/**
* author: wxhtzdy
* created: 13.11.2022 09:25:04
**/
#include <bits/stdc++.h>
using namespace std;
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend std::istream& operator>>(std::istream& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
return stream << number();
}
template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, int64_t>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int) fact.size() < n + 1) {
fact.push_back(fact.back() * (int) fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
const int N = 100;
Mint dp[3 * N][3 * N][3 * N];
Mint new_dp[4][2][3 * N][3 * N][3 * N];
bool vis[3 * N][3 * N][3 * N];
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, tt;
cin >> n >> tt;
while (tt--) {
vector<vector<int>> pp(3 * n);
for (int i = 0; i < 2 * n; i++) {
int x;
cin >> x;
--x;
pp[x].push_back(0);
}
for (int i = 0; i < 2 * n; i++) {
int x;
cin >> x;
--x;
pp[x].push_back(1);
}
for (int i = 0; i < 2 * n; i++) {
int x;
cin >> x;
--x;
pp[x].push_back(2);
}
int f0 = 0, f1 = 0, f2 = 0;
for (int i = 0; i < 3 * n; i++) {
if (pp[i][0] == 0 && pp[i][1] == 1) {
f0++;
}
if (pp[i][0] == 0 && pp[i][1] == 2) {
f1++;
}
if (pp[i][0] == 1 && pp[i][1] == 2) {
f2++;
}
}
if (f0 == 0 && f1 == 0 && f2 == 0) {
cout << 1 << '\n';
continue;
}
Mint ans = 0;
for (int a = 0; a <= 3 * n; a++) {
for (int b = 0; b <= 3 * n; b++) {
for (int c = 0; c <= 3 * n; c++) {
dp[a][b][c] = 0;
}
}
}
dp[f0][f1][f2] = 1;
new_dp[0][0][f0][f1][f2] = 1;
vector<array<int, 3>> states;
states.push_back({f0, f1, f2});
for (int ff = 0; ff <= 3 * n; ff++) {
//vector<vector<vector<vector<vector<Mint>>>>> new_dp(4, vector<vector<vector<vector<Mint>>>>(2, vector<vector<vector<Mint>>>(3 * n + 1, vector<vector<Mint>>(3 * n + 1, vector<Mint>(3 * n + 1)))));
for (auto& p : states) {
vis[p[0]][p[1]][p[2]] = true;
}
for (int r = 0; r < 3; r++) {
for (int st = 0; st < 2; st++) {
vector<array<int, 3>> to_add;
for (auto& p : states) {
int a = p[0], b = p[1], c = p[2];
if (new_dp[r][st][a][b][c] == 0) {
continue;
}
int new_r = r + 1;
if (r == 0) {
if (a > 0) {
int new_st = 1;
new_dp[new_r][new_st][a - 1][b][c] += new_dp[r][st][a][b][c] * a;
if (!vis[a - 1][b][c]) {
to_add.push_back({a - 1, b, c});
vis[a - 1][b][c] = true;
}
}
if (b > 0) {
int new_st = st;
new_dp[new_r][new_st][a][b - 1][c + 1] += new_dp[r][st][a][b][c] * b;
if (!vis[a][b - 1][c + 1]) {
to_add.push_back({a, b - 1, c + 1});
vis[a][b - 1][c + 1] = true;
}
}
if (a + b == 0) {
new_dp[new_r][st][a][b][c] += new_dp[r][st][a][b][c];
}
}
if (r == 1) {
if (c > 0) {
int new_st = 1;
new_dp[new_r][new_st][a][b][c - 1] += new_dp[r][st][a][b][c] * c;
if (!vis[a][b][c - 1]) {
to_add.push_back({a, b, c - 1});
vis[a][b][c - 1] = true;
}
}
if (a > 0) {
int new_st = st;
new_dp[new_r][new_st][a - 1][b + 1][c] += new_dp[r][st][a][b][c] * a;
if (!vis[a - 1][b + 1][c]) {
to_add.push_back({a - 1, b + 1, c});
vis[a - 1][b + 1][c] = true;
}
}
if (a + c == 0) {
new_dp[new_r][st][a][b][c] += new_dp[r][st][a][b][c];
}
}
if (r == 2) {
if (b > 0) {
int new_st = 1;
new_dp[new_r][new_st][a][b - 1][c] += new_dp[r][st][a][b][c] * b;
if (!vis[a][b - 1][c]) {
to_add.push_back({a, b - 1, c});
vis[a][b - 1][c] = true;
}
}
if (c > 0) {
int new_st = st;
new_dp[new_r][new_st][a + 1][b][c - 1] += new_dp[r][st][a][b][c] * c;
if (!vis[a + 1][b][c - 1]) {
to_add.push_back({a + 1, b, c - 1});
vis[a + 1][b][c - 1] = true;
}
}
if (b + c == 0) {
new_dp[new_r][st][a][b][c] += new_dp[r][st][a][b][c];
}
}
}
for (auto& p : to_add) {
states.push_back(p);
}
}
}
ans += new_dp[3][1][0][0][0];
vector<array<int, 3>> new_states;
for (auto& p : states) {
int a = p[0], b = p[1], c = p[2];
dp[a][b][c] = new_dp[3][1][a][b][c];
vis[a][b][c] = 0;
for (int r = 0; r < 4; r++) {
for (int st = 0; st < 2; st++) {
new_dp[r][st][a][b][c] = 0;
}
}
new_dp[0][0][a][b][c] = dp[a][b][c];
if (dp[a][b][c]() > 0) {
new_states.push_back(p);
}
}
swap(states, new_states);
if (new_states.empty()) {
break;
}
}
cout << ans << '\n';
}
return 0;
}
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
1 ms |
724 KB |
Output is correct |
| 2 |
Correct |
1 ms |
980 KB |
Output is correct |
| 3 |
Correct |
4 ms |
4436 KB |
Output is correct |
| 4 |
Correct |
30 ms |
14832 KB |
Output is correct |
| 5 |
Correct |
1770 ms |
86100 KB |
Output is correct |
| 6 |
Execution timed out |
2089 ms |
86604 KB |
Time limit exceeded |
| 7 |
Execution timed out |
2072 ms |
116224 KB |
Time limit exceeded |
| 8 |
Execution timed out |
2081 ms |
141096 KB |
Time limit exceeded |
| 9 |
Execution timed out |
2103 ms |
188120 KB |
Time limit exceeded |
| 10 |
Execution timed out |
2111 ms |
218692 KB |
Time limit exceeded |
