結果
問題 | No.1961 Clear Brackets |
ユーザー |
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提出日時 | 2022-05-27 22:32:31 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 102 ms / 2,000 ms |
コード長 | 13,625 bytes |
コンパイル時間 | 3,125 ms |
コンパイル使用メモリ | 193,792 KB |
最終ジャッジ日時 | 2025-01-29 16:08:57 |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 42 |
ソースコード
#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#include<iostream>#include<string>#include<cstdio>#include<vector>#include<cmath>#include<algorithm>#include<functional>#include<iomanip>#include<queue>#include<ciso646>#include<random>#include<map>#include<set>#include<bitset>#include<stack>#include<unordered_map>#include<unordered_set>#include<utility>#include<cassert>#include<complex>#include<numeric>#include<array>#include<chrono>using namespace std;//#define int long longtypedef long long ll;typedef unsigned long long ul;typedef unsigned int ui;constexpr ll mod = 998244353;//constexpr ll mod = 1000000007;const ll INF = mod * mod;typedef pair<int, int>P;#define rep(i,n) for(int i=0;i<n;i++)#define per(i,n) for(int i=n-1;i>=0;i--)#define Rep(i,sta,n) for(int i=sta;i<n;i++)#define rep1(i,n) for(int i=1;i<=n;i++)#define per1(i,n) for(int i=n;i>=1;i--)#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)#define all(v) (v).begin(),(v).end()typedef pair<ll, ll> LP;template<typename T>void chmin(T& a, T b) {a = min(a, b);}template<typename T>void chmax(T& a, T b) {a = max(a, b);}template<typename T>void cinarray(vector<T>& v) {rep(i, v.size())cin >> v[i];}template<typename T>void coutarray(vector<T>& v) {rep(i, v.size()) {if (i > 0)cout << " "; cout << v[i];}cout << "\n";}ll mod_pow(ll x, ll n, ll m = mod) {if (n < 0) {ll res = mod_pow(x, -n, m);return mod_pow(res, m - 2, m);}if (abs(x) >= m)x %= m;if (x < 0)x += m;//if (x == 0)return 0;ll res = 1;while (n) {if (n & 1)res = res * x % m;x = x * x % m; n >>= 1;}return res;}struct modint {int n;modint() :n(0) { ; }modint(ll m) {if (m < 0 || mod <= m) {m %= mod; if (m < 0)m += mod;}n = m;}operator int() { return n; }};bool operator==(modint a, modint b) { return a.n == b.n; }bool operator<(modint a, modint b) { return a.n < b.n; }modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }modint operator+(modint a, modint b) { return a += b; }modint operator-(modint a, modint b) { return a -= b; }modint operator*(modint a, modint b) { return a *= b; }modint operator^(modint a, ll n) {if (n == 0)return modint(1);modint res = (a * a) ^ (n / 2);if (n % 2)res = res * a;return res;}ll inv(ll a, ll p) {return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);}modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }modint operator/=(modint& a, modint b) { a = a / b; return a; }const int max_n = 1 << 20;modint fact[max_n], factinv[max_n];void init_f() {fact[0] = modint(1);for (int i = 0; i < max_n - 1; i++) {fact[i + 1] = fact[i] * modint(i + 1);}factinv[max_n - 1] = modint(1) / fact[max_n - 1];for (int i = max_n - 2; i >= 0; i--) {factinv[i] = factinv[i + 1] * modint(i + 1);}}modint comb(int a, int b) {if (a < 0 || b < 0 || a < b)return 0;return fact[a] * factinv[b] * factinv[a - b];}modint combP(int a, int b) {if (a < 0 || b < 0 || a < b)return 0;return fact[a] * factinv[a - b];}ll gcd(ll a, ll b) {a = abs(a); b = abs(b);if (a < b)swap(a, b);while (b) {ll r = a % b; a = b; b = r;}return a;}typedef long double ld;typedef pair<ld, ld> LDP;const ld eps = 1e-8;const ld pi = acosl(-1.0);template<typename T>void addv(vector<T>& v, int loc, T val) {if (loc >= v.size())v.resize(loc + 1, 0);v[loc] += val;}/*const int mn = 100005;bool isp[mn];vector<int> ps;void init() {fill(isp + 2, isp + mn, true);for (int i = 2; i < mn; i++) {if (!isp[i])continue;ps.push_back(i);for (int j = 2 * i; j < mn; j += i) {isp[j] = false;}}}*///[,val)template<typename T>auto prev_itr(set<T>& st, T val) {auto res = st.lower_bound(val);if (res == st.begin())return st.end();res--; return res;}//[val,)template<typename T>auto next_itr(set<T>& st, T val) {auto res = st.lower_bound(val);return res;}using mP = pair<modint, modint>;mP operator+(mP a, mP b) {return { a.first + b.first,a.second + b.second };}mP operator+=(mP& a, mP b) {a = a + b; return a;}mP operator-(mP a, mP b) {return { a.first - b.first,a.second - b.second };}mP operator-=(mP& a, mP b) {a = a - b; return a;}mt19937 mt(time(0));const string drul = "DRUL";//DRULint dx[4] = { 1,0,-1,0 };int dy[4] = { 0,1,0,-1 };//-----------------------------------------int get_premitive_root() {int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {set<int> fac;int v = mod - 1;for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (mod_pow(g, (mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}const int proot = get_premitive_root();int bsf(int x) {int res = 0;while (!(x & 1)) {res++; x >>= 1;}return res;}int ceil_pow2(int n) {int x = 0;while ((1 << x) < n) x++;return x;}using poly = vector<modint>;void butterfly(poly& a) {int n = int(a.size());int g = proot;int h = ceil_pow2(n);static bool first = true;static modint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if (first) {first = false;modint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mod - 1);modint e = mod_pow(g, (mod - 1) >> cnt2);modint ie = (modint)1 / e;for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}modint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for (int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);modint now = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}void butterfly_inv(poly& a) {int n = int(a.size());int g = proot;int h = ceil_pow2(n);static bool first = true;static modint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if (first) {first = false;modint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mod - 1);modint e = mod_pow(g, (mod - 1) >> cnt2);modint ie = (modint)1 / e;for (int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}modint now = 1;for (int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for (int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);modint inow = 1;for (int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for (int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] =(unsigned long long)(mod + (ll)l - (ll)r) *(ll)inow;}inow *= sum_ie[bsf(~(unsigned int)(s))];}}}poly multiply(poly g, poly h) {int n = g.size();int m = h.size();if (n == 0 || m == 0)return {};if (min(g.size(), h.size()) < 60) {poly res(g.size() + h.size() - 1);rep(i, g.size())rep(j, h.size()) {res[i + j] += g[i] * h[j];}return res;}int z = 1 << ceil_pow2(n + m - 1);g.resize(z);butterfly(g);h.resize(z);butterfly(h);rep(i, z) {g[i] *= h[i];}butterfly_inv(g);g.resize(n + m - 1);modint iz = (modint)1 / (modint)z;rep(i, n + m - 1) {g[i] *= iz;}return g;}struct FormalPowerSeries :vector<modint> {using vector<modint>::vector;using fps = FormalPowerSeries;void shrink() {while (this->size() && this->back() == (modint)0)this->pop_back();}fps operator+(const fps& r)const { return fps(*this) += r; }fps operator+(const modint& v)const { return fps(*this) += v; }fps operator-(const fps& r)const { return fps(*this) -= r; }fps operator-(const modint& v)const { return fps(*this) -= v; }fps operator*(const fps& r)const { return fps(*this) *= r; }fps operator*(const modint& v)const { return fps(*this) *= v; }fps& operator+=(const fps& r) {if (r.size() > this->size())this->resize(r.size());rep(i, r.size())(*this)[i] += r[i];shrink();return *this;}fps& operator+=(const modint& v) {if (this->empty())this->resize(1);(*this)[0] += v;shrink();return *this;}fps& operator-=(const fps& r) {if (r.size() > this->size())this->resize(r.size());rep(i, r.size())(*this)[i] -= r[i];shrink();return *this;}fps& operator-=(const modint& v) {if (this->empty())this->resize(1);(*this)[0] -= v;shrink();return *this;}fps& operator*=(const fps& r) {if (this->empty() || r.empty())this->clear();else {poly ret = multiply(*this, r);*this = fps(all(ret));}shrink();return *this;}fps& operator*=(const modint& v) {for (auto& x : (*this))x *= v;shrink();return *this;}fps operator-()const {fps ret = *this;for (auto& v : ret)v = -v;return ret;}modint sub(modint x) {modint t = 1;modint res = 0;rep(i, (*this).size()) {res += t * (*this)[i];t *= x;}return res;}fps pre(int sz)const {fps ret(this->begin(), this->begin() + min((int)this->size(), sz));ret.shrink();return ret;}fps integral() const {const int n = (int)this->size();fps ret(n + 1);ret[0] = 0;for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (modint)(i + 1);return ret;}fps inv(int deg = -1)const {const int n = this->size();if (deg == -1)deg = n;fps ret({ (modint)1 / (*this)[0] });for (int i = 1; i < deg; i <<= 1) {ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);}ret = ret.pre(deg);ret.shrink();return ret;}fps diff() const {const int n = (int)this->size();fps ret(max(0, n - 1));for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * (modint)i;return ret;}// F(0) must be 1fps log(int deg = -1) const {assert((*this)[0] == 1);const int n = (int)this->size();if (deg == -1) deg = n;return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}// F(0) must be 0fps exp(int deg = -1)const {assert((*this)[0] == 0);const int n = (int)this->size();if (deg == -1)deg = n;fps ret = { 1 };for (int i = 1; i < deg; i <<= 1) {ret = (ret * (pre(i << 1) + 1 - ret.log(i << 1))).pre(i << 1);}//cout << "!!!! " << ret.size() << "\n";return ret.pre(deg);}fps div(fps g) {assert(g.size() && g.back() != (modint)0);fps f = *this;if (f.size() < g.size())return {};int dif = f.size() - g.size();reverse(all(f));reverse(all(g));g = g.inv(dif + 1);fps fg = f * g;fps ret(dif + 1);rep(i, fg.size()) {int id = i - dif;if (-dif <= id && id <= 0) {ret[-id] = fg[i];}}return ret;}fps divr(fps g) {fps ret = (*this) - g * (*this).div(g);ret.shrink();return ret;}};using fps = FormalPowerSeries;vector<modint> Multipoint_Evaluation(fps c, vector<modint> p) {int n = p.size();vector<modint> ret(n);int sz = 1;while (sz < n)sz *= 2;vector<fps> f(2 * sz - 1);function<void(int, int, int)> dfs = [&](int k, int l, int r) {if (l + 1 == r) {f[k] = { -p[l],1 };}else {dfs(2 * k + 1, l, (l + r) / 2);dfs(2 * k + 2, (l + r) / 2, r);f[k] = f[2 * k + 1] * f[2 * k + 2];}};dfs(0, 0, n);vector<fps> g(2 * sz - 1);function<void(int, int, int)> invdfs = [&](int k, int l, int r) {if (k == 0) {g[k] = c.divr(f[k]);}else {g[k] = g[(k - 1) / 2].divr(f[k]);}if (r - l <= 100) {Rep(i, l, r) {ret[i] = g[k].sub(p[i]);}}else {invdfs(2 * k + 1, l, (l + r) / 2);invdfs(2 * k + 2, (l + r) / 2, r);}};invdfs(0, 0, n);return ret;}vector<int> calc(string s,bool ad) {int n = s.size();vector<int> a(n + 1);vector<int> b(n + 1);rep(i, n) {a[i + 1] = a[i];b[i + 1] = b[i];if (s[i] == '(')a[i + 1]++;if (s[i] == ')')b[i + 1]++;}vector<int> cs(n + 1);int c = 0;cs[0] = c;rep(i, n) {if (s[i] == '(')c++;else c--;cs[i + 1] = c;}vector<vector<int>> loc(2 * n + 1);rep(i, n + 1) {loc[cs[i] + n].push_back(i);}vector<vector<int>> dp(n + 1, { -mod,-mod });vector<int> res(n + 1, -mod);dp[0][1] = 0;rep(i, n)rep(j,2) {if (s[i] != '(')chmax(dp[i + 1][1], dp[i][j]);if (s[i] != ')'&&i+1<n) {int cur = cs[i];if (s[i] == '?')cur -= 2;int val = dp[i][j];if (j)val++;int to = upper_bound(all(loc[n + cur]), i) - loc[n + cur].begin();if (to < loc[n + cur].size()) {to = loc[n + cur][to];chmax(dp[to][0], val);}}}rep(i, n + 1)rep(j, 2) {if (!ad && j == 0)continue;chmax(res[i], dp[i][j]);}return res;}void solve() {int n; cin >> n;string s; cin >> s;vector<int> cl = calc(s,true);string t = s;reverse(all(t));rep(i, n) {if (t[i] == '(')t[i] = ')';else if (t[i] == ')')t[i] = '(';}vector<int> cr = calc(t,false);int ans = 0;rep(i, n + 1)chmax(ans, cl[i] + cr[n - i]);cout << ans << "\n";//coutarray(cl);//coutarray(cr);}signed main() {ios::sync_with_stdio(false);cin.tie(0);//cout << fixed << setprecision(10);init_f();//init();//while(true)//expr();//int t; cin >> t; rep(i, t)solve();return 0;}