#1164419 (C++23) No.1151 チャレンジゲーム

• 問題: No.1151 チャレンジゲーム
• ユーザー: coindarw
• 提出日時: 2026-05-12 02:42:31
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 159 ms / 2,000 ms
• コード長: 8,791 bytes
• コンパイル時間: 4,264 ms
• コンパイル使用メモリ: 387,448 KB
• 実行使用メモリ: 7,168 KB
• 最終ジャッジ日時: 2026-05-12 02:42:43
• 合計ジャッジ時間: 9,977 ms
• ジャッジサーバーID （参考情報）: judge3_1 / judge2_1

ファイルパターン	結果
sample	AC * 3
other	AC * 50

ソースコード

#ifdef ONLINE_JUDGE
#include <bits/stdc++.h>

#include <atcoder/all>
#else
#include <mylibs/all.h>
#endif

using ll = long long;
using lll = __int128_t;
#define rep(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define reps(i, n) for (int i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (int i = ((int)(n) - 1); i >= 0; --i)
#define rreps(i, n) for (int i = ((int)(n)); i > 0; --i)
#define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
#define repc2(i, s, n) for (int i = (s); i <= (int)(n); i++)
#define length(v) ((int)(v).size())
constexpr int inf = 2'000'000'000;
constexpr ll linf = 4'000'000'000'000'000'000, M7 = 1'000'000'007, M9 = 998'244'353;
#define all(v) begin(v), end(v)
#define rall(v) rbegin(v), rend(v)
using namespace std;
using namespace atcoder;

// clang-format off
using vint = vector<int>;using vvint = vector<vector<int>>;using vvvint = vector<vector<vector<int>>>;
using vll = vector<ll>;using vvll = vector<vector<ll>>;using vvvll = vector<vector<vector<ll>>>;
using vlll = vector<lll>;using vvlll = vector<vector<lll>>;using vvvlll = vector<vector<vector<lll>>>;
using vchar = vector<char>;using vvchar = vector<vector<char>>;using vvvchar = vector<vector<vector<char>>>;
using vstr = vector<string>;using vvstr = vector<vector<string>>;using vvvstr = vector<vector<vector<string>>>;
using vpi = vector<pair<int, int>>;using vvpi = vector<vector<pair<int, int>>>;using vvpint = vector<vector<pair<int, int>>>;
using vpl = vector<pair<ll, ll>>;using vvpl = vector<vector<pair<ll, ll>>>;using vvplint = vector<vector<pair<ll, int>>>;
using vbool = vector<bool>;using vvbool = vector<vector<bool>>;using vvvbool = vector<vector<vector<bool>>>;

#define Vec(type, ...) __make_vec<type>(__VA_ARGS__)
template <class T> vector<T> __make_vec(size_t a) {return vector<T>(a);}template <class T, class... Ts>
auto __make_vec(size_t a, Ts... ts) {return vector<decltype(__make_vec<T>(ts...))>(a, __make_vec<T>(ts...));}
#define VecI(init, type, ...) __make_vecI<type, init>(__VA_ARGS__)
template <class T, T init>vector<T> __make_vecI(size_t a) {return vector<T>(a, init);}
template <class T, T init, class... Ts>
auto __make_vecI(size_t a, Ts... ts) {return vector<decltype(__make_vecI<T, init>(ts...))>(a, __make_vecI<T, init>(ts...));}

template <typename T, typename U>inline ostream& operator<<(ostream& os, const pair<T, U>& p) noexcept {return os << p.first << " " << p.second;}
inline ostream& operator<<(ostream& os, const modint& m) noexcept { return os << m.val(); }
template <int M>inline ostream& operator<<(ostream& os, const static_modint<M>& m) noexcept { return os << m.val(); }

template <typename T> struct is_static_modint : std::false_type {}; template <int MOD> struct is_static_modint<static_modint<MOD>> : std::true_type {};
template <template <typename...> typename C, typename Number>concept MyContainer = std::is_same_v<C<Number>, std::vector<Number>> || std::is_same_v<C<Number>, std::deque<Number>> || std::is_same_v<C<Number>, std::set<Number>> || std::is_same_v<C<Number>, std::unordered_set<Number>> || std::is_same_v<C<Number>, std::unordered_multiset<Number>> || std::is_same_v<C<Number>, std::multiset<Number>>;
template <typename Number>concept MyNumber = std::is_same_v<Number, int> || std::is_same_v<Number, ll> || std::is_same_v<Number, char> || std::is_same_v<Number, modint> || is_static_modint<Number>::value;
template <template <typename...> typename C, typename Number>concept MyContainerNumber = MyContainer<C, Number> && MyNumber<Number>;
template <template <typename...> typename OutCon, template <typename...> typename InCon, typename Number>concept MyNestedContainerNumber = MyContainer<OutCon, InCon<Number>> && MyContainerNumber<InCon, Number>;
template <template <typename...> typename C, typename Number>requires MyContainerNumber<C, Number>std::ostream& operator<<(std::ostream& os, const C<Number>& t) {auto itr = t.begin();auto end = t.end();if (itr != end) {os << *itr++;for (; itr != end; ++itr) os << ' ' << *itr;}return os;}
template <template <typename...> typename OutCon, template <typename...> typename InCon, typename Number>requires MyNestedContainerNumber<OutCon, InCon, Number>std::ostream& operator<<(std::ostream& os, const OutCon<InCon<Number>>& t) {auto itr = t.begin();auto end = t.end();if (itr != end) {os << *itr++;for (; itr != end; ++itr) os << '\n' << *itr;}return os;}
template <typename T, typename U>istream& operator>>(istream& is, pair<T, U>& p) {return is >> p.first >> p.second;}
template <typename T>istream& operator>>(istream& is, vector<T>& v) {for (auto& e : v) is >> e;return is;}
void inp() {}
template <typename T, typename... Args>void inp(T& a, Args&... args) {cin >> a, inp(args...);}
template <typename T>void inp1(vector<T>& v, int offset = 1, int len = -1) {if (len == -1) len = int(v.size()) - offset;assert(offset >= 0 && len >= 0);for (int i = offset; i < offset + len; ++i) cin >> v[i];}
template <typename T>void oup(const T& a) {cout << a << "\n";}
template <typename T, typename... Args>void oup(const T& a, const Args&... args) {cout << a << " ", oup(args...);}
template <typename T>void oupl(const T& a) {cout << a;}
template <typename T, typename... Args>void oupl(const T& a, const Args&... args) {cout << a << " ", oupl(args...);}


inline string YesNo(bool cond) { return cond ? "Yes" : "No"; }
inline auto add1(auto vec, ll offset = 1) {for (auto& e : vec) e += offset;return vec;}
#ifdef ONLINE_JUDGE
#define debug(...)
#else
#define debug(...) cerr << "<" << #__VA_ARGS__ << ">: ", debug_out(__VA_ARGS__)
template <typename T>void debug_out(T t) {cerr << t << "\n";}
template <typename T, typename... Args>void debug_out(T t, Args... args) {cerr << t << ", ";debug_out(args...);}
#endif

#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
auto minE(const auto&a) {
    return min_element(a.begin(), a.end());
}
auto maxE(const auto&a) {
    return max_element(a.begin(), a.end());
}

#ifdef ONLINE_JUDGE
#define todo(...) static_assert(false)
#else
#define todo(...)
#endif
// clang-format on

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    ll n;
    inp(n);
    vll a(n);
    inp(a);

    vint vx(1 << n);
    rep(S, 1 << n) {
        int x = 0;
        rep(i, n) {
            if (!(S >> i & 1)) {
                x += a[i];
            }
        }
        vx[S] = x;
    }

    using T = tuple<short, short, bool>;
    map<T, double> memo;
    auto rec = [&](auto rec, T s) -> double {
        if (memo.contains(s)) return memo[s];
        auto [S, d, t] = s;
        if (S == ((1 << n) - 1)) {
            return d > 0;
        }
        if (t) {  // 後手
            if (d - vx[S] > 0) {
                return 1;
            }
            double mn = 1;
            rep(i, n) {
                if (S >> i & 1) continue;
                if (a[i] == 1) {
                    mn = min(mn, rec(rec, T{S | (1 << i), d - a[i], !t}));
                    continue;
                }
                double x = 1. / a[i];
                double fa = rec(rec, T{S | (1 << i), d - a[i], !t});
                double mx = 0;
                rep(j, n) {
                    if (S >> j & 1) continue;
                    double y = 1. / a[j];
                    double fb = rec(rec, T{S | (1 << j), d + a[j], t});
                    if (a[j] == 1) {
                        mx = max(mx, x * fa + (1 - x) * fb);
                    } else {
                        mx = max(mx, (x * fa + (1 - x) * y * fb) / (1. - (1 - x) * (1 - y)));
                    }
                }
                mn = min(mn, mx);
            }
            return memo[s] = mn;
        } else {  // 先手
            if (d + vx[S] <= 0) {
                return 0;
            }
            double mx = 0;
            rep(i, n) {
                if (S >> i & 1) continue;
                if (a[i] == 1) {
                    mx = max(mx, rec(rec, T{S | (1 << i), d + a[i], !t}));
                    continue;
                }
                double x = 1. / a[i];
                double fa = rec(rec, T{S | (1 << i), d + a[i], !t});
                double mn = 1;
                rep(j, n) {
                    if (S >> j & 1) continue;
                    double y = 1. / a[j];
                    double fb = rec(rec, T{S | (1 << j), d - a[j], t});
                    if (a[j] == 1) {
                        mn = min(mn, x * fa + (1 - x) * fb);
                    } else {
                        mn = min(mn, (x * fa + (1 - x) * y * fb) / (1. - (1 - x) * (1 - y)));
                    }
                }
                mx = max(mx, mn);
            }
            return memo[s] = mx;
        }
    };

    cout << fixed << setprecision(20);
    oup(rec(rec, T{0, 0, 0}));
}