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답안 #949477

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
949477 2024-03-19T09:28:49 Z MilosMilutinovic Solitaire (JOI16_solitaire) C++14
100 / 100
 1289 ms 2564 KB 
/**
 *    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

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
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 472 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct

Subtask #2
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 214 ms 1280 KB Output is correct
2 Correct 955 ms 2372 KB Output is correct
3 Correct 182 ms 1224 KB Output is correct
4 Correct 1116 ms 2344 KB Output is correct
5 Correct 1134 ms 2296 KB Output is correct
6 Correct 1101 ms 2284 KB Output is correct
7 Correct 1074 ms 2436 KB Output is correct
8 Correct 1128 ms 2344 KB Output is correct
9 Correct 1146 ms 2344 KB Output is correct
10 Correct 1289 ms 2296 KB Output is correct
11 Correct 1078 ms 2296 KB Output is correct
12 Correct 1149 ms 2296 KB Output is correct
13 Correct 1138 ms 2344 KB Output is correct
14 Correct 1155 ms 2528 KB Output is correct
15 Correct 1123 ms 2296 KB Output is correct
16 Correct 1159 ms 2504 KB Output is correct
17 Correct 1118 ms 2280 KB Output is correct
18 Correct 1153 ms 2492 KB Output is correct
19 Correct 1108 ms 2340 KB Output is correct
20 Correct 1122 ms 2340 KB Output is correct
21 Correct 1099 ms 2348 KB Output is correct
22 Correct 1108 ms 2528 KB Output is correct
23 Correct 1161 ms 2504 KB Output is correct
24 Correct 1114 ms 2504 KB Output is correct
25 Correct 1134 ms 2344 KB Output is correct

Subtask #3
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 456 KB Output is correct
4 Correct 1 ms 488 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 452 KB Output is correct
12 Correct 1 ms 344 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 344 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct

Subtask #4
38.0 / 38.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 472 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 456 KB Output is correct
16 Correct 1 ms 488 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 452 KB Output is correct
24 Correct 1 ms 344 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 344 KB Output is correct
30 Correct 1 ms 348 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 1 ms 344 KB Output is correct
33 Correct 1 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 3 ms 348 KB Output is correct
38 Correct 8 ms 600 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 32 ms 600 KB Output is correct
41 Correct 25 ms 604 KB Output is correct
42 Correct 30 ms 600 KB Output is correct
43 Correct 26 ms 604 KB Output is correct
44 Correct 25 ms 604 KB Output is correct
45 Correct 27 ms 996 KB Output is correct
46 Correct 27 ms 728 KB Output is correct
47 Correct 35 ms 728 KB Output is correct
48 Correct 26 ms 604 KB Output is correct

Subtask #5
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 472 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 214 ms 1280 KB Output is correct
14 Correct 955 ms 2372 KB Output is correct
15 Correct 182 ms 1224 KB Output is correct
16 Correct 1116 ms 2344 KB Output is correct
17 Correct 1134 ms 2296 KB Output is correct
18 Correct 1101 ms 2284 KB Output is correct
19 Correct 1074 ms 2436 KB Output is correct
20 Correct 1128 ms 2344 KB Output is correct
21 Correct 1146 ms 2344 KB Output is correct
22 Correct 1289 ms 2296 KB Output is correct
23 Correct 1078 ms 2296 KB Output is correct
24 Correct 1149 ms 2296 KB Output is correct
25 Correct 1138 ms 2344 KB Output is correct
26 Correct 1155 ms 2528 KB Output is correct
27 Correct 1123 ms 2296 KB Output is correct
28 Correct 1159 ms 2504 KB Output is correct
29 Correct 1118 ms 2280 KB Output is correct
30 Correct 1153 ms 2492 KB Output is correct
31 Correct 1108 ms 2340 KB Output is correct
32 Correct 1122 ms 2340 KB Output is correct
33 Correct 1099 ms 2348 KB Output is correct
34 Correct 1108 ms 2528 KB Output is correct
35 Correct 1161 ms 2504 KB Output is correct
36 Correct 1114 ms 2504 KB Output is correct
37 Correct 1134 ms 2344 KB Output is correct
38 Correct 1 ms 348 KB Output is correct
39 Correct 1 ms 348 KB Output is correct
40 Correct 1 ms 456 KB Output is correct
41 Correct 1 ms 488 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 1 ms 348 KB Output is correct
44 Correct 1 ms 348 KB Output is correct
45 Correct 1 ms 348 KB Output is correct
46 Correct 1 ms 348 KB Output is correct
47 Correct 1 ms 348 KB Output is correct
48 Correct 1 ms 452 KB Output is correct
49 Correct 1 ms 344 KB Output is correct
50 Correct 1 ms 348 KB Output is correct
51 Correct 1 ms 348 KB Output is correct
52 Correct 1 ms 348 KB Output is correct
53 Correct 1 ms 348 KB Output is correct
54 Correct 1 ms 344 KB Output is correct
55 Correct 1 ms 348 KB Output is correct
56 Correct 1 ms 348 KB Output is correct
57 Correct 1 ms 344 KB Output is correct
58 Correct 1 ms 348 KB Output is correct
59 Correct 1 ms 348 KB Output is correct
60 Correct 1 ms 348 KB Output is correct
61 Correct 1 ms 348 KB Output is correct
62 Correct 3 ms 348 KB Output is correct
63 Correct 8 ms 600 KB Output is correct
64 Correct 1 ms 348 KB Output is correct
65 Correct 32 ms 600 KB Output is correct
66 Correct 25 ms 604 KB Output is correct
67 Correct 30 ms 600 KB Output is correct
68 Correct 26 ms 604 KB Output is correct
69 Correct 25 ms 604 KB Output is correct
70 Correct 27 ms 996 KB Output is correct
71 Correct 27 ms 728 KB Output is correct
72 Correct 35 ms 728 KB Output is correct
73 Correct 26 ms 604 KB Output is correct
74 Correct 747 ms 1892 KB Output is correct
75 Correct 120 ms 1040 KB Output is correct
76 Correct 363 ms 1496 KB Output is correct
77 Correct 1143 ms 2320 KB Output is correct
78 Correct 1218 ms 2504 KB Output is correct
79 Correct 1100 ms 2496 KB Output is correct
80 Correct 1143 ms 2552 KB Output is correct
81 Correct 1153 ms 2292 KB Output is correct
82 Correct 1196 ms 2292 KB Output is correct
83 Correct 1167 ms 2344 KB Output is correct
84 Correct 1130 ms 2296 KB Output is correct
85 Correct 1185 ms 2344 KB Output is correct
86 Correct 1263 ms 2528 KB Output is correct
87 Correct 1256 ms 2296 KB Output is correct
88 Correct 1245 ms 2532 KB Output is correct
89 Correct 1210 ms 2332 KB Output is correct
90 Correct 1209 ms 2512 KB Output is correct
91 Correct 1228 ms 2248 KB Output is correct
92 Correct 1251 ms 2332 KB Output is correct
93 Correct 1251 ms 2344 KB Output is correct
94 Correct 1257 ms 2248 KB Output is correct
95 Correct 1224 ms 2328 KB Output is correct
96 Correct 1211 ms 2564 KB Output is correct
97 Correct 1221 ms 2324 KB Output is correct