// #define MULTEST
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <utility>
#include <variant>
#include <vector>
namespace kod {
namespace util {
template <class F> class FixedPoint : private F {
constexpr FixedPoint(F&& f) noexcept : F(std::forward<F>(f)) {}
template <class G> friend constexpr decltype(auto) make_fixed(G&&) noexcept;
public:
template <class... Args> constexpr decltype(auto) operator()(Args&&... args) const noexcept {
return F::operator()(*this, std::forward<Args>(args)...);
}
};
template <class G> [[nodiscard]] constexpr decltype(auto) make_fixed(G&& g) noexcept {
using F = std::decay_t<G>;
return FixedPoint<F>(std::forward<F>(g));
}
} // namespace util
} // namespace kod
namespace kod {
namespace util {
class ForwardLoop {
int x, y;
constexpr ForwardLoop(int x, int y) noexcept : x(x), y(y) {}
friend constexpr ForwardLoop rep(int, int) noexcept;
friend constexpr ForwardLoop rep(int) noexcept;
public:
constexpr ForwardLoop begin() const noexcept { return *this; }
constexpr std::monostate end() const noexcept { return {}; }
constexpr bool operator!=(std::monostate) const noexcept { return x < y; }
constexpr void operator++() const noexcept {}
constexpr int operator*() noexcept { return x++; }
};
[[nodiscard]] constexpr ForwardLoop rep(int l, int r) noexcept { return ForwardLoop(l, r); }
[[nodiscard]] constexpr ForwardLoop rep(int n) noexcept { return ForwardLoop(0, n); }
class BackwardLoop {
int x, y;
constexpr BackwardLoop(int x, int y) noexcept : x(x), y(y) {}
friend constexpr BackwardLoop revrep(int, int) noexcept;
friend constexpr BackwardLoop revrep(int) noexcept;
public:
constexpr BackwardLoop begin() const noexcept { return *this; }
constexpr std::monostate end() const noexcept { return {}; }
constexpr bool operator!=(std::monostate) const noexcept { return x > y; }
constexpr void operator++() const noexcept {}
constexpr int operator*() noexcept { return --x; }
};
[[nodiscard]] constexpr BackwardLoop revrep(int l, int r) noexcept { return BackwardLoop(r, l); }
[[nodiscard]] constexpr BackwardLoop revrep(int n) noexcept { return BackwardLoop(n, 0); }
template <class F> constexpr void repeat(int n, const F& f) noexcept {
assert(n >= 0);
while (n--) f();
}
} // namespace util
} // namespace kod
namespace kod {
namespace util {
namespace stdio_impl {
template <class T> T scan() {
T x;
std::cin >> x;
return x;
}
struct scan_any {
template <class T> operator T() const { return scan<T>(); }
};
} // namespace stdio_impl
template <class T = void> decltype(auto) scan() {
if constexpr (std::is_same_v<T, void>)
return stdio_impl::scan_any{};
else
return stdio_impl::scan<T>();
}
template <class T, std::size_t N> std::array<T, N> scan_arr() {
std::array<T, N> a;
for (auto& x : a) x = scan<T>();
return a;
}
template <class T> std::vector<T> scan_vec(int n) {
if (n == -1) n = scan<int>();
assert(n >= 0);
std::vector<T> v;
v.reserve(n);
while (n--) v.push_back(scan<T>());
return v;
}
void flush() { std::cout << std::flush; }
void print() {}
template <class T, class... Args> void print(const T& x, const Args&... args) {
std::cout << x;
if (sizeof...(args) != 0) std::cout << ' ';
print(args...);
}
template <class... Args> void println(const Args&... args) {
print(args...);
std::cout << '\n';
}
template <class C> void print_seq(const C& c, const char* sep = " ", const char* end = "\n") {
bool f = false;
for (const auto& x : c) {
if (f)
std::cout << sep;
else
f = true;
std::cout << x;
}
std::cout << end;
}
} // namespace util
} // namespace kod
namespace kod {
namespace sol {
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;
using std::array;
using std::pair;
using std::string;
using std::tuple;
using std::vector;
using namespace util;
constexpr int inf = std::numeric_limits<int>::max() / 2;
constexpr ll infll = std::numeric_limits<ll>::max() / 2;
constexpr ll floor_div(ll x, ll y) noexcept {
assert(y != 0);
return x / y - ((x ^ y) < 0 && x % y != 0);
}
constexpr ll ceil_div(ll x, ll y) noexcept {
assert(y != 0);
return x / y + ((x ^ y) >= 0 && x % y != 0);
}
template <class T> constexpr bool setmin(T& lhs, const T& rhs) noexcept {
if (lhs > rhs) {
lhs = rhs;
return true;
}
return false;
}
template <class T> constexpr bool setmax(T& lhs, const T& rhs) noexcept {
if (lhs < rhs) {
lhs = rhs;
return true;
}
return false;
}
void run();
} // namespace sol
} // namespace kod
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(20);
int cases = 1;
#ifdef MULTEST
std::cin >> cases;
#endif
while (cases--) kod::sol::run();
return 0;
}
#ifdef KOD_LOCAL
#define OJ_LOCAL(a, b) b
#include <kodlib/misc/debug>
#else
#define OJ_LOCAL(a, b) a
#define DBG(...)
#define SHOW(...)
#endif
namespace kod {
namespace mod {
namespace finite_field_impl {
constexpr bool is_valid_mod(unsigned m) noexcept {
if (m <= 1 || (1u << 31) <= m) return false;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) return false;
}
return true;
}
constexpr long long rem_euclid(long long x, long long y) noexcept {
if (x >= 0) return x < y ? x : x % y;
if (x >= -y) return x + y;
return (x %= y) == 0 ? 0 : x + y;
}
template <unsigned MOD, std::enable_if_t<is_valid_mod(MOD)>* = nullptr> class FiniteField {
public:
constexpr FiniteField() noexcept : v(0) {}
constexpr FiniteField(long long x) noexcept : v(rem_euclid(x, MOD)) {}
constexpr FiniteField& operator+=(const FiniteField& x) noexcept {
v += x.v;
if (v >= MOD) v -= MOD;
return *this;
}
constexpr FiniteField& operator-=(const FiniteField& x) noexcept {
if (v < x.v) v += MOD;
v -= x.v;
return *this;
}
constexpr FiniteField& operator*=(const FiniteField& x) noexcept {
v = (unsigned long long)v * x.v % MOD;
return *this;
}
constexpr FiniteField& operator/=(const FiniteField& x) noexcept { return *this *= x.inv(); }
constexpr FiniteField operator+() const noexcept { return *this; }
constexpr FiniteField operator-() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
friend constexpr FiniteField operator+(FiniteField x, const FiniteField& y) noexcept {
return x += y;
}
friend constexpr FiniteField operator-(FiniteField x, const FiniteField& y) noexcept {
return x -= y;
}
friend constexpr FiniteField operator*(FiniteField x, const FiniteField& y) noexcept {
return x *= y;
}
friend constexpr FiniteField operator/(FiniteField x, const FiniteField& y) noexcept {
return x /= y;
}
friend constexpr bool operator==(const FiniteField& x, const FiniteField& y) noexcept {
return x.v == y.v;
}
friend constexpr bool operator!=(const FiniteField& x, const FiniteField& y) noexcept {
return x.v != y.v;
}
friend std::ostream& operator<<(std::ostream& s, const FiniteField& x) noexcept {
return s << x.v;
}
constexpr unsigned val() const noexcept { return v; }
constexpr FiniteField inv() const noexcept { return pow(MOD - 2); }
constexpr FiniteField pow(long long e) const noexcept {
if (v == 0) {
assert(e >= 0);
return raw(e == 0);
}
unsigned long long x = 1, y = v;
for (e = rem_euclid(e, MOD - 1); e > 0; e >>= 1) {
if (e & 1) x = x * y % MOD;
y = y * y % MOD;
}
return raw(x);
}
static constexpr unsigned mod() noexcept { return MOD; }
static constexpr FiniteField raw(unsigned x) noexcept {
FiniteField ret;
ret.v = x;
return ret;
}
static FiniteField fact(int n) noexcept {
assert(n >= 0);
static std::vector v = {raw(1)};
for (int i = v.size(); i <= n; ++i) v.push_back(v.back() * FiniteField(i));
return v[n];
}
static FiniteField inv(int n) noexcept {
assert(n >= 1);
static std::vector v = {raw(0), raw(1)};
for (int i = v.size(); i <= n; ++i) v.push_back(-raw(mod() / i) * v[mod() % i]);
return v[n];
}
static FiniteField ifact(int n) noexcept {
assert(n >= 0);
static std::vector v = {raw(1)};
for (int i = v.size(); i <= n; ++i) v.push_back(v.back() * inv(i));
return v[n];
}
static FiniteField factpow(int n, int d) noexcept {
return 0 <= d && d <= n ? fact(n) * ifact(n - d) : raw(0);
}
static FiniteField binom(int n, int d) noexcept {
return 0 <= d && d <= n ? factpow(n, d) * ifact(d) : raw(0);
}
static FiniteField nbinom(int n, int d) noexcept {
return n >= 0 && d >= 0 ? (n == 0 ? raw(d == 0) : binom(n + d - 1, d)) : raw(0);
}
private:
unsigned v;
};
} // namespace finite_field_impl
using finite_field_impl::FiniteField;
using F_998244353 = FiniteField<998244353>;
using F_1000000007 = FiniteField<1000000007>;
} // namespace mod
} // namespace kod
namespace kod {
namespace sol {
using Fp = mod::F_1000000007;
string solve1(const string& S) {
const int N = (int)S.size();
{
int up = 0, down = 0;
for (const int i : rep(N)) {
up += (S[i] == '(');
down += (S[i] == ')');
if (up - (down + 1) / 2 < 0) {
return "impossible";
}
}
up = down = 0;
for (const int i : revrep(N)) {
up += (S[i] == ')');
down += (S[i] == '(');
if (up - (down + 1) / 2 < 0) {
return "impossible";
}
}
}
vector<int> type(N);
for (const int p : rep(2)) {
vector<int> up, down;
vector<char> use(N);
int pos = 0, min = 0;
{
int s = 0, t = 0;
for (const int i : rep(N)) {
if (S[i] == '(') {
use[i] = (s == p);
if (use[i]) {
pos += (s == p);
} else {
up.push_back(i);
}
s ^= 1;
} else {
use[i] = (t == p);
if (use[i]) {
pos -= (t == p);
} else {
down.push_back(i);
}
t ^= 1;
}
setmin(min, pos);
}
}
for (const int i : rep(std::max(0, -min))) {
use[up[i]] = true;
pos += 1;
}
std::reverse(down.begin(), down.end());
for (const int i : rep(pos)) {
use[down[i]] = true;
}
for (const int i : rep(N)) {
type[i] |= (int)use[i] << p;
}
}
string ret;
for (const int x : type) {
ret += "RBG"[x - 1];
}
return ret;
}
Fp solve2(const int N) {
Fp ret = 0;
for (const int up : rep(N + 1)) {
vector dp(N + 1, vector(N + 1, Fp(0)));
dp[0][0] = 1;
const auto check = [&](const int i, const int j) {
if (i - (j + 1) / 2 < 0) return false;
if ((N - up - j) - (up - i + 1) / 2 < 0) return false;
return true;
};
for (const int i : rep(N + 1)) {
for (const int j : rep(N + 1)) {
if (!check(i, j)) {
dp[i][j] = 0;
break;
}
if (i < N) dp[i + 1][j] += dp[i][j];
if (j < N) dp[i][j + 1] += dp[i][j];
}
}
ret += dp[up][N - up];
}
return ret;
}
void run() {
const int P = scan();
if (P == 1) {
repeat(scan<int>(), [&] { println(solve1(scan<string>())); });
} else {
repeat(scan<int>(), [&] { println(solve2(scan<int>())); });
}
}
} // namespace sol
} // namespace kod
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
1 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
1 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
1 ms |
320 KB |
Output is correct |
| 8 |
Correct |
1 ms |
324 KB |
Output is correct |
| 9 |
Correct |
0 ms |
212 KB |
Output is correct |
| 10 |
Correct |
1 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
212 KB |
Output is correct |
| 2 |
Correct |
0 ms |
212 KB |
Output is correct |
| 3 |
Correct |
0 ms |
212 KB |
Output is correct |
| 4 |
Correct |
0 ms |
212 KB |
Output is correct |
| 5 |
Correct |
0 ms |
212 KB |
Output is correct |
| 6 |
Correct |
0 ms |
212 KB |
Output is correct |
| 7 |
Correct |
1 ms |
320 KB |
Output is correct |
| 8 |
Correct |
1 ms |
324 KB |
Output is correct |
| 9 |
Correct |
0 ms |
212 KB |
Output is correct |
| 10 |
Correct |
1 ms |
212 KB |
Output is correct |
| 11 |
Correct |
1 ms |
416 KB |
Output is correct |
| 12 |
Correct |
1 ms |
340 KB |
Output is correct |
| 13 |
Correct |
1 ms |
468 KB |
Output is correct |
| 14 |
Correct |
1 ms |
324 KB |
Output is correct |
| 15 |
Correct |
1 ms |
340 KB |
Output is correct |
| 16 |
Correct |
3 ms |
468 KB |
Output is correct |
| 17 |
Correct |
4 ms |
1364 KB |
Output is correct |
| 18 |
Correct |
3 ms |
596 KB |
Output is correct |
| 19 |
Correct |
3 ms |
952 KB |
Output is correct |
| 20 |
Correct |
4 ms |
1364 KB |
Output is correct |
| 21 |
Correct |
21 ms |
2104 KB |
Output is correct |
| 22 |
Correct |
32 ms |
9832 KB |
Output is correct |
| 23 |
Correct |
20 ms |
2968 KB |
Output is correct |
| 24 |
Correct |
23 ms |
5352 KB |
Output is correct |
| 25 |
Correct |
32 ms |
10472 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
2 ms |
212 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
212 KB |
Output is correct |
| 2 |
Correct |
2 ms |
212 KB |
Output is correct |
| 3 |
Execution timed out |
1068 ms |
796 KB |
Time limit exceeded |
| 4 |
Halted |
0 ms |
0 KB |
- |
