#982731 (C++17) No.2763 Macaron Gift Box

提出ソース
結果

問題	No.2763 Macaron Gift Box
ユーザー	t98slider
提出日時	2024-05-19 04:44:23
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	95 ms / 3,000 ms
コード長	15,724 bytes
コンパイル時間	2,932 ms
コンパイル使用メモリ	215,908 KB
実行使用メモリ	12,692 KB
最終ジャッジ日時	2024-05-19 04:44:28
合計ジャッジ時間	4,209 ms
ジャッジサーバーID （参考情報）	judge1 / 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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	1 ms 6,944 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	1 ms 6,940 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	46 ms 7,044 KB
testcase_08	AC	13 ms 6,944 KB
testcase_09	AC	24 ms 6,944 KB
testcase_10	AC	92 ms 11,580 KB
testcase_11	AC	94 ms 11,908 KB
testcase_12	AC	95 ms 12,692 KB
testcase_13	AC	95 ms 12,692 KB
testcase_14	AC	12 ms 6,944 KB
testcase_15	AC	12 ms 6,944 KB
testcase_16	AC	11 ms 6,940 KB
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ソースコード

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

template<const unsigned int MOD> struct prime_modint {
    using mint = prime_modint;
    unsigned int v;
    prime_modint() : v(0) {}
    prime_modint(unsigned int a) { a %= MOD; v = a; }
    prime_modint(unsigned long long a) { a %= MOD; v = a; }
    prime_modint(int a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    prime_modint(long long a) { a %= (int)(MOD); if(a < 0)a += MOD; v = a; }
    static constexpr int mod() { return MOD; }
    mint& operator++() {v++; if(v == MOD)v = 0; return *this;}
    mint& operator--() {if(v == 0)v = MOD; v--; return *this;}
    mint operator++(int) { mint result = *this; ++*this; return result; }
    mint operator--(int) { mint result = *this; --*this; return result; }
    mint& operator+=(const mint& rhs) { v += rhs.v; if(v >= MOD) v -= MOD; return *this; }
    mint& operator-=(const mint& rhs) { if(v < rhs.v) v += MOD; v -= rhs.v; return *this; }
    mint& operator*=(const mint& rhs) {
        v = (unsigned int)((unsigned long long)(v) * rhs.v % MOD);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint r = 1, x = *this;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const { assert(v); return pow(MOD - 2); }
    friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; }
    friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; }
    friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; }
    friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; }
    friend bool operator==(const mint& lhs, const mint& rhs) { return (lhs.v == rhs.v); }
    friend bool operator!=(const mint& lhs, const mint& rhs) { return (lhs.v != rhs.v); }
    friend std::ostream& operator << (std::ostream &os, const mint& rhs) noexcept { return os << rhs.v; }
};
//using mint = prime_modint<1000000007>;
using mint = prime_modint<998244353>;

constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

template<class mint> struct fft_info {
    const int g = primitive_root(mint::mod());
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }

    int ceil_pow2(int n) {
        int x = 0;
        while ((1U << x) < (unsigned int)(n)) x++;
        return x;
    }

    int bsf(unsigned int n) {
    #ifdef _MSC_VER
        unsigned long index;
        _BitScanForward(&index, n);
        return index;
    #else
        return __builtin_ctz(n);
    #endif
    }

    constexpr long long safe_mod(long long x, long long m) {
        x %= m;
        if (x < 0) x += m;
        return x;
    }

    constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
        if (m == 1) return 0;
        unsigned int _m = (unsigned int)(m);
        unsigned long long r = 1;
        unsigned long long y = safe_mod(x, m);
        while (n) {
            if (n & 1) r = (r * y) % _m;
            y = (y * y) % _m;
            n >>= 1;
        }
        return r;
    }

    constexpr int primitive_root(int m) {
        if (m == 2) return 1;
        if (m == 167772161) return 3;
        if (m == 469762049) return 3;
        if (m == 754974721) return 11;
        if (m == 998244353) return 3;
        int divs[20] = {};
        divs[0] = 2;
        int cnt = 1;
        int x = (m - 1) / 2;
        while (x % 2 == 0) x /= 2;
        for (int i = 3; (long long)(i)*i <= x; i += 2) {
            if (x % i == 0) {
                divs[cnt++] = i;
                while (x % i == 0) x /= i;
            }
        }
        if (x > 1) divs[cnt++] = x;
        for (int g = 2;; g++) {
            bool ok = true;
            for (int i = 0; i < cnt; i++) {
                if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return g;
        }
    }

    void butterfly(std::vector<mint>& a) {
        int n = int(a.size());
        int h = ceil_pow2(n);

        int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
        while (len < h) {
            if (h - len == 1) {
                int p = 1 << (h - len - 1);
                mint rot = 1;
                for (int s = 0; s < (1 << len); s++) {
                    int offset = s << (h - len);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p] * rot;
                        a[i + offset] = l + r;
                        a[i + offset + p] = l - r;
                    }
                    if (s + 1 != (1 << len)) rot *= rate2[bsf(~(unsigned int)(s))];
                }
                len++;
            } else {
                // 4-base
                int p = 1 << (h - len - 2);
                mint rot = 1, imag = root[2];
                for (int s = 0; s < (1 << len); s++) {
                    mint rot2 = rot * rot;
                    mint rot3 = rot2 * rot;
                    int offset = s << (h - len);
                    for (int i = 0; i < p; i++) {
                        auto mod2 = 1ULL * mint::mod() * mint::mod();
                        auto a0 = 1ULL * a[i + offset].v;
                        auto a1 = 1ULL * a[i + offset + p].v * rot.v;
                        auto a2 = 1ULL * a[i + offset + 2 * p].v * rot2.v;
                        auto a3 = 1ULL * a[i + offset + 3 * p].v * rot3.v;
                        auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).v * imag.v;
                        auto na2 = mod2 - a2;
                        a[i + offset] = a0 + a2 + a1 + a3;
                        a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                        a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                        a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                    }
                    if (s + 1 != (1 << len))
                        rot *= rate3[bsf(~(unsigned int)(s))];
                }
                len += 2;
            }
        }
    }

    void butterfly_inv(std::vector<mint>& a) {
        int n = int(a.size());
        int h = ceil_pow2(n);

        int len = h;
        while (len) {
            if (len == 1) {
                int p = 1 << (h - len);
                mint irot = 1;
                for (int s = 0; s < (1 << (len - 1)); s++) {
                    int offset = s << (h - len + 1);
                    for (int i = 0; i < p; i++) {
                        auto l = a[i + offset];
                        auto r = a[i + offset + p];
                        a[i + offset] = l + r;
                        a[i + offset + p] = (unsigned long long)(mint::mod() + l.v - r.v) * irot.v;
                    }
                    if (s + 1 != (1 << (len - 1))) irot *= irate2[bsf(~(unsigned int)(s))];
                }
                len--;
            } else {
                // 4-base
                int p = 1 << (h - len);
                mint irot = 1, iimag = iroot[2];
                for (int s = 0; s < (1 << (len - 2)); s++) {
                    mint irot2 = irot * irot;
                    mint irot3 = irot2 * irot;
                    int offset = s << (h - len + 2);
                    for (int i = 0; i < p; i++) {
                        auto a0 = 1ULL * a[i + offset + 0 * p].v;
                        auto a1 = 1ULL * a[i + offset + 1 * p].v;
                        auto a2 = 1ULL * a[i + offset + 2 * p].v;
                        auto a3 = 1ULL * a[i + offset + 3 * p].v;
                        auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.v).v;

                        a[i + offset] = a0 + a1 + a2 + a3;
                        a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.v;
                        a[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.v;
                        a[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.v;
                    }
                    if (s + 1 != (1 << (len - 2))) irot *= irate3[bsf(~(unsigned int)(s))];
                }
                len -= 2;
            }
        }
    }

    std::vector<mint> convolution_naive(const std::vector<mint>& a, const std::vector<mint>& b) {
        int n = int(a.size()), m = int(b.size());
        std::vector<mint> ans(n + m - 1);
        if (n < m) {
            for (int j = 0; j < m; j++) {
                for (int i = 0; i < n; i++) {
                    ans[i + j] += a[i] * b[j];
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ans[i + j] += a[i] * b[j];
                }
            }
        }
        return ans;
    }

    std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
        int n = int(a.size()), m = int(b.size());
        int z = 1 << ceil_pow2(n + m - 1);
        a.resize(z), butterfly(a);
        b.resize(z), butterfly(b);
        for (int i = 0; i < z; i++) a[i] *= b[i];
        butterfly_inv(a);
        a.resize(n + m - 1);
        mint iz = mint(z).inv();
        for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
        return a;
    }
};

template <class mint> std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    static fft_info<mint> info;
    if (std::min(n, m) <= 60) return info.convolution_naive(a, b);
    return info.convolution_fft(a, b);
}

template <unsigned int mod = 998244353, class T>
std::vector<T> convolution(const std::vector<T> &a, const std::vector<T> &b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = prime_modint<mod>;
    std::vector<mint> a2(n), b2(m), c2;
    for (int i = 0; i < n; i++) a2[i] = mint(a[i]);
    for (int i = 0; i < m; i++) b2[i] = mint(b[i]);

    static fft_info<mint> info;
    if (std::min(n, m) <= 60) c2 = info.convolution_naive(a2, b2);
    else c2 = info.convolution_fft(a2, b2);

    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) c[i] = c2[i].v;
    return c;
}

template<class mint> struct Polynomial{
    std::vector<mint> dat;
    Polynomial() {}
    Polynomial(int _size) : dat(_size) {}
    Polynomial(std::vector<mint> rhs) : dat(rhs) {}
    const mint& operator[](int p) const {
        assert(0 <= p && p < dat.size());
        return dat[p];
    }
    mint& operator[](int p) { 
        assert(0 <= p && p < dat.size());
        return dat[p];
    }
    int size() { return dat.size(); }
    Polynomial& operator+=(const Polynomial& rhs) {
        int rn = rhs.dat.size();
        if(dat.size() < rn) dat.resize(rn);
        for(int i = 0; i < rn; i++) dat[i] += rhs.dat[i];
        return *this;
    }
    Polynomial& operator-=(const Polynomial& rhs) {
        int rn = rhs.dat.size();
        if(dat.size() < rn) dat.resize(rn);
        for(int i = 0; i < rn; i++) dat[i] -= rhs.dat[i];
        return *this;
    }
    Polynomial& operator*=(const Polynomial& rhs) {
        dat = convolution(dat, rhs.dat);
        return *this;
    }
    Polynomial& operator/=(const Polynomial& rhs) {
        // 未実装
        return *this; 
    }
    Polynomial operator+() const { return *this; }
    Polynomial operator-() const { return Polynomial() - *this; }
    Polynomial inv(){
        assert(!dat.empty());
        const int N = dat.size();
        static fft_info<mint> info;
        Polynomial invP(1);
        invP.dat.reserve(N);
        invP[0] = dat[0].inv();
        while(invP.size() < N){
            const int M = 2 * invP.size();
            std::vector<mint> buf(M), finvP(M);
            std::copy(dat.begin(), dat.begin() + min(M, N), buf.begin());
            std::copy(invP.dat.begin(), invP.dat.end(), finvP.begin());
            info.butterfly(buf);
            info.butterfly(finvP);
            for(int i = 0; i < M; i++) buf[i] *= finvP[i];
            info.butterfly_inv(buf);
            fill(buf.begin(), buf.begin() + invP.size(), 0);
            info.butterfly(buf);
            for(int i = 0; i < M; i++) buf[i] *= finvP[i];
            info.butterfly_inv(buf);
            mint coef = - (mint(1 - mint::mod()) / int(buf.size())).pow(2);
            for (int i = invP.size(); i < min(M, N + 1); i++) invP.dat.push_back(buf[i] * coef);
        }
        return invP;
    }
    friend Polynomial operator+(const Polynomial& lhs, const Polynomial& rhs) {
        return Polynomial(lhs) += rhs;
    }
    friend Polynomial operator-(const Polynomial& lhs, const Polynomial& rhs) {
        return Polynomial(lhs) -= rhs;
    }
    friend Polynomial operator*(const Polynomial& lhs, const Polynomial& rhs) {
        return Polynomial(lhs) *= rhs;
    }
    friend Polynomial operator/(const Polynomial& lhs, const Polynomial& rhs) {
        return Polynomial(lhs) /= rhs;
    }
    Polynomial diff() const {
        const int N = dat.size();
        Polynomial res(std::max(0, N - 1));
        mint coef(1);
        for(int i = 1; i < N; i++, coef++) {
            res[i - 1] = dat[i] * coef;
        }
        return res;
    }
    Polynomial integral() const {
        const int N = dat.size();
        Polynomial res(N + 1);
        res[0] = mint(0);
        if (N > 0) res[1] = mint(1);
        auto mod = mint::mod();
        for (int i = 2; i <= N; i++) res[i] = (-res[mod % i]) * (mod / i);
        for (int i = 0; i < N; i++) res[i + 1] *= dat[i];
        return res;
    }
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int N, K;
    cin >> N >> K;
    Polynomial<mint> P(N + 1), Q(N + 1);
    Q[0] = 1;
    for(int i = 1; i * (3 * i - 1) / 2 <= N; i++) {
        Q[i * (3 * i - 1) / 2] = i & 1 ? -1 : 1;
    }
    for(int i = -1; i * (3 * i - 1) / 2 <= N; i--) {
        Q[i * (3 * i - 1) / 2] = i & 1 ? -1 : 1;
    }
    for(int i = 0; i * (K + 1) <= N; i++){
        P[i * (K + 1)] = Q[i];
    }
    P *= Q.inv();
    for(int i = 1; i <= N; i++){
        cout << P[i] << (i == N ? '\n' : ' ');
    }
}
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結果

テストケース

ソースコード
