結果
| 問題 |
No.3099 Parentheses Decomposition
|
| コンテスト | |
| ユーザー |
 Astral__
|
| 提出日時 | 2025-04-11 21:26:18 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 25 ms / 2,000 ms |
| コード長 | 7,969 bytes |
| コンパイル時間 | 5,837 ms |
| コンパイル使用メモリ | 334,004 KB |
| 実行使用メモリ | 10,164 KB |
| 最終ジャッジ日時 | 2025-04-11 21:26:27 |
| 合計ジャッジ時間 | 6,754 ms |
|
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 * 4 |
| other | AC * 20 |
ソースコード
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
std::istream &operator>>(std::istream &is, atcoder::modint &v) {
long long value;
is >> value;
v = value;
return is;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint &v) {
os << v.val();
return os;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint998244353 &v) {
os << v.val();
return os;
}
std::istream &operator>>(std::istream &is, atcoder::modint998244353 &v) {
long long x;
is >> x;
v = x;
return is;
}
std::ostream &operator<<(std::ostream &os, const atcoder::modint1000000007 &v) {
os << v.val();
return os;
}
std::istream &operator>>(std::istream &is, atcoder::modint1000000007 &v) {
long long x;
is >> x;
v = x;
return is;
}
#endif
using namespace std;
using ll = long long;
using lint = __int128_t;
using pll = pair<ll, ll>;
#define newl '\n';
#define rep(i, s, t) for (ll i = s; i < (ll)(t); i++)
#define rrep(i, s, t) for (ll i = (ll)(t) - 1; i >= (ll)(s); i--)
#define all(x) begin(x), end(x)
#define SZ(x) ll(x.size())
#define eb emplace_back
#define pb push_back
#define TT template <typename T>
TT using vec = vector<T>;
TT using vvec = vec<vec<T>>;
TT using vvvec = vec<vvec<T>>;
TT using minheap = priority_queue<T, vector<T>, greater<T>>;
TT using maxheap = priority_queue<T>;
TT bool chmin(T &x, T y) {
return x > y ? (x = y, true) : false;
}
TT bool chmax(T &x, T y) {
return x < y ? (x = y, true) : false;
}
TT T smod(T x, T mod) {
x %= mod;
if (x < 0)
x += mod;
return x;
}
TT bool rng(T l, T x, T r) {
return l <= x && x < r;
}
TT T flr(T a, T b) {
if (b < 0)
a = -a, b = -b;
return a >= 0 ? a / b : (a + 1) / b - 1;
}
TT T cil(T a, T b) {
if (b < 0)
a = -a, b = -b;
return a > 0 ? (a - 1) / b + 1 : a / b;
}
TT T sqr(T x) {
return x * x;
}
//{0, 1, ... } -> {p[0], p[1], ...}
template <typename T, typename S>
void rearrange(vector<T> &A, vector<S> const &p) {
assert(p.size() == A.size());
vector<T> a = A;
for (int i = 0; i < ssize(A); ++i) {
a[i] = A[p[i]];
}
swap(a, A);
}
template <typename T, typename S, typename... Ts>
void rearrange(vector<T> &A, vector<S> p, vector<Ts> &...rest) {
rearrange(A, p);
(rearrange(rest, p), ...);
}
template <typename T, typename Compare, typename... Ts>
void rearrange(vector<T> &A, Compare cmp, vector<Ts> &...rest) {
vector<int> p(ssize(A));
iota(p.begin(), p.end(), 0);
sort(p.begin(), p.end(), cmp);
rearrange(A, p);
(rearrange(rest, p), ...);
}
struct io_setup {
io_setup() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} io_setup;
template <class T1, class T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
TT 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, 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 <typename T> ostream &operator<<(ostream &os, const vvec<T> &v) {
for (size_t i = 0; i < v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? "\n" : "");
}
return os;
}
TT istream &operator>>(istream &is, vector<T> &v) {
for (size_t i = 0; i < v.size(); i++) {
is >> v[i];
}
return is;
}
#if __has_include(<debug/debug.hpp>)
#include <debug/debug.hpp>
#else
#define dbg(...) true
#define DBG(...) true
#define OUT(...) true
#endif
template <typename T, long long mod> struct combination {
vector<long long> fac, ifac, inv;
long long N;
combination() {
fac.resize(2, 1);
ifac.resize(2, 1);
inv.resize(2, 1);
N = 1;
}
void reserve(long long n) {
expand(n);
}
T operator()(int n, int k) {
return C(n, k);
}
T raw(long long n, long long k) const {
if (k < 0)
return 0;
if (k == 0)
return 1;
if (n < k)
return 0;
if (n - k < k) {
k = n - k;
}
long long p = 1, q = 1;
for (long long i = 0; i < k; i++) {
p *= (n - i) % mod;
p %= mod;
q *= (k - i) % mod;
q %= mod;
}
return p * modinv(q) % mod;
}
T C(int n, int k) {
if (k < 0)
return 0;
if (k == 0)
return 1;
if (n < k)
return 0;
if (N < n)
expand(n);
return fac[n] * ifac[n - k] % mod * ifac[k] % mod;
}
T P(int n, int k) {
if (k < 0)
return 0;
if (k == 0)
return 1;
if (n < k)
return 0;
if (N < n)
expand(n);
return fac[n] * ifac[n - k] % mod;
}
T B(int n) {
if (N < n)
expand(n);
return (n < 0 ? 0 : fac[n]);
}
T invB(int n) {
if (N < n)
expand(n);
return (n < 0 ? 0 : ifac[n]);
}
T H(int n, int k) {
return C(n + k - 1, k);
}
T Cn(int n) {
return C(2 * n, n) * inv[n + 1] % mod;
}
private:
constexpr static bool is_prime_constexpr(long long x) {
if (x <= 1)
return false;
for (long long i = 2; i * i <= x; i++) {
if (x % i == 0)
return false;
}
return true;
}
static_assert(is_prime_constexpr(mod), "mod must be prime");
static_assert(__int128_t(mod - 1) * (mod - 1) <= __int128_t(LLONG_MAX),
"(mod - 1) * (mod - 1) <= LLONG_MAX must be satisfied");
long long extgcd(long long a, long long b, long long &x,
long long &y) const {
if (b == 0) {
x = 1;
y = 0;
return a;
}
auto d = extgcd(b, a % b, y, x);
y -= a / b * x;
return d;
}
long long modinv(long long a) const {
long long x, y;
extgcd(a, mod, x, y);
x %= mod;
if (x < 0)
x += mod;
return x;
}
void expand(long long new_max_n) {
if (new_max_n <= N)
return;
long long nx = N;
// 2冪で大きくしていく。
while (nx < new_max_n)
nx <<= 1;
new_max_n = nx;
long long pre = N;
N = new_max_n;
fac.resize(N + 1);
ifac.resize(N + 1);
inv.resize(N + 1);
for (long long i = pre + 1; i <= N; i++) {
fac[i] = fac[i - 1] * i % mod;
}
ifac[N] = modinv(fac[N]);
inv[N] = ifac[N] * fac[N - 1] % mod;
for (long long i = N - 1; i >= pre + 1; i--) {
ifac[i] = ifac[i + 1] * (i + 1) % mod;
inv[i] = ifac[i] * fac[i - 1] % mod;
}
return;
}
};
/*
@brief combination
@docs doc/cmb.md
*/
using combination998244353 = combination<atcoder::modint998244353, 998244353>;
combination998244353 cmb;
using mint = atcoder::modint998244353;
int main() {
auto type = [&](string A) {
ll n = A.size();
rep(i, 0, n / 2) if (A[i] != '(') return 1;
return 0;
};
ll n;
cin >> n;
string S;
cin >> S;
if (type(S) == 0) {
mint ret = 0;
rep(c, 0, n/2 + 1) {
ret += cmb(n/2, c) * cmb(n/2, c);
}
cout << ret << endl;
}
else {
mint ret = 0;
rep(c, 0, n/2 + 1) {
ret += cmb(n/2, c);
}
cout << ret << endl;
}
}
/*
同じ議論を繰り返さない
do smth instead of nothing and stay organized
WRITE STUFF DOWN
DON'T GET STUCK ON ONE APPROACH
*/