結果

問題 No.3033 エルハートの数え上げ
ユーザー 横山緑
提出日時 2025-02-21 23:50:31
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 22 ms / 2,000 ms
コード長 9,799 bytes
コンパイル時間 3,809 ms
コンパイル使用メモリ 288,324 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2025-02-21 23:50:36
合計ジャッジ時間 4,998 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 20
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

diff # 

#line 2 "template.hpp"
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
using namespace std;
// https://xn--kst.jp/blog/2019/08/29/cpp-comp/
// debug methods
// usage: debug(x,y);
// vector 出力できるように修正
template <typename T>
ostream& debug_print(ostream& os, const vector<T>& v) {
    os << "[";
    for (size_t i = 0; i < v.size(); ++i) {
        os << v[i];
        if (i < v.size() - 1) os << ", ";
    }
    os << "]";
    return os;
}
template <typename T>
ostream& debug_print(ostream& os, const T& var) {
    os << var;
    return os;
}
#define CHOOSE(a) CHOOSE2 a
#define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x
#define debug_1(x1) { cout << #x1 << ": "; debug_print(cout, x1) << endl; }
#define debug_2(x1, x2) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << endl; }
#define debug_3(x1, x2, x3) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << endl; }
#define debug_4(x1, x2, x3, x4) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << endl; }
#define debug_5(x1, x2, x3, x4, x5) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << ", " << #x5 << ": "; debug_print(cout, x5) << endl; }

#ifdef LOCAL
#define debug(...) CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~))(__VA_ARGS__)
#else
#define debug(...)
#endif

using ll = long long;
using vl = vector<ll>;
using Graph = vector<vector<ll>>;
using P = pair<ll, ll>;
#define all(v) v.begin(), v.end()
template <typename T> inline bool chmax(T &a, T b) {
    return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
    return ((a > b) ? (a = b, true) : (false));
}
#define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i)
// https://trap.jp/post/1224/
template <class... T> constexpr auto min(T... a) {
    return min(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> constexpr auto max(T... a) {
    return max(initializer_list<common_type_t<T...>>{a...});
}
template <class... T> void input(T &...a) { (cin >> ... >> a); }
template <class T> void input(vector<T> &a) {
    for(T &x : a)
        cin >> x;
}
void print() { cout << '\n'; }
template <class T, class... Ts> void print(const T &a, const Ts &...b) {
    cout << a;
    (cout << ... << (cout << ' ', b));
    cout << '\n';
}
void print(const string &s) {
    cout << s << '\n';
}
template <class Container, typename = void>
struct is_container : std::false_type {};
template <class Container>
struct is_container<Container, std::void_t<decltype(std::declval<Container>().begin()), decltype(std::declval<Container>().end())>> : std::true_type {};
template <class Container>
typename enable_if<is_container<Container>::value>::type print(const Container& x) {
    if (!x.empty()) {
        auto it = x.begin();
        for (; it != prev(x.end()); ++it) {
            cout << *it << " ";
        }
        cout << *it << "\n";  // 最後の要素を出力して改行
    }
}
#define INT(...)                                                               \
    int __VA_ARGS__;                                                           \
    input(__VA_ARGS__)
#define LL(...)                                                                \
    long long __VA_ARGS__;                                                     \
    input(__VA_ARGS__)
#define STR(...)                                                               \
    string __VA_ARGS__;                                                        \
    input(__VA_ARGS__)
#define REP1(a) for(ll i = 0; i < a; i++)
#define REP2(i, a) for(ll i = 0; i < a; i++)
#define REP3(i, a, b) for(ll i = a; i < b; i++)
#define REP4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)

ll inf = 3e18;
vl dx = {1, -1, 0, 0};
vl dy = {0, 0, 1, -1};
#line 2 "/home/y_midori/cp/04_yukicoder/457/g.cpp"
// #include <atcoder/all>
// using namespace atcoder;
// using mint = modint998244353;
// https://ei1333.github.io/luzhiled/snippets/math/lagrange-polynomial.htmlから
template <int mod> struct ModInt {
    int x;

    ModInt() : x(0) {
    }

    ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {
    }

    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod)
            x -= mod;
        return *this;
    }

    ModInt &operator*=(const ModInt &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }

    ModInt operator-() const {
        return ModInt(-x);
    }

    ModInt operator+(const ModInt &p) const {
        return ModInt(*this) += p;
    }

    ModInt operator-(const ModInt &p) const {
        return ModInt(*this) -= p;
    }

    ModInt operator*(const ModInt &p) const {
        return ModInt(*this) *= p;
    }

    ModInt operator/(const ModInt &p) const {
        return ModInt(*this) /= p;
    }

    bool operator==(const ModInt &p) const {
        return x == p.x;
    }

    bool operator!=(const ModInt &p) const {
        return x != p.x;
    }

    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }

    ModInt pow(int64_t n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1)
                ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const ModInt &p) {
        return os << p.x;
    }

    friend istream &operator>>(istream &is, ModInt &a) {
        int64_t t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }

    static int get_mod() {
        return mod;
    }
};

using modint = ModInt<998244353>;
template <typename T> struct Combination {
    vector<T> _fact, _rfact, _inv;

    Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
        _fact[0] = _rfact[sz] = _inv[0] = 1;
        for(int i = 1; i <= sz; i++)
            _fact[i] = _fact[i - 1] * i;
        _rfact[sz] /= _fact[sz];
        for(int i = sz - 1; i >= 0; i--)
            _rfact[i] = _rfact[i + 1] * (i + 1);
        for(int i = 1; i <= sz; i++)
            _inv[i] = _rfact[i] * _fact[i - 1];
    }

    inline T fact(int k) const {
        return _fact[k];
    }

    inline T rfact(int k) const {
        return _rfact[k];
    }

    inline T inv(int k) const {
        return _inv[k];
    }

    T P(int n, int r) const {
        if(r < 0 || n < r)
            return 0;
        return fact(n) * rfact(n - r);
    }

    T C(int p, int q) const {
        if(q < 0 || p < q)
            return 0;
        return fact(p) * rfact(q) * rfact(p - q);
    }

    T H(int n, int r) const {
        if(n < 0 || r < 0)
            return (0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }
};
template <typename T> T lagrange_polynomial(const vector<T> &y, int64_t t) {
    int N = y.size() - 1;
    Combination<T> comb(N);
    if(t <= N)
        return y[t];
    T ret(0);
    vector<T> dp(N + 1, 1), pd(N + 1, 1);
    for(int i = 0; i < N; i++)
        dp[i + 1] = dp[i] * (t - i);
    for(int i = N; i > 0; i--)
        pd[i - 1] = pd[i] * (t - i);
    for(int i = 0; i <= N; i++) {
        T tmp = y[i] * dp[i] * pd[i] * comb.rfact(i) * comb.rfact(N - i);
        if((N - i) & 1)
            ret -= tmp;
        else
            ret += tmp;
    }
    return ret;
}
void solve() {
    LL(n, m);
    using T = tuple<ll, ll, ll, ll>;
    vector<T> abcd(m);
    rep(i, m) {
        LL(a, b, c, d);
        abcd[i] = T(a, b, c, d);
    }
    vector<modint> f(4, 1);
    rep(t, 1, 4) {
        // if(t > 1)
        //     break;
        ll cnt = 0;
        ll lim = 16 * t + 5;
        for(ll i = -lim; i <= lim; i++)
            for(ll j = -lim; j <= lim; j++)
                for(ll k = -lim; k <= lim; k++) {
                    bool flag = true;
                    for(auto [a, b, c, d] : abcd) {
                        d *= t;
                        if(a * i + b * j + c * k + d < 0) {
                            flag = false;
                            break;
                        }
                    }
                    if(flag) {
                        // debug(i, j, k);
                        cnt++;
                    }
                }
        f[t] = cnt;
    }
    // vector<mint> x(4);
    // rep(i, 4) x[i] = i;
    // auto g = lagrange_interpolation(x, f);
    // mint ans = 0;
    // rep(i, 4) {
    //     ans -= g[i] * (modint(-n).pow(i));
    // }
    ll _n = (998244353 * 2 - n) % 998244353;
    // _n = (n + 998244353) % 998244353;
    debug(f, n, _n);
    modint ans = -lagrange_polynomial(f, _n);
    // modint ans = lagrange_polynomial(f, n);
    cout << ans << endl;
}
int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << std::setprecision(16);
    int t = 1;
    rep(_, t) {
        solve();
    }
    // int N, T;
    // cin >> N;
    // vector<modint> A(N + 1);
    // input(A);
    // cin >> T;
    // cout << lagrange_polynomial(A, T) << endl;
}
0