test/berlekamp_massey.test.cpp

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• Last update: 2022-01-07 21:48:21+09:00
• Problem: https://judge.yosupo.jp/problem/find_linear_recurrence

Depends on

• algorithm/berlekamp_massey.cpp
• math/rem_euclid.cpp
• math/static_modint.cpp
• math/totient.cpp
• utility/int_alias.cpp
• utility/rep.cpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/find_linear_recurrence"
#include <iostream>
#include <vector>
#include "../algorithm/berlekamp_massey.cpp"
#include "../math/static_modint.cpp"
#include "../utility/int_alias.cpp"

using Fp = Modint998244353;

int main() { 
    int n;
    std::cin >> n;
    std::vector<Fp> a(n);
    for (auto& x : a) {
        u32 t;
        std::cin >> t;
        x = t;
    }
    const auto c = berlekamp_massey(a);
    std::cout << c.size() << '\n';
    for (const int i : rep(0, c.size())) {
        std::cout << c[i] << " \n"[i + 1 == c.size()];
    }
    return 0; 
}

#line 1 "test/berlekamp_massey.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/find_linear_recurrence"
#include <iostream>
#include <vector>
#line 2 "utility/rep.cpp"
#include <algorithm>

class Range {
    struct Iter {
        int itr;
        constexpr Iter(const int pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr int operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr Range(const int first, const int last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

constexpr Range rep(const int l, const int r) noexcept { return Range(l, r); }
constexpr Range rep(const int n) noexcept { return Range(0, n); }
#line 4 "algorithm/berlekamp_massey.cpp"

template <class T> std::vector<T> berlekamp_massey(const std::vector<T>& a) {
    const int n = a.size();
    std::vector<T> c = {T(-1)}, c2 = {T(0)};
    T r2 = 1;
    int i2 = 0;
    for (const int i : rep(n)) {
        T r = 0;
        const int d = c.size();
        for (const int j : rep(d)) r += c[j] * a[i - j];
        if (r == T(0)) continue;
        T coeff = -r / r2;
        const int d2 = c2.size(), shift = i - i2 + 1;
        if (d2 + shift <= d) {
            for (const int j : rep(d2)) c[j + shift] += c2[j] * coeff;
        } else {
            std::vector<T> tmp = c;
            c.resize(d2 + shift);
            for (const int j : rep(d2)) c[j + shift] += c2[j] * coeff;
            c2 = std::move(tmp);
            i2 = i + 1;
            r2 = r;
        }
    }
    c.erase(c.begin());
    return c;
}
#line 2 "math/static_modint.cpp"
#include <ostream>
#include <type_traits>
#line 2 "utility/int_alias.cpp"
#include <cstdint>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
#line 2 "math/rem_euclid.cpp"
#include <cassert>

template <class T> constexpr T rem_euclid(T value, const T& mod) {
    assert(mod > 0);
    return (value %= mod) >= 0 ? value : value + mod;
}
#line 2 "math/totient.cpp"

template <class T> constexpr T totient(T x) {
    T ret = x;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i;
            ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) {
        ret /= x;
        ret *= x - 1;
    }
    return ret;
}
#line 7 "math/static_modint.cpp"

template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
    using Self = StaticModint;

    static inline constexpr u32 PHI = totient(MOD);
    u32 v;

  public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T, std::enable_if_t<std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T& x) noexcept {
        return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
    }

    constexpr StaticModint() noexcept : v(0) {}
    template <class T> constexpr StaticModint(const T& x) noexcept : v(normalize(x)) {}
    template <class T> static constexpr Self raw(const T& x) noexcept {
        Self ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 val() const noexcept { return v; }
    constexpr Self neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Self inv() const noexcept { return pow(PHI - 1); }
    constexpr Self pow(u64 exp) const noexcept {
        Self ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Self operator-() const noexcept { return neg(); }
    constexpr Self operator~() const noexcept { return inv(); }

    constexpr Self operator+(const Self& rhs) const noexcept { return Self(*this) += rhs; }
    constexpr Self& operator+=(const Self& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }

    constexpr Self operator-(const Self& rhs) const noexcept { return Self(*this) -= rhs; }
    constexpr Self& operator-=(const Self& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }

    constexpr Self operator*(const Self& rhs) const noexcept { return Self(*this) *= rhs; }
    constexpr Self& operator*=(const Self& rhs) noexcept {
        v = (u64)v * rhs.v % MOD;
        return *this;
    }

    constexpr Self operator/(const Self& rhs) const noexcept { return Self(*this) /= rhs; }
    constexpr Self& operator/=(const Self& rhs) noexcept { return *this *= rhs.inv(); }

    constexpr bool operator==(const Self& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const Self& rhs) const noexcept { return v != rhs.v; }
    friend std::ostream& operator<<(std::ostream& stream, const Self& rhs) { return stream << rhs.v; }
};

using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;
#line 7 "test/berlekamp_massey.test.cpp"

using Fp = Modint998244353;

int main() { 
    int n;
    std::cin >> n;
    std::vector<Fp> a(n);
    for (auto& x : a) {
        u32 t;
        std::cin >> t;
        x = t;
    }
    const auto c = berlekamp_massey(a);
    std::cout << c.size() << '\n';
    for (const int i : rep(0, c.size())) {
        std::cout << c[i] << " \n"[i + 1 == c.size()];
    }
    return 0; 
}

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