結果

問題 No.1873 Bracket Swapping
ユーザー rniya
提出日時 2022-03-11 22:20:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 935 ms / 2,000 ms
コード長 12,251 bytes
コンパイル時間 2,197 ms
コンパイル使用メモリ 204,420 KB
最終ジャッジ日時 2025-01-28 08:44:49
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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 * 27
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 #
プレゼンテーションモードにする

#define LOCAL
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
typedef long long ll;
typedef __int128_t i128;
typedef unsigned int uint;
typedef unsigned long long ull;
#define ALL(x) (x).begin(), (x).end()
template <typename T> istream& operator>>(istream& is, vector<T>& v) {
    for (T& x : v) is >> x;
    return is;
}
template <typename T> ostream& operator<<(ostream& os, const vector<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << '(' << p.first << ',' << p.second << ')';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T, typename U> ostream& operator<<(ostream& os, const unordered_map<T, U>& m) {
    os << '{';
    for (auto itr = m.begin(); itr != m.end();) {
        os << '(' << itr->first << ',' << itr->second << ')';
        if (++itr != m.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const multiset<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const unordered_set<T>& s) {
    os << '{';
    for (auto itr = s.begin(); itr != s.end();) {
        os << *itr;
        if (++itr != s.end()) os << ',';
    }
    os << '}';
    return os;
}
template <typename T> ostream& operator<<(ostream& os, const deque<T>& v) {
    for (size_t i = 0; i < v.size(); i++) {
        os << v[i] << (i + 1 == v.size() ? "" : " ");
    }
    return os;
}
template <typename T, size_t N> ostream& operator<<(ostream& os, const array<T, N>& v) {
    for (size_t i = 0; i < N; i++) {
        os << v[i] << (i + 1 == N ? "" : " ");
    }
    return os;
}
template <int i, typename T> void print_tuple(ostream&, const T&) {}
template <int i, typename T, typename H, class... Args> void print_tuple(ostream& os, const T& t) {
    if (i) os << ',';
    os << get<i>(t);
    print_tuple<i + 1, T, Args...>(os, t);
}
template <typename... Args> ostream& operator<<(ostream& os, const tuple<Args...>& t) {
    os << '{';
    print_tuple<0, tuple<Args...>, Args...>(os, t);
    return os << '}';
}
void debug_out() { cerr << '\n'; }
template <class Head, class... Tail> void debug_out(Head&& head, Tail&&... tail) {
    cerr << head;
    if (sizeof...(Tail) > 0) cerr << ", ";
    debug_out(move(tail)...);
}
#ifdef LOCAL
#define debug(...)                                                                   \
    cerr << " ";                                                                     \
    cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \
    cerr << " ";                                                                     \
    debug_out(__VA_ARGS__)
#else
#define debug(...) void(0)
#endif
template <typename T> T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; }
template <typename T> T lcm(T x, T y) { return x / gcd(x, y) * y; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(signed t) { return __builtin_popcount(t); }
int popcount(long long t) { return __builtin_popcountll(t); }
bool ispow2(int i) { return i && (i & -i) == i; }
long long MSK(int n) { return (1LL << n) - 1; }
template <class T> T ceil(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <class T> T floor(T x, T y) {
    assert(y >= 1);
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <class T1, class T2> inline bool chmin(T1& a, T2 b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T1, class T2> inline bool chmax(T1& a, T2 b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <typename T> void mkuni(vector<T>& v) {
    sort(v.begin(), v.end());
    v.erase(unique(v.begin(), v.end()), v.end());
}
template <typename T> int lwb(const vector<T>& v, const T& x) { return lower_bound(v.begin(), v.end(), x) - v.begin(); }
#pragma endregion
#include <iostream>
#include "atcoder/modint"
namespace atcoder {
template <int MOD> std::istream& operator>>(std::istream& is, static_modint<MOD>& x) {
    int64_t v;
    x = static_modint<MOD>{(is >> v, v)};
    return is;
}
template <int MOD> std::ostream& operator<<(std::ostream& os, const static_modint<MOD>& x) { return os << x.val(); }
template <int ID> std::ostream& operator<<(std::ostream& os, const dynamic_modint<ID>& x) { return os << x.val(); }
}  // namespace atcoder
#include <cassert>
#include <iostream>
#include <vector>
template <typename T> struct Matrix {
    std::vector<std::vector<T>> A;
    Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}
    Matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}
    size_t size() const { return A.size(); }
    size_t height() const { return A.size(); }
    size_t width() const { return A[0].size(); }
    inline const std::vector<T>& operator[](int k) const { return A[k]; }
    inline std::vector<T>& operator[](int k) { return A[k]; }
    static Matrix I(size_t n) {
        Matrix res(n);
        for (size_t i = 0; i < n; i++) res[i][i] = 1;
        return res;
    }
    Matrix& operator+=(const Matrix& B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (size_t i = 0; i < n; i++) {
            for (size_t j = 0; j < m; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return *this;
    }
    Matrix& operator-=(const Matrix& B) {
        size_t n = height(), m = width();
        assert(n == B.height() && m == B.width());
        for (size_t i = 0; i < n; i++) {
            for (size_t j = 0; j < m; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return *this;
    }
    Matrix& operator*=(const Matrix& B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
        for (size_t i = 0; i < n; i++) {
            for (size_t k = 0; k < p; k++) {
                for (size_t j = 0; j < m; j++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        return *this;
    }
    Matrix& operator*=(const T& v) {
        for (size_t i = 0; i < height(); i++) {
            for (size_t j = 0; j < width(); j++) {
                (*this)[i][j] *= v;
            }
        }
        return *this;
    }
    Matrix& operator/=(const T& v) {
        T inv = T(1) / v;
        for (size_t i = 0; i < height(); i++) {
            for (size_t j = 0; j < width(); j++) {
                (*this)[i][j] *= inv;
            }
        }
        return *this;
    }
    Matrix& operator^=(long long k) {
        assert(0 <= k);
        Matrix B = Matrix::I(size());
        while (k > 0) {
            if (k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        A.swap(B.A);
        return *this;
    }
    Matrix operator-() const {
        Matrix res(height(), width());
        for (size_t i = 0; i < height(); i++) {
            for (size_t j = 0; j < width(); j++) {
                res[i][j] = -(*this)[i][j];
            }
        }
        return res;
    }
    Matrix operator+(const Matrix& B) const { return Matrix(*this) += B; }
    Matrix operator-(const Matrix& B) const { return Matrix(*this) -= B; }
    Matrix operator*(const Matrix& B) const { return Matrix(*this) *= B; }
    Matrix operator*(const T& v) const { return Matrix(*this) *= v; }
    Matrix operator/(const T& v) const { return Matrix(*this) /= v; }
    Matrix operator^(const long long k) const { return Matrix(*this) ^= k; }
    bool operator==(const Matrix& B) const {
        assert(height() == B.height() && width() == B.width());
        return A == B.A;
    }
    bool operator!=(const Matrix& B) const {
        assert(height() == B.height() && width() == B.width());
        return A != B.A;
    }
    Matrix transpose() const {
        Matrix res(width(), height());
        for (size_t i = 0; i < height(); i++) {
            for (size_t j = 0; j < width(); j++) {
                res[j][i] = (*this)[i][j];
            }
        }
        return res;
    }
    T determinant() const {
        assert(height() == width());
        Matrix B(*this);
        T res = 1;
        for (size_t i = 0; i < height(); i++) {
            int pivot = -1;
            for (size_t j = i; j < height(); j++) {
                if (B[j][i] != 0) {
                    pivot = j;
                    break;
                }
            }
            if (pivot == -1) return 0;
            if (pivot != (int)i) {
                res *= -1;
                std::swap(B[i], B[pivot]);
            }
            res *= B[i][i];
            T inv = T(1) / B[i][i];
            for (size_t j = 0; j < width(); j++) B[i][j] *= inv;
            for (size_t j = i + 1; j < height(); j++) {
                T a = B[j][i];
                for (size_t k = 0; k < width(); k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return res;
    }
    friend std::ostream& operator<<(std::ostream& os, const Matrix& p) {
        size_t n = p.height(), m = p.width();
        os << "[(" << n << " * " << m << " Matrix)";
        os << "\n[columun sums: ";
        for (size_t j = 0; j < m; j++) {
            T sum = 0;
            for (size_t i = 0; i < n; i++) sum += p[i][j];
            ;
            os << sum << (j + 1 < m ? "," : "");
        }
        os << "]";
        for (size_t i = 0; i < n; i++) {
            os << "\n[";
            for (size_t j = 0; j < m; j++) os << p[i][j] << (j + 1 < m ? "," : "");
            os << "]";
        }
        os << "]\n";
        return os;
    }
};
const int INF = 1e9;
const long long IINF = 1e18;
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const char dir[4] = {'D', 'R', 'U', 'L'};
const long long MOD = 1000000007;
// const long long MOD = 998244353;
using mint = atcoder::modint998244353;
int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    string S;
    int K;
    cin >> S >> K;
    int N = S.size();
    vector<vector<mint>> dp(N + 1, vector<mint>(N + 1, 0)), ndp(N + 1, vector<mint>(N + 1, 0));
    dp[0][0] = 1;
    for (int k = 0; k < N; k++) {
        int cur = (S[k] == '(' ? 1 : -1);
        for (int i = 0; i <= k; i++) {
            for (int j = 0; j <= k; j++) {
                mint& val = dp[i][j];
                if (val == 0) continue;
                for (int di : {-1, 1}) {
                    if (i + di < 0) continue;
                    ndp[i + di][j + (di != cur)] += val;
                }
                val = 0;
            }
        }
        swap(dp, ndp);
    }
    Matrix<mint> M(N + 1);
    for (int i = 0; i <= N; i++) {
        if (i & 1) continue;
        M[i][i] += (N / 2) * (N / 2 - 1) / 2;
        M[i][i] += (N / 2) * (N / 2 - 1) / 2;
        if (i >= 2) M[i][i - 2] += (i / 2) * (i / 2);
        if (N - i >= 2) M[i][i + 2] += ((N - i) / 2) * ((N - i) / 2);
        M[i][i] += (i / 2) * ((N - i) / 2);
        M[i][i] += (i / 2) * ((N - i) / 2);
    }
    M ^= K;
    mint ans = 0;
    for (int j = 0; j <= N; j++) ans += dp[0][j] * M[j][0];
    cout << ans << '\n';
    return 0;
}
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