結果
問題 | No.1873 Bracket Swapping |
ユーザー | shiomusubi496 |
提出日時 | 2021-12-22 23:41:52 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 213 ms / 2,000 ms |
コード長 | 20,069 bytes |
コンパイル時間 | 2,317 ms |
コンパイル使用メモリ | 217,536 KB |
実行使用メモリ | 69,504 KB |
最終ジャッジ日時 | 2024-06-11 09:31:15 |
合計ジャッジ時間 | 5,213 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,376 KB |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 21 ms
10,624 KB |
testcase_04 | AC | 9 ms
6,016 KB |
testcase_05 | AC | 8 ms
6,016 KB |
testcase_06 | AC | 99 ms
35,200 KB |
testcase_07 | AC | 2 ms
5,376 KB |
testcase_08 | AC | 184 ms
63,872 KB |
testcase_09 | AC | 181 ms
69,376 KB |
testcase_10 | AC | 135 ms
51,584 KB |
testcase_11 | AC | 3 ms
5,376 KB |
testcase_12 | AC | 71 ms
29,568 KB |
testcase_13 | AC | 57 ms
24,448 KB |
testcase_14 | AC | 175 ms
61,824 KB |
testcase_15 | AC | 37 ms
16,128 KB |
testcase_16 | AC | 2 ms
5,376 KB |
testcase_17 | AC | 94 ms
41,344 KB |
testcase_18 | AC | 3 ms
5,376 KB |
testcase_19 | AC | 7 ms
5,376 KB |
testcase_20 | AC | 136 ms
53,376 KB |
testcase_21 | AC | 3 ms
5,376 KB |
testcase_22 | AC | 13 ms
7,168 KB |
testcase_23 | AC | 213 ms
69,376 KB |
testcase_24 | AC | 163 ms
69,376 KB |
testcase_25 | AC | 181 ms
69,504 KB |
testcase_26 | AC | 96 ms
41,472 KB |
testcase_27 | AC | 137 ms
58,240 KB |
testcase_28 | AC | 67 ms
67,456 KB |
testcase_29 | AC | 2 ms
5,376 KB |
ソースコード
#include<bits/stdc++.h> #ifndef __COUNTER__ #define __COUNTER__ __LINE__ #endif #define REP_SELECTER(a, b, c, d, e, ...) e #define REP1_0(b, c) REP1_1(b, c) #define REP1_1(b, c) for (ll REP_COUNTER_ ## c = 0; REP_COUNTER_ ## c < (ll)(b); ++ REP_COUNTER_ ## c) #define REP1(b) REP1_0(b, __COUNTER__) #define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i) #define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i) #define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c)) #define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1) (__VA_ARGS__) #define RREP2(i, a) for (ll i = (ll)(a) - 1; i >= 0; --i) #define RREP3(i, a, b) for (ll i = (ll)(a) - 1; i >= (ll)(b); --i) #define RREP4(i, a, b, c) for (ll i = (ll)(a) - 1; i >= (ll)(b); i -= (ll)(c)) #define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2) (__VA_ARGS__) #define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i) #define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i) #define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c)) #define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2) (__VA_ARGS__) #define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i) #define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i) #define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c)) #define rreps(...) REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2) (__VA_ARGS__) #define all(v) (v).begin(), (v).end() #if __cplusplus >= 201402L #define CONSTEXPR constexpr #else #define CONSTEXPR #endif using ll = long long; using ull = unsigned long long; using ld = long double; using PLL = std::pair<ll, ll>; template<class T> using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>; template<class T> class infinity { public: static constexpr T value = std::numeric_limits<T>::max() / 2; static constexpr T mvalue = std::numeric_limits<T>::min() / 2; static constexpr T max = std::numeric_limits<T>::max(); static constexpr T min = std::numeric_limits<T>::min(); }; #if __cplusplus <= 201402L template<class T> constexpr T infinity<T>::value; template<class T> constexpr T infinity<T>::mvalue; template<class T> constexpr T infinity<T>::max; template<class T> constexpr T infinity<T>::min; #endif #if __cplusplus >= 201402L template<class T> constexpr T INF = infinity<T>::value; #endif constexpr ll inf = infinity<ll>::value; constexpr ld EPS = 1e-8; constexpr ld PI = 3.1415926535897932384626; template<class T, class U> std::ostream& operator<<(std::ostream& ost, const std::pair<T, U>& p) { return ost << p.first << ' ' << p.second; } template<class T, class U> std::istream& operator>>(std::istream& ist, std::pair<T, U>& p) { return ist >> p.first >> p.second; } template<class Container, typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr> auto operator<<(std::ostream& ost, const Container& cont) -> decltype(cont.begin(), cont.end(), ost) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) { if (itr != cont.begin()) ost << ' '; ost << *itr; } return ost; } template<class Container, typename std::enable_if<!std::is_same<Container, std::string>::value>::type* = nullptr> auto operator>>(std::istream& ist, Container& cont) -> decltype(cont.begin(), cont.end(), ist) { for (auto itr = cont.begin(); itr != cont.end(); ++itr) ist >> *itr; return ist; } template<class T, class U> inline constexpr bool chmin(T &a, const U &b) noexcept { return a > b ? a = b, true : false; } template<class T, class U> inline constexpr bool chmax(T &a, const U &b) noexcept { return a < b ? a = b, true : false; } inline CONSTEXPR ll gcd(ll a, ll b) noexcept { while (b) { const ll c = a; a = b; b = c % b; } return a; } inline CONSTEXPR ll lcm(ll a, ll b) noexcept { return a / gcd(a, b) * b; } inline CONSTEXPR bool is_prime(ll N) noexcept { if (N <= 1) return false; for (ll i = 2; i * i <= N; ++i) { if (N % i == 0) return false; } return true; } inline std::vector<ll> prime_factor(ll N) noexcept { std::vector<ll> res; for (ll i = 2; i * i <= N; ++i) { while (N % i == 0) { res.push_back(i); N /= i; } } if (N != 1) res.push_back(N); return res; } inline CONSTEXPR ll my_pow(ll a, ll b) noexcept { ll res = 1; while (b) { if (b & 1) res *= a; b >>= 1; a *= a; } return res; } inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) noexcept { a %= mod; ll res = 1; while (b) { if (b & 1) (res *= a) %= mod; b >>= 1; (a *= a) %= mod; } return res; } PLL extGCD(ll a, ll b) noexcept { if (b == 0) return PLL{1, 0}; PLL p = extGCD(b, a % b); std::swap(p.first, p.second); p.second -= p.first * (a / b); if (p.first < 0) { p.first += b; p.second -= a; } return p; } ll mod_inv(ll a, ll mod) noexcept { const PLL p = extGCD(a, mod); assert(p.first * a + p.second * mod == 1); return p.first; } PLL ChineseRemainder(ll b1, ll m1, ll b2, ll m2) noexcept { const PLL p = extGCD(m1, m2); const ll g = p.first * m1 + p.second * m2; const ll l = m1 / g * m2; if ((b2 - b1) % g != 0) return PLL{-1, -1}; const ll x = (b2 - b1) / g * p.first % (m2 / g); return {(x * m1 + b1 + l) % l, l}; } PLL ChineseRemainders(const std::vector<ll>& b, const std::vector<ll>& m) noexcept { PLL res{0, 1}; rep (i, b.size()) { res = ChineseRemainder(res.first, res.second, b[i], m[i]); if (res.first == -1) return res; } return res; } template<class F> class RecLambda { private: F f; public: explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {} template<class... Args> constexpr auto operator()(Args&&... args) const -> decltype(f(*this, std::forward<Args>(args)...)) { return f(*this, std::forward<Args>(args)...); } }; template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) { return RecLambda<F>(std::forward<F>(f)); } template<class Head, class... Tails> struct multi_dim_vector { using type = std::vector<typename multi_dim_vector<Tails...>::type>; }; template<class T> struct multi_dim_vector<T> { using type = T; }; template<class T, class Arg> constexpr std::vector<T> make_vec(int n, Arg&& arg) { return std::vector<T>(n, arg); } template<class T, class... Args> constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n, Args&&... args) { return typename multi_dim_vector<Args..., T>::type (n, make_vec<T>(std::forward<Args>(args)...)); } inline CONSTEXPR int popcnt(ull x) { #if __cplusplus >= 202002L return std::popcount(x); #endif x = (x & 0x5555555555555555) + ((x >> 1 ) & 0x5555555555555555); x = (x & 0x3333333333333333) + ((x >> 2 ) & 0x3333333333333333); x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4 ) & 0x0f0f0f0f0f0f0f0f); x = (x & 0x00ff00ff00ff00ff) + ((x >> 8 ) & 0x00ff00ff00ff00ff); x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff); return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff); } template<class T> class presser : public std::vector<T> { private: using Base = std::vector<T>; public: using Base::Base; presser(const std::vector<T>& vec) : Base(vec) {} void push(const std::vector<T>& vec) { int n = this->size(); this->resize(n + vec.size()); std::copy(all(vec), this->begin() + n); } int build() { std::sort(this->begin(), this->end()); this->erase(std::unique(this->begin(), this->end()), this->end()); return this->size(); } int get_index(const T& val) const { return static_cast<int>(std::lower_bound(this->begin(), this->end(), val) - this->begin()); } std::vector<int> pressed(const std::vector<T>& vec) const { std::vector<int> res(vec.size()); rep (i, vec.size()) res[i] = this->get_index(vec[i]); return res; } void press(std::vector<T>& vec) const { static_assert(std::is_integral<T>::value, "cannot convert from int type"); rep (i, vec.size()) vec[i] = this->get_index(vec[i]); } }; class ModIntBase {}; class StaticModIntBase : ModIntBase {}; class DynamicModIntBase : ModIntBase {}; template<class T> using is_ModInt = std::is_base_of<ModIntBase, T>; template<class T> using is_StaticModInt = std::is_base_of<StaticModIntBase, T>; template<class T> using is_DynamicModInt = std::is_base_of<DynamicModIntBase, T>; template<ll mod> class StaticModInt : StaticModIntBase { protected: ll val; static constexpr ll inv1000000007[] = {-1, 1, 500000004, 333333336, 250000002, 400000003, 166666668, 142857144, 125000001, 111111112, 700000005}; static constexpr ll inv998244353 [] = {-1, 1, 499122177, 332748118, 748683265, 598946612, 166374059, 855638017, 873463809, 443664157, 299473306}; public: StaticModInt() : StaticModInt(0) {} template<class T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr> StaticModInt(T v) : val(v) { val %= mod; if (val < 0) val += mod; } ll get() const { return val; } static ll get_mod() { return mod; } static StaticModInt raw(ll v) { StaticModInt res; res.val = v; return res; } StaticModInt inv() const { #if __cplusplus >= 201703L if constexpr (mod == 1000000007) { if (val <= 10) return inv1000000007[val]; } else if constexpr (mod == 998244353) { if (val <= 10) return inv998244353[val]; } #else if (mod == 1000000007) { if (val <= 10) return inv1000000007[val]; } else if (mod == 998244353) { if (val <= 10) return inv998244353[val]; } #endif return mod_inv(val, mod); } StaticModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } StaticModInt operator++(int) { StaticModInt res = *this; ++ *this; return res; } StaticModInt& operator--() { if (val == 0) val = mod; --val; return *this; } StaticModInt operator--(int) { StaticModInt res = *this; -- *this; return res; } StaticModInt& operator+=(const StaticModInt& other) { val += other.val; if (val >= mod) val -= mod; return *this; } StaticModInt& operator-=(const StaticModInt& other) { val -= other.val; if (val < 0) val += mod; return *this; } StaticModInt& operator*=(const StaticModInt& other) { (val *= other.val) %= mod; return *this; } StaticModInt& operator/=(const StaticModInt& other) { (val *= other.inv().get()) %= mod; return *this; } friend StaticModInt operator+(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) += rhs; } friend StaticModInt operator-(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) -= rhs; } friend StaticModInt operator*(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) *= rhs; } friend StaticModInt operator/(const StaticModInt& lhs, const StaticModInt& rhs) { return StaticModInt(lhs) /= rhs; } StaticModInt operator+() const { return StaticModInt(*this); } StaticModInt operator-() const { return StaticModInt(0) - *this; } StaticModInt pow(ll a) const { StaticModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } friend std::ostream& operator<<(std::ostream& ost, const StaticModInt& sm) { return ost << sm.val; } friend std::istream& operator>>(std::istream& ist, StaticModInt& sm) { return ist >> sm.val; } }; #if __cplusplus < 201703L template<ll mod> constexpr ll StaticModInt<mod>::inv1000000007[]; template<ll mod> constexpr ll StaticModInt<mod>::inv998244353 []; #endif using modint1000000007 = StaticModInt<1000000007>; using modint998244353 = StaticModInt<998244353>; template<int id> class DynamicModInt : DynamicModIntBase { protected: ll val; static ll mod; public: DynamicModInt() : DynamicModInt(0) {} template<class T, typename std::enable_if<std::is_integral<T>::value>::type* = nullptr> DynamicModInt(T v) : val(v) { val %= mod; if (val < 0) val += mod; } ll get() const { return val; } static ll get_mod() { return mod; } static void set_mod(ll v) { mod = v; } static DynamicModInt raw(ll v) { DynamicModInt res; res.val = v; return res; } DynamicModInt inv() const { return mod_inv(val, mod); } DynamicModInt& operator++() { ++val; if (val == mod) val = 0; return *this; } DynamicModInt operator++(int) { DynamicModInt res = *this; ++ *this; return res; } DynamicModInt& operator--() { if (val == 0) val = mod; --val; return *this; } DynamicModInt operator--(int) { DynamicModInt res = *this; -- *this; return res; } DynamicModInt& operator+=(const DynamicModInt& other) { val += other.val; if (val >= mod) val -= mod; return *this; } DynamicModInt& operator-=(const DynamicModInt& other) { val -= other.val; if (val < 0) val += mod; return *this; } DynamicModInt& operator*=(const DynamicModInt& other) { (val *= other.val) %= mod; return *this; } DynamicModInt& operator/=(const DynamicModInt& other) { (val *= other.inv().get()) %= mod; return *this; } friend DynamicModInt operator+(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) += rhs; } friend DynamicModInt operator-(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) -= rhs; } friend DynamicModInt operator*(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) *= rhs; } friend DynamicModInt operator/(const DynamicModInt& lhs, const DynamicModInt& rhs) { return DynamicModInt(lhs) /= rhs; } DynamicModInt operator+() const { return DynamicModInt(*this); } DynamicModInt operator-() const { return DynamicModInt(0) - *this; } DynamicModInt pow(ll a) const { DynamicModInt v = *this, res = 1; while (a) { if (a & 1) res *= v; a >>= 1; v *= v; } return res; } friend std::ostream& operator<<(std::ostream& ost, const DynamicModInt& sm) { return ost << sm.val; } friend std::istream& operator>>(std::istream& ist, DynamicModInt& sm) { return ist >> sm.val; } }; template<int id> ll DynamicModInt<id>::mod = 1000000007; using modint = DynamicModInt<-1>; /** * @brief ModInt * @docs docs/ModInt.md */ template<class T> class IntCombinatorics { protected: static std::vector<T> factorial; public: static void init(ll n) { factorial.reserve(n + 1); while ((ll)factorial.size() <= n) factorial.push_back(factorial.back() * factorial.size()); } static T fact(ll x) { init(x); return factorial[x]; } static T perm(ll n, ll r) { if (r < 0 || r > n) return T(0); init(n); return factorial[n] / factorial[n - r]; } static T comb(ll n, ll r) { if (r < 0 || r > n) return T(0); init(n); return factorial[n] / factorial[n - r] / factorial[r]; } static T homo(ll n, ll r) { return comb(n + r - 1, r); } }; template<class T> std::vector<T> IntCombinatorics<T>::factorial = std::vector<T>(1, 1); template<class T> class Combinatorics { protected: static std::vector<T> factorial; static std::vector<T> factinv; public: static void init(ll n) { int b = factorial.size(); if (n < b) return; factorial.reserve(n + 1); while ((ll)factorial.size() <= n) factorial.push_back(factorial.back() * factorial.size()); factinv.resize(n + 1); factinv[n] = T(1) / factorial[n]; rreps (i, n, b) factinv[i - 1] = factinv[i] * i; } static T fact(ll x) { init(x); return factorial[x]; } static T finv(ll x) { init(x); return factinv[x]; } static T perm(ll n, ll r) { if (r < 0 || r > n) return 0; init(n); return factorial[n] * factinv[n - r]; } static T comb(ll n, ll r) { if (r < 0 || r > n) return 0; init(n); return factorial[n] * factinv[n - r] * factinv[r]; } static T homo(ll n, ll r) { return comb(n + r - 1, r); } }; template<class T> std::vector<T> Combinatorics<T>::factorial = std::vector<T>(1, 1); template<class T> std::vector<T> Combinatorics<T>::factinv = std::vector<T>(1, 1); /** * @brief Combinatorics * @docs docs/Combinatorics.md */ template<class T> class Matrix : public std::vector<std::vector<T>> { protected: using Base = std::vector<std::vector<T>>; public: Matrix() = default; Matrix(int h, int w) : Base(h, std::vector<T>(w)) {} Matrix(int h, int w, const T& v) : Base(h, std::vector<T>(w, v)) {} Matrix(const Matrix& mt) : Base(mt) {} Matrix(Matrix&& mt) : Base(std::move(mt)) {} static Matrix get_id(int sz) { Matrix res(sz, sz, T{0}); rep (i, sz) res[i][i] = T{1}; return res; } Matrix& operator+=(const Matrix& other) { rep (i, this->size()) { rep (j, (*this)[i]->size()) (*this)[i][j] += other[i][j]; } return *this; } Matrix& operator-=(const Matrix& other) { rep (i, this->size()) { rep (j, (*this)[i]->size()) (*this)[i][j] -= other[i][j]; } return *this; } Matrix& operator*=(const Matrix& other) { Matrix res(this->size(), other[0].size()); rep (i, this->size()) { rep (j, other[0].size()) { rep (k, other.size()) res[i][j] += (*this)[i][k] * other[k][j]; } } this->swap(res); return *this; } friend Matrix operator+(const Matrix& a, const Matrix& b) { return Matrix(a) += b; } friend Matrix operator-(const Matrix& a, const Matrix& b) { return Matrix(a) -= b; } friend Matrix operator*(const Matrix& a, const Matrix& b) { return Matrix(a) *= b; } Matrix pow(ll b) { Matrix a = *this, res = get_id(this->size()); while (b) { if (b & 1) res *= a; a *= a; b >>= 1; } return res; } }; using namespace std; using mint = modint998244353; using comb = Combinatorics<mint>; using mat = Matrix<mint>; int main() { string S; cin >> S; int K; cin >> K; int N = S.size(); auto dp = make_vec<mint>(N + 1, N + 2, N + 2, mint{0}); dp[0][0][0] = 1; rep (i, N) { rep (j, N + 1) { rep (k, N + 1) { dp[i + 1][j + 1][k + (S[i] != '(')] += dp[i][j][k]; if (j != 0) dp[i + 1][j - 1][k + (S[i] != ')')] += dp[i][j][k]; } } } int L = N / 2; mat A(L + 1, L + 1, mint{0}), B(L + 1, 1, mint{0}); B[0][0] = 1; rep (i, L + 1) { if (i != 0) A[i - 1][i] += i * i; if (i != L) A[i + 1][i] += (L - i) * (L - i); A[i][i] += N * (N - 1) / 2 - (i * i) - ((L - i) * (L - i)); } mat C = A.pow(K) * B; mint ans = 0; rep (i, L + 1) ans += (C[i][0] / comb::comb(L, i).pow(2)) * dp[N][0][i * 2]; cout << ans << endl; }