Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub ebi-fly13/Library

:heavy_check_mark: test/set_function/Polynomial_Composite_Set_Power_Series.test.cpp

Depends on

Code

#define PROBLEM \
    "https://judge.yosupo.jp/problem/polynomial_composite_set_power_series"

#include <iostream>
#include <vector>

#include "../../modint/modint.hpp"
#include "../../set_function/poly_composite_sps.hpp"

using mint = ebi::modint998244353;

int main() {
    int m, n;
    std::cin >> m >> n;
    std::vector<mint> f(m);
    for (int i = 0; i < m; i++) std::cin >> f[i];
    std::vector<mint> b(1 << n);
    for (int i = 0; i < (1 << n); i++) std::cin >> b[i];
    auto c = ebi::poly_composite_sps<mint, 20>(b, f);
    for (int i = 0; i < (1 << n); i++) {
        std::cout << c[i] << " \n"[i == (1 << n) - 1];
    }
}
#line 1 "test/set_function/Polynomial_Composite_Set_Power_Series.test.cpp"
#define PROBLEM \
    "https://judge.yosupo.jp/problem/polynomial_composite_set_power_series"

#include <iostream>
#include <vector>

#line 2 "modint/modint.hpp"

#include <cassert>

#line 5 "modint/modint.hpp"

#line 2 "modint/base.hpp"

#include <concepts>
#line 5 "modint/base.hpp"
#include <utility>

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 7 "modint/modint.hpp"

namespace ebi {

template <int m> struct static_modint {
  private:
    using modint = static_modint;

  public:
    static constexpr int mod() {
        return m;
    }

    static constexpr modint raw(int v) {
        modint x;
        x._v = v;
        return x;
    }

    constexpr static_modint() : _v(0) {}

    constexpr static_modint(long long v) {
        v %= (long long)umod();
        if (v < 0) v += (long long)umod();
        _v = (unsigned int)v;
    }

    constexpr unsigned int val() const {
        return _v;
    }

    constexpr unsigned int value() const {
        return val();
    }

    constexpr modint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    constexpr modint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }

    constexpr modint operator++(int) {
        modint res = *this;
        ++*this;
        return res;
    }
    constexpr modint operator--(int) {
        modint res = *this;
        --*this;
        return res;
    }

    constexpr modint &operator+=(const modint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr modint &operator-=(const modint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr modint &operator*=(const modint &rhs) {
        unsigned long long x = _v;
        x *= rhs._v;
        _v = (unsigned int)(x % (unsigned long long)umod());
        return *this;
    }
    constexpr modint &operator/=(const modint &rhs) {
        return *this = *this * rhs.inv();
    }

    constexpr modint operator+() const {
        return *this;
    }
    constexpr modint operator-() const {
        return modint() - *this;
    }

    constexpr modint pow(long long n) const {
        assert(0 <= n);
        modint x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    constexpr modint inv() const {
        assert(_v);
        return pow(umod() - 2);
    }

    friend modint operator+(const modint &lhs, const modint &rhs) {
        return modint(lhs) += rhs;
    }
    friend modint operator-(const modint &lhs, const modint &rhs) {
        return modint(lhs) -= rhs;
    }
    friend modint operator*(const modint &lhs, const modint &rhs) {
        return modint(lhs) *= rhs;
    }

    friend modint operator/(const modint &lhs, const modint &rhs) {
        return modint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.val() == rhs.val();
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }

  private:
    unsigned int _v = 0;

    static constexpr unsigned int umod() {
        return m;
    }
};

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;

}  // namespace ebi
#line 2 "set_function/poly_composite_sps.hpp"

#line 5 "set_function/poly_composite_sps.hpp"

#line 2 "set_function/egf_composite_sps.hpp"

#line 5 "set_function/egf_composite_sps.hpp"

#line 2 "convolution/subset_convolution.hpp"

/*
    refernce: https://www.slideshare.net/wata_orz/ss-12131479
              https://37zigen.com/subset-convolution/
*/

#include <array>

#include <bit>

#line 12 "convolution/subset_convolution.hpp"

#line 2 "set_function/ranked_subset_transform.hpp"

#line 7 "set_function/ranked_subset_transform.hpp"

namespace ebi {

template <class T, int LIM = 20>
std::vector<std::array<T, LIM + 1>> ranked_zeta(const std::vector<T> &f) {
    int n = std::bit_width(f.size()) - 1;
    assert(n <= LIM);
    assert((int)f.size() == (1 << n));
    std::vector<std::array<T, LIM + 1>> rf(1 << n);
    for (int s = 0; s < (1 << n); s++)
        rf[s][std::popcount((unsigned int)(s))] = f[s];
    for (int i = 0; i < n; i++) {
        int w = 1 << i;
        for (int p = 0; p < (1 << n); p += 2 * w) {
            for (int s = p; s < p + w; s++) {
                int t = s | (1 << i);
                for (int d = 0; d <= n; d++) rf[t][d] += rf[s][d];
            }
        }
    }
    return rf;
}

template <class T, int LIM = 20>
std::vector<T> ranked_mobius(std::vector<std::array<T, LIM + 1>> rf) {
    int n = std::bit_width(rf.size()) - 1;
    assert((int)rf.size() == (1 << n));
    for (int i = 0; i < n; i++) {
        int w = 1 << i;
        for (int p = 0; p < (1 << n); p += 2 * w) {
            for (int s = p; s < p + w; s++) {
                int t = s | (1 << i);
                for (int d = 0; d <= n; d++) rf[t][d] -= rf[s][d];
            }
        }
    }
    std::vector<T> f(1 << n);
    for (int s = 0; s < (1 << n); s++) {
        f[s] = rf[s][std::popcount((unsigned int)(s))];
    }
    return f;
}

}  // namespace ebi
#line 14 "convolution/subset_convolution.hpp"

namespace ebi {

template <class T, int LIM = 20>
std::vector<T> subset_convolution(const std::vector<T> &a,
                                  const std::vector<T> &b) {
    auto ra = ranked_zeta<T, LIM>(a);
    auto rb = ranked_zeta<T, LIM>(b);
    int n = std::bit_width(a.size()) - 1;
    for (int s = (1 << n) - 1; s >= 0; s--) {
        auto &f = ra[s];
        const auto &g = rb[s];
        for (int d = n; d >= 0; d--) {
            T x = 0;
            for (int i = 0; i <= d; i++) {
                x += f[i] * g[d - i];
            }
            f[d] = x;
        }
    }
    return ranked_mobius<T, LIM>(ra);
}

}  // namespace ebi
#line 7 "set_function/egf_composite_sps.hpp"

namespace ebi {

template <class T, int LIM>
std::vector<T> egf_composite_sps(const std::vector<T> &a, std::vector<T> egf) {
    int n = std::bit_width(a.size()) - 1;
    assert(n <= LIM);
    assert((int)a.size() == (1 << n) && a[0] == T(0));
    if ((int)egf.size() > n) egf.resize(n + 1);
    int d = egf.size() - 1;
    std::vector<T> f(1 << n);
    f[0] = egf[d];
    for (int k = d - 1; k >= 0; k--) {
        std::vector<T> fk(1 << n);
        fk[0] = egf[k];
        for (int i = 0; i < n - k; i++) {
            std::vector<T> s = {a.begin() + (1 << i), a.begin() + (2 << i)};
            std::vector<T> t = {f.begin(), f.begin() + (1 << i)};
            auto c = subset_convolution<T, LIM>(s, t);
            std::copy(c.begin(), c.end(), fk.begin() + (1 << i));
        }
        f = fk;
    }
    return f;
}

}  // namespace ebi
#line 7 "set_function/poly_composite_sps.hpp"

namespace ebi {

template <class T, int LIM>
std::vector<T> poly_composite_sps(std::vector<T> a, const std::vector<T> &f) {
    int n = std::bit_width(a.size()) - 1;
    assert(n <= LIM);
    if (f.empty()) return std::vector<T>(1 << n, 0);
    int d = std::min((int)f.size() - 1, n);
    std::vector<T> g(d + 1);
    T c = a[0];
    a[0] = 0;
    std::vector<T> pow(d + 1);
    pow[0] = 1;
    for (int i = 0; i < (int)f.size(); i++) {
        for (int j = 0; j < d + 1; j++) g[j] += f[i] * pow[j];
        for (int j = d; j >= 0; j--)
            pow[j] = pow[j] * c + (j == 0 ? 0 : pow[j - 1]);
    }
    T fact = 1;
    for (int i = 0; i < d + 1; i++) {
        g[i] *= fact;
        fact *= (i + 1);
    }
    return egf_composite_sps<T, LIM>(a, g);
}

}  // namespace ebi
#line 9 "test/set_function/Polynomial_Composite_Set_Power_Series.test.cpp"

using mint = ebi::modint998244353;

int main() {
    int m, n;
    std::cin >> m >> n;
    std::vector<mint> f(m);
    for (int i = 0; i < m; i++) std::cin >> f[i];
    std::vector<mint> b(1 << n);
    for (int i = 0; i < (1 << n); i++) std::cin >> b[i];
    auto c = ebi::poly_composite_sps<mint, 20>(b, f);
    for (int i = 0; i < (1 << n); i++) {
        std::cout << c[i] << " \n"[i == (1 << n) - 1];
    }
}
Back to top page