#414497 (C++14) No.963 門松列列（2）

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問題	No.963 門松列列（2）
ユーザー	hitonanode
提出日時	2020-01-05 21:58:37
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	420 ms / 3,000 ms
コード長	15,484 bytes
コンパイル時間	2,212 ms
コンパイル使用メモリ	191,152 KB
実行使用メモリ	43,448 KB
最終ジャッジ日時	2024-05-02 10:32:44
合計ジャッジ時間	4,318 ms
ジャッジサーバーID （参考情報）	judge5 / 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	202 ms 23,872 KB
testcase_06	AC	21 ms 5,848 KB
testcase_07	AC	188 ms 23,716 KB
testcase_08	AC	385 ms 42,168 KB
testcase_09	AC	396 ms 43,448 KB
testcase_10	AC	420 ms 42,952 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;

constexpr int MOD = 1012924417;
template <int mod>
struct ModInt
{
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&](){
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    bool operator<(const ModInt &x) const { return val < x.val; }  // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod;
            n /= 2;
        }
        return ans;
    }
    constexpr lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return this->fac() / ((*this - r).fac() * r.fac());
    }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.val));
    }
};
using mint = ModInt<MOD>;


// Arbitrary mod convolution
// Based on <https://ei1333.github.io/luzhiled/snippets/math/arbitrary-mod-convolution.html>
struct cmplx{
    double x, y;
    cmplx() : x(0), y(0) {}
    cmplx(double x, double y) : x(x), y(y) {}
    inline cmplx operator+(const cmplx &r) const { return cmplx(x + r.x, y + r.y); }
    inline cmplx operator-(const cmplx &r) const { return cmplx(x - r.x, y - r.y); }
    inline cmplx operator*(const cmplx &r) const { return cmplx(x * r.x - y * r.y, x * r.y + y * r.x); }
    inline cmplx conj() const { return cmplx(x, -y); }
};
int fftbase = 1;
vector<cmplx> fftrts = {{0, 0}, {1, 0}};
vector<int> fftrev = {0, 1};
void ensure_base(int nbase) {
    if (nbase <= fftbase) return;
    fftrev.resize(1 << nbase);
    fftrts.resize(1 << nbase);
    for (int i = 0; i < (1 << nbase); i++) {
        fftrev[i] = (fftrev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    while (fftbase < nbase) {
        double angle = M_PI * 2.0 / (1 << (fftbase + 1));
        for (int i = 1 << (fftbase - 1); i < (1 << fftbase); i++) {
            fftrts[i << 1] = fftrts[i];
            double angle_i = angle * (2 * i + 1 - (1 << fftbase));
            fftrts[(i << 1) + 1] = {cos(angle_i), sin(angle_i)};
        }
        ++fftbase;
    }
}
void fft(int n, vector<cmplx> &a) {
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = fftbase - zeros;
    for (int i = 0; i < n; i++) {
        if (i < (fftrev[i] >> shift)) {
            swap(a[i], a[fftrev[i] >> shift]);
        }
    }
    for (int k = 1; k < n; k <<= 1) {
        for (int i = 0; i < n; i += 2 * k) {
            for (int j = 0; j < k; j++) {
                cmplx z = a[i + j + k] * fftrts[j + k];
                a[i + j + k] = a[i + j] - z;
                a[i + j] = a[i + j] + z;
            }
        }
    }
}


// Convolution for ModInt class
// retval[i] = \sum_j a[j] b[i - j]
template <typename MODINT>
vector<MODINT> convolution_mod(vector<MODINT> a, vector<MODINT> b)
{
    int need = int(a.size() + b.size()) - 1;
    int nbase = 0;
    while ((1 << nbase) < need) nbase++;
    int sz = 1 << nbase;
    vector<cmplx> fa(sz);
    for (int i = 0; i < (int)a.size(); i++) fa[i] = {double(a[i].val & ((1 << 15) - 1)), double(a[i].val >> 15)};
    fft(sz, fa);
    vector<cmplx> fb(sz);
    if (a == b) fb = fa;
    else {
        for (int i = 0; i < (int)b.size(); i++) fb[i] = {double(b[i].val & ((1 << 15) - 1)), double(b[i].val >> 15)};
        fft(sz, fb);
    }
    double ratio = 0.25 / sz;
    cmplx r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for (int i = 0; i <= (sz >> 1); i++) {
        int j = (sz - i) & (sz - 1);
        cmplx a1 = (fa[i] + fa[j].conj());
        cmplx a2 = (fa[i] - fa[j].conj()) * r2;
        cmplx b1 = (fb[i] + fb[j].conj()) * r3;
        cmplx b2 = (fb[i] - fb[j].conj()) * r4;
        if (i != j) {
            cmplx c1 = (fa[j] + fa[i].conj());
            cmplx c2 = (fa[j] - fa[i].conj()) * r2;
            cmplx d1 = (fb[j] + fb[i].conj()) * r3;
            cmplx d2 = (fb[j] - fb[i].conj()) * r4;
            fa[i] = c1 * d1 + c2 * d2 * r5;
            fb[i] = c1 * d2 + c2 * d1;
        }
        fa[j] = a1 * b1 + a2 * b2 * r5;
        fb[j] = a1 * b2 + a2 * b1;
    }
    fft(sz, fa);
    fft(sz, fb);
    vector<MODINT> ret(sz);
    for (int i = 0; i < need; i++) {
      int64_t aa = llround(fa[i].x);
      int64_t bb = llround(fb[i].x);
      int64_t cc = llround(fa[i].y);
      aa = MODINT(aa).val, bb = MODINT(bb).val, cc = MODINT(cc).val;
      ret[i] = aa + (bb << 15) + (cc << 30);
    }
    return ret;
}


template<typename T>
struct FormalPowerSeries : vector<T>
{
    using vector<T>::vector;
    using P = FormalPowerSeries;

    void shrink() { while (this->size() and this->back() == T(0)) this->pop_back(); }

    P operator+(const P &r) const { return P(*this) += r; }
    P operator+(const T &v) const { return P(*this) += v; }
    P operator-(const P &r) const { return P(*this) -= r; }
    P operator-(const T &v) const { return P(*this) -= v; }
    P operator*(const P &r) const { return P(*this) *= r; }
    P operator*(const T &v) const { return P(*this) *= v; }
    P operator/(const P &r) const { return P(*this) /= r; }
    P operator/(const T &v) const { return P(*this) /= v; }
    P operator%(const P &r) const { return P(*this) %= r; }

    P &operator+=(const P &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
        shrink();
        return *this;
    }
    P &operator+=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        shrink();
        return *this;
    }
    P &operator-=(const P &r) {
        if(r.size() > this->size()) this->resize(r.size());
        for(int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }
    P &operator-=(const T &v) {
        if(this->empty()) this->resize(1);
        (*this)[0] -= v;
        shrink();
        return *this;
    }
    P &operator*=(const T &v) {
        for (auto &x : (*this)) x *= v;
        shrink();
        return *this;
    }
    P &operator*=(const P &r) {
        if (this->empty() || r.empty()) this->clear();
        else {
            auto ret = convolution_mod(*this, r);
            *this = P(ret.begin(), ret.end());
        }
        return *this;
    }
    P &operator%=(const P &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }
    P operator-() const {
        P ret = *this;
        for (auto &v : ret) v = -v;
        return ret;
    }
    P &operator/=(const T &v) {
        assert(v != T(0));
        for (auto &x : (*this)) x /= v;
        return *this;
    }
    P &operator/=(const P &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = (int)this->size() - r.size() + 1;
        return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
    }
    P pre(int sz) const {
         P ret(this->begin(), this->begin() + min((int)this->size(), sz));
         ret.shrink();
         return ret;
    }
    P operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        return P(this->begin() + sz, this->end());
    }
    P operator<<(int sz) const {
        if (this->empty()) return {};
        P ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

    P reversed(int deg = -1) const {
        assert(deg >= -1);
        P ret(*this);
        if (deg != -1) ret.resize(deg, T(0));
        reverse(ret.begin(), ret.end());
        ret.shrink();
        return ret;
    }

    P differential() const { // formal derivative (differential) of f.p.s.
        const int n = (int)this->size();
        P ret(max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }

    P inv(int deg) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0
        const int n = this->size();
        if (deg == -1) deg = n;
        P ret({T(1) / (*this)[0]});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
        }
        ret = ret.pre(deg);
        ret.shrink();
        return ret;
    }

    P log(int deg = -1) const {
        assert(deg >= -1);
        assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1
        const int n = (int)this->size();
        if (deg == 0) return {};
        if (deg == -1) deg = n;
        return (this->differential() * this->inv(deg)).pre(deg - 1).integral();
    }

    P sqrt(int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return {};
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++) if ((*this)[i] != T(0)) {
                if ((i & 1) or deg - i / 2 <= 0) return {};
                return (*this >> i).sqrt(deg - i / 2) << (i / 2);
            }
            return {};
        }
        T sqrtf0 = (*this)[0].sqrt();
        if (sqrtf0 == T(0)) return {};

        P y = (*this) / (*this)[0], ret({T(1)});
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;
        }
        return ret.pre(deg) * sqrtf0;
    }

    P exp(int deg = -1) const {
        assert(deg >= -1);
        assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1)});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
        }
        return ret.pre(deg);
    }

    P pow(long long int k, int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P C(*this * rev);
                P D(n - i);
                for (int j = i; j < n; j++) D[j - i] = C[j];
                D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].power(k);
                P E(deg);
                if (k * (i > 0) > deg or k * i > deg) return {};
                long long int S = i * k;
                for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
                E.shrink();
                return E;
            }
        }
        return *this;
    }

    T coeff(int i) const {
        if ((int)this->size() <= i) return T(0);
        return (*this)[i];
    }

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



int main()
{
    int N;
    cin >> N;
    FormalPowerSeries<mint> cos_xper2(N + 10), sin_xper2(N + 10);
    for (int i = 0; i < N / 2 + 5; i++) {
        cos_xper2.at(i * 2) = mint(1) / mint(i * 2).fac() / mint(2).power(i * 2) * (i % 2 ? -1 : 1);
        sin_xper2.at(i * 2 + 1) = mint(1) / mint(i * 2 + 1).fac() / mint(2).power(i * 2 + 1) * (i % 2 ? -1 : 1);
    }
    auto cos_plus_sin = cos_xper2 + sin_xper2;
    auto cos_minus_sin_inv = (cos_xper2 - sin_xper2).inv(N + 1);
    auto ret = cos_plus_sin * cos_minus_sin_inv;
    cout << ret.coeff(N) * 2 * mint(N).fac() << endl;
}
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結果

テストケース

ソースコード
