Submission #949477

#	Time	Username	Problem	Language	Result	Execution time	Memory
949477		MilosMilutinovic	Solitaire (JOI16_solitaire)	C++14	100 / 100	1289 ms	2564 KiB

solitaire

/**
 *    author:  wxhtzdy
 *    created: 19.08.2023 09:44:51
**/
#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 = 1000000007;
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;
  cin >> n;
  vector<string> s(3);
  for (int i = 0; i < 3; i++) {
    cin >> s[i];
  }
  for (int i = 0; i < 3; i++) {
    if (i == 1) {
      continue;
    }
    for (int j = 1; j + 1 < n; j++) {
      if (s[i][j] == 'x') {
        if (s[i][j - 1] == 'x' || s[i][j + 1] == 'x') {
          cout << 0 << '\n';
          return 0;
        }
      }
    }
  }
  if (s[0][0] == 'x' || s[0][n - 1] == 'x' || s[2][0] == 'x' || s[2][n - 1] == 'x') {
    cout << 0 << '\n';
    return 0;
  }
  vector<vector<vector<Mint>>> dp(3 * n + 1, vector<vector<Mint>>(2, vector<Mint>(2)));
  // (0, 0) -> prosli nije x
  // (1, 0) -> pocetak
  // (0, 1) -> prosli je x i ostao je x
  // (1, 1) -> prosli je x i postao je zid
  int cnt = 0;
  dp[0][1][0] = 1;
  for (int i = 0; i < n; i++) {
    int f = (s[0][i] == 'x' ? 1 : 0) + (s[2][i] == 'x' ? 1 : 0);
    vector<vector<vector<Mint>>> new_dp(3 * n + 1, vector<vector<Mint>>(2, vector<Mint>(2)));
    if (s[1][i] == 'x') {
      cnt += f + 1;
      Mint lst_done = dp[0][1][0];
      for (int j = 0; j < cnt; j++) {
        lst_done += dp[j][0][0];
        lst_done += dp[j][1][1];
      }
      Mint lst_not_done = 0;
      int ptr = cnt - 1;
      for (int j = cnt - f - 1; j >= 0; j--) {
        while (ptr >= j) {
          lst_not_done += dp[ptr][0][1];
          ptr -= 1;
        }
        new_dp[j + f][1][1] += (f == 2 ? C(j + 1, 1) * C(j + 1, 1) + j + 1 : C(j + 1, f)) * lst_done;
        new_dp[j + f][1][1] += (f == 2 ? C(j + 1, 1) * C(j + 1, 1) + j + 1 : C(j + 1, f)) * lst_not_done;
      }
      vector<Mint> pref_sum(cnt + 1);
      for (int j = 0; j <= cnt; j++) {
        if (j > 0) {
          pref_sum[j] = pref_sum[j - 1];
        }
        pref_sum[j] += dp[j][1][1];
      }    
      auto Get = [&](int idx) {
        Mint res = 0;
        if (idx >= 0) {
          res = pref_sum[idx];
        }
        return res;
      };
      for (int j = 0; j < cnt - f; j++) {
        if (f == 0) {
          continue;
        }
        if (f == 1) {
          Mint coeff = C(cnt - (j + 1), 1);
          new_dp[j][0][1] += dp[0][0][0] * coeff;
          new_dp[j][0][1] += Get(j - 1) * coeff;
        }
        if (f == 2) {
          Mint coeff0 = 2 * C(cnt - 2 - j, 1) * C(j + 1, 1);
          Mint coeff1 = C(cnt - j - 2, 1) * C(cnt - j - 2, 1) + C(cnt - j - 2, 1);
          Mint coeff2 = 2 * C(cnt - 2 - j, 1) * C(j, 1);
          new_dp[j][0][1] += dp[0][0][0] * coeff1;
          new_dp[j + 1][0][1] += dp[0][0][0] * coeff0;
          new_dp[j][0][1] += Get(j - 1) * coeff1;
          new_dp[j + 1][0][1] += Get(j - 1) * coeff0;
        }
        //new_dp[j][0][1] += dp[0][0][0] * coeff;
        //new_dp[j][0][1] += s * coeff;  
      }
    } else {                          
      cnt += f;
      Mint coeff = max(1, f) * C(cnt, f);
      new_dp[0][0][0] += dp[0][0][0] * coeff;
      new_dp[0][0][0] += dp[0][1][0] * coeff;
      for (int j = 0; j <= cnt; j++) {
        new_dp[0][0][0] += dp[j][0][1] * coeff;
        new_dp[0][0][0] += dp[j][1][1] * coeff; 
      }
    }
    swap(dp, new_dp);
    if (i == 1) {
    //  cout << "--- " << dp[2][0][1] << '\n';
    }
  }
  Mint ans = 0;
  for (int i = 0; i <= cnt; i++) {
    ans += dp[i][0][0];
    ans += dp[i][1][1];
  }
  cout << ans << '\n';               
  return 0;
}

Compilation message (stderr)

solitaire.cpp: In function 'int main()':
solitaire.cpp:236:16: warning: variable 'coeff2' set but not used [-Wunused-but-set-variable]
  236 |           Mint coeff2 = 2 * C(cnt - 2 - j, 1) * C(j, 1);
      |                ^~~~~~

• Subtask 1: 10 / 10
• Subtask 2: 12 / 12
• Subtask 3: 20 / 20
• Subtask 4: 38 / 38
• Subtask 5: 20 / 20