結果

問題 No.3043 括弧列の数え上げ
ユーザー Nauclhlt🪷
提出日時 2025-01-10 21:55:07
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 760 ms / 2,000 ms
コード長 5,697 bytes
コンパイル時間 1,980 ms
コンパイル使用メモリ 199,348 KB
実行使用メモリ 222,336 KB
最終ジャッジ日時 2025-01-11 17:13:49
合計ジャッジ時間 12,554 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 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 # 

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

using ll = long long;

ll CONST_MOD = 998244353LL;
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;
    }
};

int main()
{
    int N;
    cin >> N;
    
    const int OPEN = 0;
    const int CLOSE = 1;

    if ((N & 1) == 1)
    {
        cout << 0 << endl;
        return 0;
    }

    vector<vector<vector<ModInt>>> dp(N + 1, vector<vector<ModInt>>(N + 1, vector<ModInt>(2, 0LL)));
    dp[1][1][OPEN] = 1LL;
    for (int i = 2; i <= N; i++)
    {
        for (int j = 0; j <= N; j++)
        {
            // ')'を追加
            if (j <= N - 1)
            {
                dp[i][j][CLOSE] += dp[i - 1][j + 1][OPEN] + dp[i - 1][j + 1][CLOSE];
            }

            // '('を追加
            if (j >= 1)
            {
                dp[i][j][OPEN] += dp[i - 1][j - 1][OPEN] + dp[i - 1][j - 1][CLOSE];
            }
        }
    }

    ModInt ans = 0LL;
    for (int i = 1; i <= N; i++)
    {
        // i文字目の')'の寄与
        for (int j = 1; j <= N; j++)
        {
            int right = N - i;
            ans += dp[i][j][CLOSE] * (dp[right][j][OPEN] + dp[right][j][CLOSE]) * ModInt(j);
        }
    }

    cout << ans.Value << endl;
}
0