs)
    {
        x = norm(x + rhs.x);
        return *this;
    }
    Z &operator-=(const Z &rhs)
    {
        x = norm(x - rhs.x);
        return *this;
    }
    Z &operator/=(const Z &rhs)
    {
        return *this *= rhs.inv();
    }
    friend Z operator*(const Z &lhs, const Z &rhs)
    {
        Z res = lhs;
        res *= rhs;
        return res;
    }
    friend Z operator+(const Z &lhs, const Z &rhs)
    {
        Z res = lhs;
        res += rhs;
        return res;
    }
    friend Z operator-(const Z &lhs, const Z &rhs)
    {
        Z res = lhs;
        res -= rhs;
        return res;
    }
    friend Z operator/(const Z &lhs, const Z &rhs)
    {
        Z res = lhs;
        res /= rhs;
        return res;
    }
    friend std::istream &operator>>(std::istream &is, Z &a)
    {
        i64 v;
        is >> v;
        a = Z(v);
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const Z &a)
    {
        return os << a.val();
    }
};

std::vector<int> rev;
std::vector<Z> roots{0, 1};
void dft(std::vector<Z> &a)
{
    int n = a.size();

    if (int(rev.size()) != n)
    {
        int k = __builtin_ctz(n) - 1;
        rev.resize(n);
        for (int i = 0; i < n; i++)
        {
            rev[i] = rev[i >> 1] >> 1 | (i & 1) << k;
        }
    }

    for (int i = 0; i < n; i++)
    {
        if (rev[i] < i)
        {
            std::swap(a[i], a[rev[i]]);
        }
    }
    if (int(roots.size()) < n)
    {
        int k = __builtin_ctz(roots.size());
        roots.resize(n);
        while ((1 << k) < n)
        {
            Z e = power(Z(3), (P - 1) >> (k + 1));
            for (int i = 1 << (k - 1); i < (1 << k); i++)
            {
                roots[2 * i] = roots[i];
                roots[2 * i + 1] = roots[i] * e;
            }
            k++;
        }
    }
    for (int k = 1; k < n; k *= 2)
    {
        for (int i = 0; i < n; i += 2 * k)
        {
            for (int j = 0; j < k; j++)
            {
                Z u = a[i + j];
                Z v = a[i + j + k] * roots[k + j];
                a[i + j] = u + v;
                a[i + j + k] = u - v;
            }
        }
    }
}
void idft(std::vector<Z> &a)
{
    int n = a.size();
    std::reverse(a.begin() + 1, a.end());
    dft(a);
    Z inv = (1 - P) / n;
    for (int i = 0; i < n; i++)
    {
        a[i] *= inv;
    }
}
struct Poly
{
    std::vector<Z> a;
    Poly() {}
    Poly(const std::vector<Z> &a) : a(a) {}
    Poly(const std::initializer_list<Z> &a) : a(a) {}
    int size() const
    {
        return a.size();
    }
    void resize(int n)
    {
        a.resize(n);
    }
    Z operator[](int idx) const
    {
        if (idx < size())
        {
            return a[idx];
        }
        else
        {
            return 0;
        }
    }
    Z &operator[](int idx)
    {
        return a[idx];
    }
    Poly mulxk(int k) const
    {
        auto b = a;
        b.insert(b.begin(), k, 0);
        return Poly(b);
    }
    Poly modxk(int k) const
    {
        k = std::min(k, size());
        return Poly(std::vector<Z>(a.begin(), a.begin() + k));
    }
    Poly divxk(int k) const
    {
        if (size() <= k)
        {
            return Poly();
        }
        return Poly(std::vector<Z>(a.begin() + k, a.end()));
    }
    friend Poly operator+(const Poly &a, const Poly &b)
    {
        std::vector<Z> res(std::max(a.size(), b.size()));
        for (int i = 0; i < int(res.size()); i++)
        {
            res[i] = a[i] + b[i];
        }
        return Poly(res);
    }
    friend Poly operator-(const Poly &a, const Poly &b)
    {
        std::vector<Z> res(std::max(a.size(), b.size()));
        for (int i = 0; i < int(res.size()); i++)
        {
            res[i] = a[i] - b[i];
        }
        return Poly(res);
    }
    friend Poly operator*(Poly a, Poly b)
    {
        if (a.size() == 0 || b.size() == 0)
        {
            return Poly();
        }
        int sz = 1, tot = a.size() + b.size() - 1;
        while (sz < tot)
        {
            sz *= 2;
        }
        a.a.resize(sz);
        b.a.resize(sz);
        dft(a.a);
        dft(b.a);
        for (int i = 0; i < sz; ++i)
        {
            a.a[i] = a[i] * b[i];
        }
        idft(a.a);
        a.resize(tot);
        return a;
    }
    friend Poly operator*(Z a, Poly b)
    {
        for (int i = 0; i < int(b.size()); i++)
        {
            b[i] *= a;
        }
        return b;
    }
    friend Poly operator*(Poly a, Z b)
    {
        for (int i = 0; i < int(a.size()); i++)
        {
            a[i] *= b;
        }
        return a;
    }
    Poly &operator+=(Poly b)
    {
        return (*this) = (*this) + b;
    }
    Poly &operator-=(Poly b)
    {
        return (*this) = (*this) - b;
    }
    Poly &operator*=(Poly b)
    {
        return (*this) = (*this) * b;
    }
    Poly deriv() const
    {
        if (a.empty())
        {
            return Poly();
        }
        std::vector<Z> res(size() - 1);
        for (int i = 0; i < size() - 1; ++i)
        {
            res[i] = (i + 1) * a[i + 1];
        }
        return Poly(res);
    }
    Poly integr() const
    {
        std::vector<Z> res(size() + 1);
        for (int i = 0; i < size(); ++i)
        {
            res[i + 1] = a[i] / (i + 1);
        }
        return Poly(res);
    }
    Poly inv(int m) const
    {
        Poly x{a[0].inv()};
        int k = 1;
        while (k < m)
        {
            k *= 2;
            x = (x * (Poly{2} - modxk(k) * x)).modxk(k);
        }
        return x.modxk(m);
    }
    Poly log(int m) const
    {
        return (deriv() * inv(m)).integr().modxk(m);
    }
    Poly exp(int m) const
    {
        Poly x{1};
        int k = 1;
        while (k < m)
        {
            k *= 2;
            x = (x * (Poly{1} - x.log(k) + modxk(k))).modxk(k);
        }
        return x.modxk(m);
    }
    Poly pow(int k, int m) const
    {
        int i = 0;
        while (i < size() && a[i].val() == 0)
        {
            i++;
        }
        if (i == size() || 1LL * i * k >= m)
        {
            return Poly(std::vector<Z>(m));
        }
        Z v = a[i];
        auto f = divxk(i) * v.inv();
        return (f.log(m - i * k) * k).exp(m - i * k).mulxk(i * k) * power(v, k);
    }
    Poly sqrt(int m) const
    {
        Poly x{1};
        int k = 1;
        while (k < m)
        {
            k *= 2;
            x = (x + (modxk(k) * x.inv(k)).modxk(k)) * ((P + 1) / 2);
        }
        return x.modxk(m);
    }
    Poly mulT(Poly b) const
    {
        if (b.size() == 0)
        {
            return Poly();
        }
        int n = b.size();
        std::reverse(b.a.begin(), b.a.end());
        return ((*this) * b).divxk(n - 1);
    }
    std::vector<Z> eval(std::vector<Z> x) const
    {
        if (size() == 0)
        {
            return std::vector<Z>(x.size(), 0);
        }
        const int n = std::max(int(x.size()), size());
        std::vector<Poly> q(4 * n);
        std::vector<Z> ans(x.size());
        x.resize(n);
        std::function<void(int, int, int)> build = [&](int p, int l, int r)
        {
            if (r - l == 1)
            {
                q[p] = Poly{1, -x[l]};
            }
            else
            {
                int m = (l + r) / 2;
                build(2 * p, l, m);
                build(2 * p + 1, m, r);
                q[p] = q[2 * p] * q[2 * p + 1];
            }
        };
        build(1, 0, n);
        std::function<void(int, int, int, const Poly &)> work = [&](int p, int l, int r, const Poly &num)
        {
            if (r - l == 1)
            {
                if (l < int(ans.size()))
                {
                    ans[l] = num[0];
                }
            }
            else
            {
                int m = (l + r) / 2;
                work(2 * p, l, m, num.mulT(q[2 * p + 1]).modxk(m - l));
                work(2 * p + 1, m, r, num.mulT(q[2 * p]).modxk(r - m));
            }
        };
        work(1, 0, n, mulT(q[1].inv(n)));
        return ans;
    }
};
int main()
{
    int n;
    cin >> n;
    Poly g{1};
    int k = 1;
    Poly e = {1};
    while (k < n)
    {
        k *= 2;
        Poly H = ((e + g).log(k) - g.log(k)) * g - e + g - g.mulxk(1);
        Poly H1i = g + g * g;
        g = (g - H * H1i).modxk(k);
    }
    Poly f = (e - g.integr()).inv(n + 1);
    Z fac = 1;
    for (int i = 1; i <= n; i++)
    {
        fac *= i;
    }
    cout << f[n] * fac;
}
源文件, 语言: C++20

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3620kb

input:

3

output:

28

result:

ok 1 number(s): "28"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3848kb

input:

1

output:

1

result:

ok 1 number(s): "1"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3592kb

input:

2

output:

4

result:

ok 1 number(s): "4"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3552kb

input:

4

output:

282

result:

ok 1 number(s): "282"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3556kb

input:

5

output:

3718

result:

ok 1 number(s): "3718"

Test #6:

score: 0
Accepted
time: 0ms
memory: 3560kb

input:

6

output:

60694

result:

ok 1 number(s): "60694"

Test #7:

score: 0
Accepted
time: 0ms
memory: 3608kb

input:

7

output:

1182522

result:

ok 1 number(s): "1182522"

Test #8:

score: 0
Accepted
time: 0ms
memory: 3548kb

input:

8

output:

26791738

result:

ok 1 number(s): "26791738"

Test #9:

score: 0
Accepted
time: 0ms
memory: 3560kb

input:

9

output:

692310518

result:

ok 1 number(s): "692310518"

Test #10:

score: 0
Accepted
time: 0ms
memory: 3624kb

input:

10

output:

135061370

result:

ok 1 number(s): "135061370"

Test #11:

score: 0
Accepted
time: 1ms
memory: 3596kb

input:

100

output:

423669705

result:

ok 1 number(s): "423669705"

Test #12:

score: 0
Accepted
time: 16ms
memory: 4076kb

input:

1234

output:

878522960

result:

ok 1 number(s): "878522960"

Test #13:

score: 0
Accepted
time: 717ms
memory: 10440kb

input:

54321

output:

827950477

result:

ok 1 number(s): "827950477"

Test #14:

score: 0
Accepted
time: 804ms
memory: 10804kb

input:

65536

output:

380835743

result:

ok 1 number(s): "380835743"

Test #15:

score: 0
Accepted
time: 1691ms
memory: 18004kb

input:

131072

output:

842796122

result:

ok 1 number(s): "842796122"

Test #16:

score: 0
Accepted
time: 1526ms
memory: 17816kb

input:

131071

output:

981021531

result:

ok 1 number(s): "981021531"

Test #17:

score: 0
Accepted
time: 1542ms
memory: 17792kb

input:

131070

output:

480197639

result:

ok 1 number(s): "480197639"

Test #18:

score: -100
Time Limit Exceeded

input:

131074

output:

result:
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