結果

問題 No.3146 RE: Parentheses Counting
コンテスト
ユーザー Nauclhlt🪷
提出日時 2025-03-13 17:37:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 188 ms / 2,000 ms
コード長 6,353 bytes
コンパイル時間 2,041 ms
コンパイル使用メモリ 197,272 KB
実行使用メモリ 50,684 KB
最終ジャッジ日時 2025-05-16 20:52:20
合計ジャッジ時間 12,095 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
sample AC * 1
other AC * 43
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 # 

#include <bits/stdc++.h>
using namespace std;

#define CONST_MOD 998244353LL
//#define CONST_MOD 1000000007LL
struct ModInt
{
    long long Value;

public:
    ModInt()
    {
        Value = 0L;
    }

    ModInt(long long value)
    {
        Value = value;
    }

    ModInt Power(long long exp) const
    {
        if (exp <= -1L)
        {
            return ModInt(1L) / Power(-exp);
        }
        if (exp == 0L)
            return 1L;
        if (exp == 1L)
            return *this;

        ModInt m = Power(exp / 2L);
        m = m * m;
        if (exp % 2L == 1L)
        {
            m = m * (*this);
        }

        return m;
    }

    ModInt Inv() const
    {
        return this->Power(CONST_MOD - 2L);
    }

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

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

    friend ModInt operator+(const ModInt& left, const ModInt& right)
    {
        return ModInt(SafeMod(left.Value + right.Value));
    }

    friend ModInt operator+(const ModInt& left, const long long& right)
    {
        return ModInt(SafeMod(left.Value + right));
    }

    friend ModInt operator+(const long long& left, const ModInt& right)
    {
        return ModInt(SafeMod(left + right.Value));
    }

    ModInt& operator+=(const ModInt& x)
    {
        Value += x.Value;
        Value = SafeMod(Value);

        return *this;
    }

    ModInt& operator+=(const long long& x)
    {
        Value += x;
        Value = SafeMod(Value);

        return *this;
    }

    friend ModInt operator-(const ModInt& left, const ModInt& right)
    {
        return ModInt(SafeMod(left.Value - right.Value));
    }

    friend ModInt operator-(const ModInt& left, const long long& right)
    {
        return ModInt(SafeMod(left.Value - right));
    }

    friend ModInt operator-(const long long& left, const ModInt& right)
    {
        return ModInt(SafeMod(left - right.Value));
    }

    ModInt& operator-=(const ModInt& x)
    {
        Value -= x.Value;
        Value = SafeMod(Value);

        return *this;
    }

    ModInt& operator-=(const long long& x)
    {
        Value -= x;
        Value = SafeMod(Value);

        return *this;
    }

    friend ModInt operator*(const ModInt& left, const ModInt& right)
    {
        return ModInt(SafeMod(left.Value * right.Value));
    }

    friend ModInt operator*(const ModInt& left, const long long& right)
    {
        return ModInt(SafeMod(left.Value * right));
    }

    friend ModInt operator*(const long long& left, const ModInt& right)
    {
        return ModInt(SafeMod(left * right.Value));
    }

    ModInt& operator*=(const ModInt& x)
    {
        Value *= x.Value;
        Value = SafeMod(Value);

        return *this;
    }

    ModInt& operator*=(const long long& x)
    {
        Value *= x;
        Value = SafeMod(Value);

        return *this;
    }

    friend ModInt operator /(const ModInt& left, const ModInt& right)
    {
        ModInt inv = right.Inv();
        return ModInt(SafeMod(left.Value * inv.Value));
    }

    friend ModInt operator/(const ModInt& left, const long long& right)
    {
        return ModInt(SafeMod(left.Value * ModInt(right).Inv().Value));
    }

    friend ModInt operator/(const long long& left, const ModInt& right)
    {
        return ModInt(SafeMod(left * right.Inv().Value));
    }

    ModInt& operator/=(const ModInt& x)
    {
        Value *= x.Inv().Value;
        Value = SafeMod(Value);

        return *this;
    }

    ModInt& operator/=(const long long& x)
    {
        Value *= ModInt(x).Inv().Value;
        Value = SafeMod(Value);

        return *this;
    }

    ModInt& operator++()
    {
        ++Value;
        Value = SafeMod(Value);
        return *this;
    }

    ModInt operator++(int)
    {
        ModInt temp = *this;
        Value++;
        Value = SafeMod(Value);
        return temp;
    }

    ModInt& operator--()
    {
        --Value;
        Value = SafeMod(Value);
        return *this;
    }

    ModInt operator--(int)
    {
        ModInt temp = *this;
        Value--;
        Value = SafeMod(Value);
        return temp;
    }

    inline static ModInt One()
    {
        return ModInt(1L);
    }

    static ModInt Combination(long long n, long long r)
    {
        ModInt c = 1L;
        for (ModInt i = 1; i.Value <= r; i++)
        {
            c = c * (ModInt(n) - i + ModInt::One()) / i;
        }
        return c;
    }

private:
    inline static long long SafeMod(long long a)
    {
        a %= CONST_MOD;
        if (a < 0)
        {
            a += CONST_MOD;
        }
        return a;
    }
};

class ModFactorialCache
{
private:
    vector<ModInt> _factorial;
    vector<ModInt> _inverseFactorial;

public:
    ModFactorialCache(int max)
    {
        _factorial.resize(max + 1);
        _inverseFactorial.resize(max + 1);
        vector<ModInt> inv(max + 1);
        inv[1] = 1;
        for (int i = 2; i <= max; i++)
        {
            inv[i] = -(CONST_MOD / i) * inv[CONST_MOD % i];
        }

        _factorial[0] = 1;
        _inverseFactorial[0] = 1;

        for (long long p = 1; p <= max; p++)
        {
            ModInt pm = ModInt(p);
            _factorial[p] = _factorial[p - 1] * pm;
            _inverseFactorial[p] = _inverseFactorial[p - 1] * inv[p];
        }
    }

    ModInt Combination(int n, int r)
    {
        return _factorial[n] * (_inverseFactorial[n - r] * _inverseFactorial[r]);
    }

    ModInt Permutation(int n, int r)
    {
        return _factorial[n] * _inverseFactorial[n - r];
    }

    ModInt Factorial(int n)
    {
        return _factorial[n];
    }
};

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    ModFactorialCache cache(2000050);
    int T;
    cin >> T;

    vector<ModInt> powers = {1};

    while (T--)
    {
        int N;
        cin >> N;
        if (N % 2 == 1) cout << "0\n";
        else
        {
            if (N == 2) cout << "0\n";
            else
            {
                N = N / 2 - 1;
                while (powers.size() <= 2 * N)
                {
                    powers.push_back(powers[powers.size() - 1] * 2);
                }
                ModInt ans = powers[2 * N] - cache.Combination(2 * N + 1, N);
                cout << ans.Value << "\n";
            }
        }
    }
}
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