結果

問題 No.3043 括弧列の数え上げ
ユーザー 横山緑
提出日時 2025-02-28 22:24:20
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 6,748 bytes
コンパイル時間 3,320 ms
コンパイル使用メモリ 282,440 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2025-02-28 22:24:27
合計ジャッジ時間 4,779 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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ファイルパターン 結果
sample AC * 3
other AC * 45
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 3 "math/factorial.hpp"
// https://suisen-cp.github.io/cp-library-cpp/library/math/factorial.hpp
template <class T> struct factorial {
    factorial() {};
    void ensure(const int n) {
        int sz = size(fac);
        if(sz > n) {
            return;
        }
        int new_sz = max(2 * sz, n + 1);
        fac.resize(new_sz), fac_inv.resize(new_sz);
        for(int i = sz; i < new_sz; i++) {
            if(i == 0) {
                fac[i] = 1;
                continue;
            }
            fac[i] = fac[i - 1] * i;
        }
        fac_inv[new_sz - 1] = T(1) / fac[new_sz - 1];
        for(int i = new_sz - 2; i >= sz; i--) {
            fac_inv[i] = fac_inv[i + 1] * (i + 1);
        }
        return;
    }
    T get(int i) {
        ensure(i);
        return fac[i];
    }
    T operator[](int i) { return get(i); }
    T inv(int i) {
        ensure(i);
        return fac_inv[i];
    }
    T binom(int n, int i) {
        if(n < 0 || i < 0 || n < i) {
            return T(0);
        }
        ensure(n);
        return fac[n] * fac_inv[i] * fac_inv[n - i];
    }
    T perm(int n, int i) {
        if(n < 0 || i < 0 || n < i) {
            return T(0);
        }
        ensure(n);
        return fac[n] * fac_inv[n - i];
    }

  private:
    vector<T> fac, fac_inv;
};
#line 3 "/home/y_midori/cp/04_yukicoder/458/i.cpp"
#include <atcoder/modint>
// using namespace atcoder;
using mint = atcoder::modint998244353;
factorial<mint> fac;
ll naive_cnt(ll n) {
    ll c = 0;
    rep(i, 1 << n) {
        if(popcount(unsigned(i)) * 2 != n)
            continue;
        ll cur = 0;
        ll num = 0;
        rep(j, n) {
            if((i >> j) & 1) {
                num--;
                if(num < 0) {
                    cur = 0;
                    break;
                }
                cur += num;
            } else {
                num++;
            }
        }
        if(num)
            continue;
        c += cur;
    }
    return c;
}
void solve() {
    // rep(i, 2, 17, 2) {
    //     debug(i, naive_cnt(i));
    // }
    LL(n);
    if(n & 1) {
        print(0);
        return;
    }
    n = n / 2 - 1;
    mint ans = 0;
    ans = mint(2).pow(2 * n + 1) - fac.binom(2 * n + 3, n + 1) +
          fac.binom(2 * n + 1, n);
    print(ans.val());
}

int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << std::setprecision(16);
    int t = 1;
    rep(_, t) {
        solve();
    }
}
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