結果
| 問題 | No.1873 Bracket Swapping |
| ユーザー |
 milanis48663220
|
| 提出日時 | 2022-03-11 23:13:55 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 331 ms / 2,000 ms |
| コード長 | 7,101 bytes |
| コンパイル時間 | 1,412 ms |
| コンパイル使用メモリ | 127,660 KB |
| 最終ジャッジ日時 | 2025-01-28 09:03:52 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge6 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 27 |
ソースコード
#include <iostream>#include <algorithm>#include <iomanip>#include <vector>#include <queue>#include <deque>#include <set>#include <map>#include <tuple>#include <cmath>#include <numeric>#include <functional>#include <cassert>#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }using namespace std;typedef long long ll;template<typename T>vector<vector<T>> vec2d(int n, int m, T v){return vector<vector<T>>(n, vector<T>(m, v));}template<typename T>vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));}template<typename T>void print_vector(vector<T> v, char delimiter=' '){if(v.empty()) {cout << endl;return;}for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;cout << v.back() << endl;}const ll MOD = 998244353;class ModInt{public:ll v;ModInt(ll _v = 0){if(_v < 0) _v = (_v%MOD)+MOD;if(_v >= MOD) _v %= MOD;v = _v;}ModInt operator+(ll n){return ModInt((v+n)%MOD);}ModInt operator-(ll n){return ModInt((v-n+MOD)%MOD);}ModInt operator*(ll n){if(n >= MOD) n %= MOD;return ModInt((v*n)%MOD);}ModInt operator/(ll n){return ModInt((ModInt(n).inv()*v).v%MOD);}ModInt &operator+=(ll n){v = (v+n)%MOD;return *this;}ModInt &operator-=(ll n){v = (v-n+MOD)%MOD;return *this;}ModInt &operator*=(ll n){v = (v*n+MOD)%MOD;return *this;}ModInt operator+(ModInt n){return ModInt((v+n.v)%MOD);}ModInt operator-(ModInt n){return ModInt((v-n.v+MOD)%MOD);}ModInt operator*(ModInt n){return ModInt((v*n.v)%MOD);}ModInt operator/(ModInt n){return ModInt((n.inv()*v).v%MOD);}ModInt &operator+=(ModInt n){v = (v+n.v)%MOD;return *this;}ModInt &operator-=(ModInt n){v = (v-n.v+MOD)%MOD;return *this;}ModInt &operator*=(ModInt n){v = (v*n.v)%MOD;return *this;}bool operator==(ModInt n){return v == n.v;}bool operator!=(ModInt n){return v != n.v;}ModInt &operator=(ll n){v = n%MOD;return *this;}ModInt inv(){if(v == 1) return ModInt(1);else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);}};ostream& operator<<(ostream& os, const ModInt& m){os << m.v;return os;}istream & operator >> (istream &in, ModInt &m){in >> m.v;return in;}ModInt pow(ModInt a, ll n) {assert(n >= 0);ModInt ans = 1;while (n > 0) {if (n&1) ans = ans*a;a = a*a;n >>= 1;}return ans;}template <typename T>struct matrix{int n, m;vector<vector<T>> dat;matrix(int n_, int m_){n = n_; m = m_;for(int i = 0; i < n; i++){dat.push_back(vector<T>(m));}}matrix(int n, int m, T val): n(n), m(m){for(int i = 0; i < n; i++){dat.push_back(vector<T>(m, val));}}matrix(int n, int m, vector<vector<T>> dat): n(n), m(m), dat(dat){assert((int)dat.size() == n);for(int i = 0; i < n; i++) assert(dat[i].size() == m);}vector<T>& operator[](int x) {return dat[x];}};template <typename T>bool prod(matrix<T> a, matrix<T> b, matrix<T> &ans){assert(a.m == b.n);for(int i = 0; i < a.n; i++){for(int j = 0; j < b.m; j++){ans.dat[i][j] = 0;for(int k = 0; k < b.n; k++){ans.dat[i][j] += (a.dat[i][k]*b.dat[k][j]);}}}return true;}template <typename T>void copy_mat(matrix<T> a, matrix<T> &b){assert(a.n == b.n);assert(a.m == b.m);for(int i = 0; i < a.n; i++){for(int j = 0; j < a.m; j++){b.dat[i][j] = a.dat[i][j];}}}template <typename T>void pow_mat(matrix<T> a, ll n, matrix<T> &ans){assert(n < ((ll)1<<61));matrix<T> buf(a.n, a.n);matrix<T> tmp(a.n, a.n);copy_mat(a, tmp);for(int i = 0; i < a.n; i++) {for(int j = 0; j < a.n; j++){ans.dat[i][j] = 0;}ans.dat[i][i] = 1;}while (n > 0) {if (n&1) {prod(tmp, ans, buf);copy_mat(buf, ans);}prod(tmp, tmp, buf);copy_mat(buf, tmp);n >>= 1;}}template <typename T>void print_mat(matrix<T> a){for(int i = 0; i < a.n; i++){for(int j = 0; j < a.m; j++){cout << a.dat[i][j] << ' ';}cout << endl;}}template <typename T>ostream& operator<<(ostream& os, const matrix<T>& m){print_mat<T>(m);return os;}template<typename T>matrix<T> operator*(matrix<T> m1, matrix<T> m2){matrix<T> ans(m1.n, m2.m);prod(m1, m2, ans);return ans;}/*** 累乗*/template<typename T>matrix<T> operator^(matrix<T> m, ll r){matrix<T> ans(m.n, m.n);pow_mat(m, r, ans);return ans;}#define N_MAX 200002ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];void init(){fac[0]=1;fac[1]=1;finv[0]=1;finv[1]=1;inv[1]=1;for(int i=2;i<N_MAX;i++){inv[i]=ModInt(MOD)-inv[MOD%i]*(MOD/i);fac[i]=fac[i-1]*(ll) i;finv[i]=finv[i-1]*inv[i];}}ModInt comb(ll n, ll r){if(n < r){return ModInt(0);}else{return fac[n]*finv[r]*finv[n-r];}}using mint = ModInt;int main(){ios::sync_with_stdio(false);cin.tie(0);cout << setprecision(10) << fixed;init();string s; cin >> s;ll k; cin >> k;int n = s.size();int m = n/2;auto dp = vec3d(n+1, n+1, m+1, mint(0));dp[0][0][0] = 1;for(int i = 0; i < n; i++){for(int j = 0; j <= n; j++){for(int k = 0; k <= m; k++){if(j != 0){int add = s[i] == '(' ? 1 : 0;if(k+add <= m) dp[i+1][j-1][k+add] += dp[i][j][k];}if(j != n){dp[i+1][j+1][k] += dp[i][j][k];}}}}matrix<mint> A(m+1, m+1, mint(0));matrix<mint> v(m+1, 1, mint(0));for(int i = 0; i <= m; i++){v[i][0] = dp[n][0][i];}for(int a = 0; a <= m; a++){if(a != m){A[a+1][a] = mint(m-a)*mint(m-a);}if(a != 0){A[a-1][a] = mint(a)*mint(a);}A[a][a] += comb(n, 2)-a*a-(m-a)*(m-a);}auto u = (A^k)*v;mint ans = u[0][0];cout << ans << endl;}