#816201 (C++17) No.174 カードゲーム（Hard）

• 問題: No.174 カードゲーム（Hard）
• ユーザー: keijak
• 提出日時: 2022-11-15 07:33:56
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 247 ms / 2,000 ms
• コード長: 6,294 bytes
• コンパイル時間: 2,106 ms
• コンパイル使用メモリ: 209,388 KB
• 最終ジャッジ日時: 2025-02-08 20:23:01
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
other	AC * 12

ソースコード

// #define NDEBUG
#include <bits/stdc++.h>

#define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i)
#define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define ALL(x) std::begin(x), std::end(x)
using Int = long long;
using Uint = unsigned long long;
using Real = long double;

template<typename T, typename U>
inline bool chmax(T &a, U b) { return a < b and ((a = b), true); }
template<typename T, typename U>
inline bool chmin(T &a, U b) { return a > b and ((a = b), true); }
template<typename T>
constexpr T kBig = std::numeric_limits<T>::max() / 2;
#if __cplusplus < 202002L
template<typename T>
inline int ssize(const T &a) { return (int) a.size(); }
#endif

template<size_t BufSize>
class InputReader {
 public:
  void skip() {
    [[maybe_unused]] static const bool lazy_init = [this]() {
      const size_t len = fread(buf_, 1, sizeof(buf_) - 1, stdin);
      buf_[len] = '\0';
      ptr_ = buf_;
      bufend_ = buf_ + len;
      return true;
    }();
    while (isspace(*ptr_)) ++ptr_;
  }

  template<typename T>
  operator T() {
    T x;
    skip();
    assert(not is_eof());  // Couldn't read reached the end of input.
    read_one(x);
    return x;
  }

  struct Sized {
    InputReader<BufSize> &reader;
    int n;
    template<typename T>
    operator T() const {
      T xs(n);
      for (auto &x: xs) {
        reader.skip();
        assert(not reader.is_eof());
        reader.read_one(x);
      }
      return xs;
    }
  };
  Sized operator()(int n) { return {*this, n}; }

  bool is_eof() const { return ptr_ >= bufend_; }

 private:
  template<class T>
  std::enable_if_t<std::is_integral_v<T>> read_one(T &x) {
    [[maybe_unused]] int sign = 1;
    if constexpr (std::is_signed_v<T>) {
      sign = (*ptr_ == '-') ? (++ptr_, -1) : 1;
    }
    x = 0;
    while (isdigit(*ptr_)) x = x * 10 + (*ptr_++ & 0x0F);
    if constexpr (std::is_signed_v<T>) {
      x *= sign;
    }
  }
  template<class T>
  std::enable_if_t<std::is_floating_point_v<T>> read_one(T &x) {
    [[maybe_unused]] int sign = 1;
    if constexpr (std::is_signed_v<T>) {
      sign = (*ptr_ == '-') ? (++ptr_, -1) : 1;
    }
    x = 0;
    while (isdigit(*ptr_)) x = x * 10 + (*ptr_++ & 0x0F);
    if (*ptr_ == '.') {
      ++ptr_;
      for (T base = 0.1; isdigit(*ptr_); ++ptr_, base *= 0.1) {
        x += (*ptr_ & 0x0F) * base;
      }
    }
    if constexpr (std::is_signed_v<T>) {
      x *= sign;
    }
  }
  void read_one(std::string &s) {
    char *p0 = ptr_;
    while (not isspace(*ptr_)) ptr_++;
    s.assign(p0, ptr_);
  }
  void read_one(std::string_view &s) {
    const char *p0 = ptr_;
    while (not isspace(*ptr_)) ptr_++;
    s = std::string_view(p0, ptr_ - p0);
  }

  static inline char buf_[BufSize];
  char *ptr_, *bufend_;
};
InputReader<(1 << 26)> in;

template<typename Container>
std::ostream &out_seq(const Container &seq, const char *sep = " ",
                      const char *ends = "\n", std::ostream &os = std::cout) {
  const auto itl = std::begin(seq), itr = std::end(seq);
  for (auto it = itl; it != itr; ++it) {
    if (it != itl) os << sep;
    os << *it;
  }
  return os << ends;
}

template<typename T>
std::ostream &out_one(const T &x, char endc) {
  if constexpr (std::is_same<T, bool>::value) {
    return std::cout << (x ? "Yes" : "No") << endc;
  } else {
    return std::cout << x << endc;
  }
}
template<typename T>
std::ostream &out(const T &x) {
  return out_one(x, '\n');
}
template<typename T, typename... Ts>
std::ostream &out(const T &head, Ts... tail) {
  return out_one(head, ' '), out(tail...);
}

void init_() {
  // std::ios::sync_with_stdio(false);
  // std::cin.tie(nullptr);
  std::cout << std::fixed << std::setprecision(18);
}

[[noreturn]] void exit_() {
#ifdef MY_DEBUG
  in.skip();
  assert(in.is_eof());  // Some input is left.
#endif
  fflush(stdout), fflush(stderr);
  std::cout.flush(), std::cerr.flush();
  std::_Exit(0);
}

#ifdef MY_DEBUG
#include "debug_dump.hpp"
#include "backward.hpp"
backward::SignalHandling kSignalHandling;
#else
#define DUMP(...)
#define test_case(...)
#define cerr if(false)cerr
#endif

using namespace std;
template<typename T>
bool has_bit(const T &x, int i) { return (x >> i) & 1; }

template<typename T, typename U = std::make_unsigned_t<T>>
int popcount(T x) {
  if constexpr (std::is_same_v<U, unsigned>) {
    return __builtin_popcount(static_cast<U>(x));
  } else if constexpr (std::is_same_v<U, unsigned long>) {
    return __builtin_popcountl(static_cast<U>(x));
  } else if constexpr (std::is_same_v<U, unsigned long long>) {
    return __builtin_popcountll(static_cast<U>(x));
  }
  assert(false);  // unsupported type
}

int countr_zero(unsigned x) {
  if (x == 0) return std::numeric_limits<unsigned>::digits;
  return __builtin_ctz(x);
}
int countr_one(unsigned x) {
  x = ~x;
  if (x == 0) return std::numeric_limits<unsigned>::digits;
  return __builtin_ctz(x);
}

auto solve() {
  const int n = in;
  const Real Pa = in, Pb = in;
  vector<int> A = in(n), B = in(n);
  sort(ALL(A));
  sort(ALL(B));
  const int kFull = (1 << n) - 1;

  auto f = [&](Real P, vector<Real> &dp, vector<vector<Real>> &H) {
    dp[0] = 1.0;
    REP(bits, kFull) {
      int pc = popcount(bits);
      Real cur = dp[bits];
      if (cur == 0.0) continue;
      int smallest = countr_one(bits);
      if (pc + 1 == n) {
        dp[kFull] += cur;
        H[pc][smallest] += cur;
        continue;
      }
      dp[bits | (1 << smallest)] += cur * P;
      H[pc][smallest] += cur * P;
      if (n - (pc + 1) == 0) continue;
      Real R = (1.0 - P) / Real(n - (pc + 1));
      for (int i = smallest + 1; i < n; ++i) {
        if (has_bit(bits, i)) continue;
        dp[bits | (1 << i)] += cur * R;
        H[pc][i] += cur * R;
      }
    }
  };
  auto dpa = vector(1 << n, Real(0.0));
  auto dpb = vector(1 << n, Real(0.0));
  auto Ha = vector(n + 1, vector(n, Real(0.0)));
  auto Hb = vector(n + 1, vector(n, Real(0.0)));
  f(Pa, dpa, Ha);
  f(Pb, dpb, Hb);
  Real ans = 0;
  REP(i, n) {
    REP(x, n) {
      REP(y, n) {
        if (A[x] > B[y]) {
          ans += (A[x] + B[y]) * Ha[i][x] * Hb[i][y];
        }
      }
    }
  }
  out(ans);
}

int main() {
  init_();
  const int T = 1;//in;
  REP(t, T) {
    test_case(t, T);
    (solve());
  }
  exit_();
}