#847992 (C++17) No.2243 Coaching Schedule

提出ソース
結果

問題	No.2243 Coaching Schedule
ユーザー	rniya
提出日時	2023-03-10 22:50:14
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,172 ms / 4,000 ms
コード長	19,064 bytes
コンパイル時間	4,787 ms
コンパイル使用メモリ	264,496 KB
実行使用メモリ	48,484 KB
最終ジャッジ日時	2024-09-18 04:57:14
合計ジャッジ時間	31,028 ms
ジャッジサーバーID （参考情報）	judge2 / judge1
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	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	1,168 ms 48,232 KB
testcase_06	AC	1,165 ms 48,328 KB
testcase_07	AC	1,165 ms 48,184 KB
testcase_08	AC	1,160 ms 48,328 KB
testcase_09	AC	1,161 ms 48,360 KB
testcase_10	AC	1,164 ms 48,360 KB
testcase_11	AC	1,166 ms 48,484 KB
testcase_12	AC	1,159 ms 48,232 KB
testcase_13	AC	1,164 ms 48,352 KB
testcase_14	AC	1,172 ms 48,340 KB
testcase_15	AC	1,164 ms 48,364 KB
testcase_16	AC	621 ms 40,628 KB
testcase_17	AC	294 ms 15,216 KB
testcase_18	AC	801 ms 41,084 KB
testcase_19	AC	1,059 ms 45,736 KB
testcase_20	AC	638 ms 27,932 KB
testcase_21	AC	496 ms 24,452 KB
testcase_22	AC	409 ms 22,868 KB
testcase_23	AC	57 ms 6,016 KB
testcase_24	AC	623 ms 27,660 KB
testcase_25	AC	82 ms 7,748 KB
testcase_26	AC	236 ms 14,100 KB
testcase_27	AC	650 ms 28,324 KB
testcase_28	AC	106 ms 8,456 KB
testcase_29	AC	810 ms 41,252 KB
testcase_30	AC	949 ms 44,668 KB
testcase_31	AC	1,076 ms 46,496 KB
testcase_32	AC	369 ms 21,696 KB
testcase_33	AC	273 ms 14,784 KB
testcase_34	AC	775 ms 40,592 KB
testcase_35	AC	889 ms 43,588 KB
testcase_36	AC	937 ms 44,332 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

raw source code
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define ALL(x) (x).begin(), (x).end()
#ifdef LOCAL
#include "debug.hpp"
#else
#define debug(...) void(0)
#endif

template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}

template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }

int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }

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

template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }

const int INF = (1 << 30) - 1;
const long long IINF = (1LL << 60) - 1;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const int MOD = 998244353;
// const int MOD = 1000000007;

#include <iostream>
#include "atcoder/modint"

namespace atcoder {

template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
    int64_t v;
    x = static_modint<MOD>{(is >> v, v)};
    return is;
}

template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }

template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }

}  // namespace atcoder

#include <cassert>
#include <vector>

template <typename T> struct Binomial {
    Binomial(int MAX = 0) : n(1), facs(1, T(1)), finvs(1, T(1)), invs(1, T(1)) {
        while (n <= MAX) extend();
    }

    T fac(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return facs[i];
    }

    T finv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return finvs[i];
    }

    T inv(int i) {
        assert(i >= 0);
        while (n <= i) extend();
        return invs[i];
    }

    T P(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r);
    }

    T C(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        return fac(n) * finv(n - r) * finv(r);
    }

    T H(int n, int r) {
        if (n < 0 || r < 0) return T(0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }

    T C_naive(int n, int r) {
        if (n < 0 || n < r || r < 0) return T(0);
        T res = 1;
        r = std::min(r, n - r);
        for (int i = 1; i <= r; i++) res *= inv(i) * (n--);
        return res;
    }

private:
    int n;
    std::vector<T> facs, finvs, invs;

    inline void extend() {
        int m = n << 1;
        facs.resize(m);
        finvs.resize(m);
        invs.resize(m);
        for (int i = n; i < m; i++) facs[i] = facs[i - 1] * i;
        finvs[m - 1] = T(1) / facs[m - 1];
        invs[m - 1] = finvs[m - 1] * facs[m - 2];
        for (int i = m - 2; i >= n; i--) {
            finvs[i] = finvs[i + 1] * (i + 1);
            invs[i] = finvs[i] * facs[i - 1];
        }
        n = m;
    }
};

#include <algorithm>
#include <cassert>
#include <functional>
#include <queue>
#include <utility>
#include <vector>

#include "atcoder/convolution"

template <typename T> struct FormalPowerSeries : std::vector<T> {
private:
    using std::vector<T>::vector;
    using FPS = FormalPowerSeries;
    void shrink() {
        while (this->size() and this->back() == T(0)) this->pop_back();
    }

    FPS pre(size_t sz) const { return FPS(this->begin(), this->begin() + std::min(this->size(), sz)); }

    FPS rev() const {
        FPS ret(*this);
        std::reverse(ret.begin(), ret.end());
        return ret;
    }

    FPS operator>>(size_t sz) const {
        if (this->size() <= sz) return {};
        return FPS(this->begin() + sz, this->end());
    }

    FPS operator<<(size_t sz) const {
        if (this->empty()) return {};
        FPS ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

public:
    FPS& operator+=(const FPS& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (size_t i = 0; i < r.size(); i++) (*this)[i] += r[i];
        shrink();
        return *this;
    }

    FPS& operator+=(const T& v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        shrink();
        return *this;
    }

    FPS& operator-=(const FPS& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (size_t i = 0; i < r.size(); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }

    FPS& operator-=(const T& v) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= v;
        shrink();
        return *this;
    }

    FPS& operator*=(const FPS& r) {
        auto res = atcoder::convolution(*this, r);
        return *this = {res.begin(), res.end()};
    }

    FPS& operator*=(const T& v) {
        for (auto& x : (*this)) x *= v;
        shrink();
        return *this;
    }

    FPS& operator/=(const FPS& r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }

    FPS& operator%=(const FPS& r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }

    FPS operator+(const FPS& r) const { return FPS(*this) += r; }

    FPS operator+(const T& v) const { return FPS(*this) += v; }

    FPS operator-(const FPS& r) const { return FPS(*this) -= r; }

    FPS operator-(const T& v) const { return FPS(*this) -= v; }

    FPS operator*(const FPS& r) const { return FPS(*this) *= r; }

    FPS operator*(const T& v) const { return FPS(*this) *= v; }

    FPS operator/(const FPS& r) const { return FPS(*this) /= r; }

    FPS operator%(const FPS& r) const { return FPS(*this) %= r; }

    FPS operator-() const {
        FPS ret = *this;
        for (auto& v : ret) v = -v;
        return ret;
    }

    FPS differential() const {
        const int n = (int)this->size();
        FPS ret(std::max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = T(0);
        if (n > 0) ret[1] = T(1);
        auto mod = T::mod();
        for (int i = 2; i <= n; i++) ret[i] = -ret[mod % i] * (mod / i);
        for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
        return ret;
    }

    FPS inv(int deg = -1) const {
        assert((*this)[0] != T(0));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        FPS ret{(*this)[0].inv()};
        ret.reserve(deg);
        for (int d = 1; d < deg; d <<= 1) {
            FPS f(d << 1), g(d << 1);
            std::copy(this->begin(), this->begin() + std::min(n, d << 1), f.begin());
            std::copy(ret.begin(), ret.end(), g.begin());
            atcoder::internal::butterfly(f);
            atcoder::internal::butterfly(g);
            for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
            atcoder::internal::butterfly_inv(f);
            std::fill(f.begin(), f.begin() + d, T(0));
            atcoder::internal::butterfly(f);
            for (int i = 0; i < (d << 1); i++) f[i] *= g[i];
            atcoder::internal::butterfly_inv(f);
            T iz = T(d << 1).inv();
            iz *= -iz;
            for (int i = d; i < std::min(d << 1, deg); i++) ret.push_back(f[i] * iz);
        }
        return ret.pre(deg);
    }

    FPS log(int deg = -1) const {
        assert((*this)[0] == T(1));
        if (deg == -1) deg = (int)this->size();
        return (differential() * inv(deg)).pre(deg - 1).integral();
    }

    FPS sqrt(const std::function<T(T)>& get_sqrt, int deg = -1) const {
        const int n = this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return FPS(deg, 0);
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++) {
                if ((*this)[i] != T(0)) {
                    if (i & 1) return {};
                    if (deg - i / 2 <= 0) break;
                    auto ret = (*this >> i).sqrt(get_sqrt, deg - i / 2);
                    if (ret.empty()) return {};
                    ret = ret << (i / 2);
                    if ((int)ret.size() < deg) ret.resize(deg, T(0));
                    return ret;
                }
            }
            return FPS(deg, T(0));
        }
        auto sqrtf0 = T(get_sqrt((*this)[0]));
        if (sqrtf0 * sqrtf0 != (*this)[0]) return {};
        FPS ret{sqrtf0};
        T inv2 = T(2).inv();
        for (int i = 1; i < deg; i <<= 1) ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
        return ret.pre(deg);
    }

    /**
     * @brief Exp of Formal Power Series
     *
     * @see https://arxiv.org/pdf/1301.5804.pdf
     */
    FPS exp(int deg = -1) const {
        assert(this->empty() or (*this)[0] == T(0));
        if (this->size() == 0) return {};
        if (this->size() == 1) return {T(1)};
        if (deg == -1) deg = (int)this->size();
        FPS inv;
        inv.reserve(deg + 1);
        inv.push_back(T(0));
        inv.push_back(T(1));
        auto inplace_integral = [&](FPS& F) -> void {
            const int n = (int)F.size();
            auto mod = T::mod();
            while ((int)inv.size() <= n) {
                int i = inv.size();
                inv.push_back(-inv[mod % i] * (mod / i));
            }
            F.insert(F.begin(), T(0));
            for (int i = 1; i <= n; i++) F[i] *= inv[i];
        };
        auto inplace_differential = [](FPS& F) -> void {
            if (F.empty()) return;
            F.erase(F.begin());
            for (size_t i = 0; i < F.size(); i++) F[i] *= T(i + 1);
        };
        FPS f{1, (*this)[1]}, g{T(1)}, g_fft{T(1), T(1)};
        for (int m = 2; m < deg; m <<= 1) {
            const T iz1 = T(m).inv(), iz2 = T(m << 1).inv();
            auto f_fft = f;
            f_fft.resize(m << 1);
            atcoder::internal::butterfly(f_fft);
            {
                // Step 2.a'
                FPS _g(m);
                for (int i = 0; i < m; i++) _g[i] = f_fft[i] * g_fft[i];
                atcoder::internal::butterfly_inv(_g);
                std::fill(_g.begin(), _g.begin() + (m >> 1), T(0));
                atcoder::internal::butterfly(_g);
                for (int i = 0; i < m; i++) _g[i] *= -g_fft[i] * iz1 * iz1;
                atcoder::internal::butterfly_inv(_g);
                g.insert(g.end(), _g.begin() + (m >> 1), _g.end());

                g_fft = g;
                g_fft.resize(m << 1);
                atcoder::internal::butterfly(g_fft);
            }
            FPS x(this->begin(), this->begin() + std::min((int)this->size(), m));
            {
                // Step 2.b'
                x.resize(m);
                inplace_differential(x);
                x.push_back(T(0));
                atcoder::internal::butterfly(x);
            }
            {
                // Step 2.c'
                for (int i = 0; i < m; i++) x[i] *= f_fft[i] * iz1;
                atcoder::internal::butterfly_inv(x);
            }
            {
                // Step 2.d' and 2.e'
                x -= f.differential();
                x.resize(m << 1);
                for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = T(0);
                atcoder::internal::butterfly(x);
                for (int i = 0; i < (m << 1); i++) x[i] *= g_fft[i] * iz2;
                atcoder::internal::butterfly_inv(x);
            }
            {
                // Step 2.f'
                x.pop_back();
                inplace_integral(x);
                for (int i = m; i < std::min((int)this->size(), m << 1); i++) x[i] += (*this)[i];
                std::fill(x.begin(), x.begin() + m, T(0));
            }
            {
                // Step 2.g' and 2.h'
                atcoder::internal::butterfly(x);
                for (int i = 0; i < (m << 1); i++) x[i] *= f_fft[i] * iz2;
                atcoder::internal::butterfly_inv(x);
                f.insert(f.end(), x.begin() + m, x.end());
            }
        }
        return FPS{f.begin(), f.begin() + deg};
    }

    FPS pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (k == 0) {
            auto res = FPS(deg, T(0));
            res[0] = T(1);
            return res;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                if (i >= (deg + k - 1) / k) return FPS(deg, T(0));
                T rev = (*this)[i].inv();
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, T(0));
                return ret;
            }
        }
        return FPS(deg, T(0));
    }

    T eval(T x) const {
        T ret = 0, w = 1;
        for (const auto& v : *this) ret += w * v, w *= x;
        return ret;
    }

    static FPS product_of_polynomial_sequence(const std::vector<FPS>& fs) {
        if (fs.empty()) return {T(1)};
        auto comp = [](const FPS& f, const FPS& g) { return f.size() > g.size(); };
        std::priority_queue<FPS, std::vector<FPS>, decltype(comp)> pq{comp};
        for (const auto& f : fs) pq.emplace(f);
        while (pq.size() > 1) {
            auto f = pq.top();
            pq.pop();
            auto g = pq.top();
            pq.pop();
            pq.emplace(f * g);
        }
        return pq.top();
    }

    static FPS pow_sparse(const std::vector<std::pair<int, T>>& f, int64_t k, int n) {
        assert(k >= 0);
        int d = f.size(), offset = 0;
        while (offset < d and f[offset].second == 0) offset++;
        FPS res(n, 0);
        if (offset == d) {
            if (k == 0) res[0]++;
            return res;
        }
        if (f[offset].first > 0) {
            int deg = f[offset].first;
            if (k > (n - 1) / deg) return res;
            std::vector<std::pair<int, T>> g(f.begin() + offset, f.end());
            for (auto& p : g) p.first -= deg;
            auto tmp = pow_sparse(g, k, n - k * deg);
            for (int i = 0; i < n - k * deg; i++) res[k * deg + i] = tmp[i];
            return res;
        }
        std::vector<T> invs(n + 1);
        invs[0] = T(0);
        invs[1] = T(1);
        auto mod = T::mod();
        for (int i = 2; i <= n; i++) invs[i] = -invs[mod % i] * (mod / i);
        res[0] = f[0].second.pow(k);
        T coef = f[0].second.inv();
        for (int i = 1; i < n; i++) {
            for (int j = 1; j < d; j++) {
                if (i - f[j].first < 0) break;
                res[i] += f[j].second * res[i - f[j].first] * (T(k) * f[j].first - (i - f[j].first));
            }
            res[i] *= invs[i] * coef;
        }
        return res;
    }

    FPS taylor_shift(T c) const {
        FPS f(*this);
        const int n = f.size();
        std::vector<T> fac(n), finv(n);
        fac[0] = 1;
        for (int i = 1; i < n; i++) {
            fac[i] = fac[i - 1] * i;
            f[i] *= fac[i];
        }
        finv[n - 1] = fac[n - 1].inv();
        for (int i = n - 1; i > 0; i--) finv[i - 1] = finv[i] * i;
        std::reverse(f.begin(), f.end());
        FPS g(n);
        g[0] = T(1);
        for (int i = 1; i < n; i++) g[i] = g[i - 1] * c * finv[i] * fac[i - 1];
        f = (f * g).pre(n);
        std::reverse(f.begin(), f.end());
        for (int i = 0; i < n; i++) f[i] *= finv[i];
        return f;
    }
};

#include <vector>

template <typename T> struct subproduct_tree {
    using poly = FormalPowerSeries<T>;
    int m;
    std::vector<poly> prod;
    subproduct_tree(const std::vector<T>& x) : m(x.size()) {
        int k = 1;
        while (k < m) k <<= 1;
        prod.assign(k << 1, {1});
        for (int i = 0; i < m; i++) prod[k + i] = {-x[i], 1};
        for (int i = k - 1; i > 0; i--) prod[i] = prod[i << 1] * prod[i << 1 | 1];
    }

    int size() const { return prod.size() >> 1; }

    poly mid_prod(const poly& a, const poly& b) const {}

    std::vector<T> multipoint_evaluation(poly f) const {
        std::vector<poly> rem(size() << 1);
        rem[1] = f % prod[1];
        for (int i = 2; i < size() + m; i++) rem[i] = rem[i >> 1] % prod[i];
        std::vector<T> res(m);
        for (int i = 0; i < m; i++) res[i] = (rem[size() + i].empty() ? 0 : rem[size() + i][0]);
        return res;
    }
};

using mint = atcoder::modint998244353;
using FPS = FormalPowerSeries<mint>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    Binomial<mint> BINOM;
    int N, M;
    cin >> M >> N;
    vector<int> cnt(M, 0);
    for (int i = 0; i < N; i++) {
        int A;
        cin >> A;
        cnt[--A]++;
    }

    vector<FPS> fs;
    for (int i = 0; i < M; i++) {
        for (int j = 0; j < cnt[i]; j++) {
            FPS v = {-j, 1};
            fs.emplace_back(v);
        }
    }
    auto comb = FPS::product_of_polynomial_sequence(fs);
    vector<mint> xs(N + 1);
    iota(xs.begin(), xs.end(), 0);
    subproduct_tree<mint> tree(xs);
    auto dp = tree.multipoint_evaluation(comb);
    vector<mint> sub(N + 1, 0);

    auto dfs = [&](auto self, int l, int r) -> void {
        if (r - l == 1) {
            sub[l] *= BINOM.fac(l);
            dp[l] -= sub[l];
            return;
        }
        int m = (l + r) >> 1;
        self(self, l, m);
        FPS a, b;
        for (int i = l; i < m; i++) a.emplace_back(dp[i] * BINOM.finv(i));
        for (int i = 0; i < r - l; i++) b.emplace_back(BINOM.finv(i));
        auto c = a * b;
        for (int i = m; i < r and i - l < int(c.size()); i++) sub[i] += c[i - l];
        self(self, m, r);
    };
    dfs(dfs, 0, N + 1);
    mint ans = accumulate(dp.begin(), dp.end(), mint(0));

    cout << ans << '\n';
    return 0;
}
yukicoder

結果

テストケース

ソースコード
