#848261 (C++17) No.2243 Coaching Schedule

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問題	No.2243 Coaching Schedule
コンテスト
ユーザー	jiangly
提出日時	2023-03-11 01:44:08
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	2,583 ms / 4,000 ms
コード長	13,741 bytes
コンパイル時間	2,867 ms
コンパイル使用メモリ	218,516 KB
最終ジャッジ日時	2025-02-11 09:48:02
ジャッジサーバーID （参考情報）	judge5 / judge3
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ファイルパターン	結果
other	AC * 37
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ソースコード

raw source code
#include <bits/stdc++.h>

using i64 = long long;
template<class T>
constexpr T power(T a, i64 b) {
    T res = 1;
    for (; b; b /= 2, a *= a) {
        if (b % 2) {
            res *= a;
        }
    }
    return res;
}

template<int P>
struct MInt {
    int x;
    constexpr MInt() : x{} {}
    constexpr MInt(i64 x) : x{norm(x % P)} {}
    
    constexpr int norm(int x) const {
        if (x < 0) {
            x += P;
        }
        if (x >= P) {
            x -= P;
        }
        return x;
    }
    constexpr int val() const {
        return x;
    }
    explicit constexpr operator int() const {
        return x;
    }
    constexpr MInt operator-() const {
        MInt res;
        res.x = norm(P - x);
        return res;
    }
    constexpr MInt inv() const {
        assert(x != 0);
        return power(*this, P - 2);
    }
    constexpr MInt &operator*=(MInt rhs) {
        x = 1LL * x * rhs.x % P;
        return *this;
    }
    constexpr MInt &operator+=(MInt rhs) {
        x = norm(x + rhs.x);
        return *this;
    }
    constexpr MInt &operator-=(MInt rhs) {
        x = norm(x - rhs.x);
        return *this;
    }
    constexpr MInt &operator/=(MInt rhs) {
        return *this *= rhs.inv();
    }
    friend constexpr MInt operator*(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res *= rhs;
        return res;
    }
    friend constexpr MInt operator+(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res += rhs;
        return res;
    }
    friend constexpr MInt operator-(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res -= rhs;
        return res;
    }
    friend constexpr MInt operator/(MInt lhs, MInt rhs) {
        MInt res = lhs;
        res /= rhs;
        return res;
    }
    friend constexpr std::istream &operator>>(std::istream &is, MInt &a) {
        i64 v;
        is >> v;
        a = MInt(v);
        return is;
    }
    friend constexpr std::ostream &operator<<(std::ostream &os, const MInt &a) {
        return os << a.val();
    }
    friend constexpr bool operator==(MInt lhs, MInt rhs) {
        return lhs.val() == rhs.val();
    }
    friend constexpr bool operator!=(MInt lhs, MInt rhs) {
        return lhs.val() != rhs.val();
    }
};

template<int V, int P>
constexpr MInt<P> CInv = MInt<P>(V).inv();

constexpr int P = 998244353;
using Z = MInt<P>;

std::vector<int> rev;
template<int P>
std::vector<MInt<P>> roots{0, 1};

template<int P>
constexpr MInt<P> findPrimitiveRoot() {
    MInt<P> i = 2;
    int k = __builtin_ctz(P - 1);
    while (true) {
        if (power(i, 1 << (k - 1)) != 1 && power(i, 1 << k) == 1) {
            break;
        }
        i += 1;
    }
    return i;
}

template<int P>
constexpr MInt<P> primitiveRoot = findPrimitiveRoot<P>();

template<>
constexpr MInt<998244353> primitiveRoot<998244353> {31};

template<int P>
constexpr void dft(std::vector<MInt<P>> &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 (roots<P>.size() < n) {
        int k = __builtin_ctz(roots<P>.size());
        roots<P>.resize(n);
        while ((1 << k) < n) {
            auto e = power(primitiveRoot<P>, 1 << (__builtin_ctz(P - 1) - k - 1));
            for (int i = 1 << (k - 1); i < (1 << k); i++) {
                roots<P>[2 * i] = roots<P>[i];
                roots<P>[2 * i + 1] = roots<P>[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++) {
                MInt<P> u = a[i + j];
                MInt<P> v = a[i + j + k] * roots<P>[k + j];
                a[i + j] = u + v;
                a[i + j + k] = u - v;
            }
        }
    }
}

template<int P>
constexpr void idft(std::vector<MInt<P>> &a) {
    int n = a.size();
    std::reverse(a.begin() + 1, a.end());
    dft(a);
    MInt<P> inv = (1 - P) / n;
    for (int i = 0; i < n; i++) {
        a[i] *= inv;
    }
}

template<int P = 998244353>
struct Poly {
    using Value = MInt<P>;

    std::vector<Value> a;
    constexpr Poly() : a{} {}
    
    explicit constexpr Poly(int n) : a(n) {}
    
    template<class F>
    explicit constexpr Poly(int n, F f) : a(n) {
        for (int i = 0; i < n; i++) {
            a[i] = f(i);
        }
    }
    explicit constexpr Poly(const std::vector<Value> &a) : a(a) {}
    explicit constexpr Poly(const std::initializer_list<Value> &a) : a(a) {}
    
    template<class InputIt, class = std::_RequireInputIter<InputIt>>
    explicit constexpr Poly(InputIt first, InputIt last) : a(first, last) {}
    
    constexpr int size() const {
        return a.size();
    }
    explicit constexpr operator std::vector<Value>() const {
        return a;
    }
    constexpr Value operator[](int idx) const {
        if (idx < size()) {
            return a[idx];
        } else {
            return 0;
        }
    }
    constexpr Value &operator[](int idx) {
        return a[idx];
    }
    constexpr Poly shift(int k) const {
        if (k >= 0) {
            auto b = a;
            b.insert(b.begin(), k, 0);
            return Poly(b);
        } else if (size() <= -k) {
            return Poly();
        } else {
            return Poly(a.begin() + (-k), a.end());
        }
    }
    constexpr Poly resize(int k) const {
        Poly f{a};
        f.a.resize(k);
        return f;
    }
    constexpr friend Poly operator+(const Poly &a, const Poly &b) {
        std::vector<Value> 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);
    }
    constexpr friend Poly operator-(const Poly &a, const Poly &b) {
        std::vector<Value> 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);
    }
    constexpr friend Poly operator-(const Poly &a) {
        std::vector<Value> res(a.size());
        for (int i = 0; i < int(res.size()); i++) {
            res[i] = -a[i];
        }
        return Poly(res);
    }
    constexpr friend Poly operator*(Poly a, Poly b) {
        if (a.size() == 0 || b.size() == 0) {
            return Poly();
        }
        if (a.size() < b.size()) {
            std::swap(a, b);
        }
        if (b.size() < 128) {
            Poly c(a.size() + b.size() - 1);
            for (int i = 0; i < a.size(); i++) {
                for (int j = 0; j < b.size(); j++) {
                    c[i + j] += a[i] * b[j];
                }
            }
            return c;
        }
        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;
    }
    constexpr friend Poly operator*(Value a, Poly b) {
        for (int i = 0; i < int(b.size()); i++) {
            b[i] *= a;
        }
        return b;
    }
    constexpr friend Poly operator*(Poly a, Value b) {
        for (int i = 0; i < int(a.size()); i++) {
            a[i] *= b;
        }
        return a;
    }
    constexpr Poly &operator+=(Poly b) {
        return (*this) = (*this) + b;
    }
    constexpr Poly &operator-=(Poly b) {
        return (*this) = (*this) - b;
    }
    constexpr Poly &operator*=(Poly b) {
        return (*this) = (*this) * b;
    }
    constexpr Poly &operator*=(Value b) {
        return (*this) = (*this) * b;
    }
    constexpr Poly deriv() const {
        if (a.empty()) {
            return Poly();
        }
        std::vector<Value> res(size() - 1);
        for (int i = 0; i < size() - 1; ++i) {
            res[i] = (i + 1) * a[i + 1];
        }
        return Poly(res);
    }
    constexpr Poly integr() const {
        std::vector<Value> res(size() + 1);
        for (int i = 0; i < size(); ++i) {
            res[i + 1] = a[i] / (i + 1);
        }
        return Poly(res);
    }
    constexpr Poly inv(int m) const {
        Poly x{a[0].inv()};
        int k = 1;
        while (k < m) {
            k *= 2;
            x = (x * (Poly{2} - resize(k) * x)).resize(k);
        }
        return x.resize(m);
    }
    constexpr Poly log(int m) const {
        return (deriv() * inv(m)).integr().resize(m);
    }
    constexpr Poly exp(int m) const {
        Poly x{1};
        int k = 1;
        while (k < m) {
            k *= 2;
            x = (x * (Poly{1} - x.log(k) + resize(k))).resize(k);
        }
        return x.resize(m);
    }
    constexpr Poly pow(int k, int m) const {
        int i = 0;
        while (i < size() && a[i] == 0) {
            i++;
        }
        if (i == size() || 1LL * i * k >= m) {
            return Poly(m);
        }
        Value v = a[i];
        auto f = shift(-i) * v.inv();
        return (f.log(m - i * k) * k).exp(m - i * k).mulxk(i * k) * power(v, k);
    }
    constexpr Poly sqrt(int m) const {
        Poly x{1};
        int k = 1;
        while (k < m) {
            k *= 2;
            x = (x + (resize(k) * x.inv(k)).resize(k)) * CInv<2, P>;
        }
        return x.resize(m);
    }
    constexpr 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).shift(-(n - 1));
    }
    constexpr std::vector<Value> eval(std::vector<Value> x) const {
        if (size() == 0) {
            return std::vector<Value>(x.size(), 0);
        }
        const int n = std::max(int(x.size()), size());
        std::vector<Poly> q(4 * n);
        std::vector<Value> 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]).resize(m - l));
                work(2 * p + 1, m, r, num.mulT(q[2 * p]).resize(r - m));
            }
        };
        work(1, 0, n, mulT(q[1].inv(n)));
        return ans;
    }
    constexpr auto begin() const {
        return a.begin();
    }
    constexpr auto end() const {
        return a.end();
    }
};

struct Comb {
    int n;
    std::vector<Z> _fac;
    std::vector<Z> _invfac;
    std::vector<Z> _inv;
    
    Comb() : n{0}, _fac{1}, _invfac{1}, _inv{0} {}
    Comb(int n) : Comb() {
        init(n);
    }
    
    void init(int m) {
        if (m <= n) return;
        _fac.resize(m + 1);
        _invfac.resize(m + 1);
        _inv.resize(m + 1);
        
        for (int i = n + 1; i <= m; i++) {
            _fac[i] = _fac[i - 1] * i;
        }
        _invfac[m] = _fac[m].inv();
        for (int i = m; i > n; i--) {
            _invfac[i - 1] = _invfac[i] * i;
            _inv[i] = _invfac[i] * _fac[i - 1];
        }
        n = m;
    }
    
    Z fac(int m) {
        if (m > n) init(2 * m);
        return _fac[m];
    }
    Z invfac(int m) {
        if (m > n) init(2 * m);
        return _invfac[m];
    }
    Z inv(int m) {
        if (m > n) init(2 * m);
        return _inv[m];
    }
    Z binom(int n, int m) {
        if (n < m || m < 0) return 0;
        return fac(n) * invfac(m) * invfac(n - m);
    }
} comb;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int M, N;
    std::cin >> M >> N;
    
    std::vector<int> A(N);
    for (int i = 0; i < N; i++) {
        std::cin >> A[i];
        A[i] -= 1;
    }
    
    std::vector<int> c(M);
    for (int i = 0; i < N; i++) {
        c[A[i]] += 1;
    }
    
    std::function<Poly<P>(int, int)> prod = [&](int l, int r) {
        if (r - l == 1) {
            return Poly{-c[l], 1};
        }
        int m = (l + r) / 2;
        return prod(l, m) * prod(m, r);
    };
    auto pr = prod(0, M);
    
    std::vector<Z> x(N + 1);
    std::iota(x.begin(), x.end(), 0);
    auto val = pr.eval(x);
    
    std::vector<Z> f(N + 1);
    int maxc = *std::max_element(c.begin(), c.end());
    for (int i = maxc; i <= N; i++) {
        if (i == maxc) {
            f[i] = 1;
            for (int j = 0; j < M; j++) {
                f[i] *= comb.invfac(i - c[j]);
            }
        } else {
            f[i] = f[i - 1] / val[i];
        }
    }
    for (int i = maxc; i <= N; i++) {
        f[i] *= power(comb.fac(i), M);
    }
    
    for (int i = 0; i <= N; i++) {
        f[i] *= comb.invfac(i);
        if (i % 2 == 1) {
            f[i] *= -1;
        }
    }
    
    f = std::vector<Z>((Poly(f) * Poly(N + 1, [&](int n) { return comb.invfac(n); })).resize(N + 1));
    
    for (int i = 0; i <= N; i++) {
        f[i] *= comb.fac(i);
        if (i % 2 == 1) {
            f[i] *= -1;
        }
    }
    
    auto ans = std::accumulate(f.begin(), f.end(), Z(0));
    std::cout << ans << "\n";
    
    return 0;
}
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結果

ソースコード
