Submission #658449

#	Time	Username	Problem	Language	Result	Execution time	Memory
658449		MilosMilutinovic	Fishing Game (RMI19_fishing)	C++14	0 / 100	2120 ms	524288 KiB

fishing

/**
 *    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];
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);  
  int n, tt;
  cin >> n >> tt;
  while (tt--) {
    vector<vector<int>> p(3 * n);
    for (int i = 0; i < 2 * n; i++) {
      int x;
      cin >> x;
      --x;
      p[x].push_back(0);  
    }
    for (int i = 0; i < 2 * n; i++) {
      int x;
      cin >> x;
      --x;
      p[x].push_back(1);  
    }
    for (int i = 0; i < 2 * n; i++) {
      int x;
      cin >> x;
      --x;
      p[x].push_back(2);  
    }
    int f0 = 0, f1 = 0, f2 = 0;  
    for (int i = 0; i < 3 * n; i++) {
      if (p[i][0] == 0 && p[i][1] == 1) {
        f0++;
      }
      if (p[i][0] == 0 && p[i][1] == 2) {
        f1++;
      }        
      if (p[i][0] == 1 && p[i][1] == 2) {
        f2++;
      }
    }
    if (f0 == 0 && f1 == 0 && f2 == 0) {
      cout << 1 << '\n';
      continue;
    }
    Mint ans = 0;
    vector<vector<vector<Mint>>> dp(3 * n + 1, vector<vector<Mint>>(3 * n + 1, vector<Mint>(3 * n + 1)));
    dp[f0][f1][f2] = 1;            
    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)))));            
      new_dp[0][0] = dp;
      for (int r = 0; r < 3; r++) {
        for (int st = 0; st < 2; st++) {
          for (int a = 3 * n; a >= 0; a--) {
            for (int b = 3 * n; b >= 0; b--) {
              for (int c = 3 * n; c >= 0; c--) {
                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 (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 (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 (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 (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 (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;
                  }
                }
              }
            }
          }
        }            
      }                   
      for (int r = 1; r < 4; r++) {
        ans += new_dp[r][1][0][0][0];          
      }
      dp = new_dp[3][1];
    }
    cout << ans << '\n';
  }
  return 0;
}         

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