結果

問題 No.1151 チャレンジゲーム
ユーザー opt
提出日時 2020-08-08 00:51:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 67 ms / 2,000 ms
コード長 3,837 bytes
コンパイル時間 3,177 ms
コンパイル使用メモリ 202,760 KB
最終ジャッジ日時 2025-01-12 18:41:44
ジャッジサーバーID
（参考情報） 		judge1 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 50
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using V = vector<int>;
using Vll = vector<ll>;
using Vld = vector<ld>;
using Vbo = vector<bool>;
using VV = vector<V>;
using VVll = vector<Vll>;
using VVld = vector<Vld>;
using VVbo = vector<Vbo>;
using VVV = vector<VV>;
using VVVll = vector<VVll>;
using VVVld = vector<VVld>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using Pld = pair<ld, ld>;
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define rep(i, n) rep2(i, 0, n)
#define drep(i, n) drep2(i, n, 0)
#define all(a) (a).begin(), (a).end()
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
template<typename T> inline int sz(T &x) { return x.size(); }
template<typename T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; }
template<typename T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p) { is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p) { os << '(' << p.first << ", " << p.second << ')'; return 
    os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<typename T> inline int count_between(vector<T> &a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r)
inline int fLog2(const int x) { assert(x > 0); return 31-__builtin_clz(x); } // floor(log2(x))
inline int fLog2(const ll x) { assert(x > 0); return 63-__builtin_clzll(x); }
inline int cLog2(const int x) { assert(x > 0); return (x == 1) ? 0 : 32-__builtin_clz(x-1); } // ceil(log2(x))
inline int cLog2(const ll x) { assert(x > 0); return (x == 1) ? 0 : 64-__builtin_clzll(x-1); }
inline int popcount(const int x) { return __builtin_popcount(x); }
inline int popcount(const ll x) { return __builtin_popcountll(x); }
void fail() { puts("-1"); exit(0); }
// const int INF  = 1<<30;
// const ll INFll = 1ll<<62;
// const ld EPS   = 1e-10;
// const ld PI    = acos(-1.0);
// const int MOD  = int(1e9)+7;
// const int MOD  = 998244353;
V convert(ll x, int b, int n) {
  V res;
  for (int i = 0; i < n; ++i) {
    res.push_back(x%b);
    x /= b;
  }
  return res;
}
int main() {
  int n; cin >> n;
  V a(n); cin >> a;
  Vld b(n);
  rep(i, n) b[i] = ld(1) / a[i];
  int N = 1;
  rep(i, n) N *= 3;
  VVld p(2, Vld(N, -1));
  rep(S, N) {
    V v = convert(S, 3, n);
    bool ini = true;
    rep(i, n) if (v[i] == 0) ini = false;
    if (!ini) {
      p[0][S] = 0;
      p[1][S] = 1;
      continue;
    }
    V s(2);
    rep(i, n) s[v[i]-1] += a[i];
    if (s[0] <= s[1]) p[0][S] = 0, p[1][S] = 0;
    else              p[0][S] = 1, p[1][S] = 1;
  }
  V pw3(n);
  pw3[0] = 1;
  rep(i, n-1) pw3[i+1] = pw3[i] * 3;
  drep(S, N) {
    V v = convert(S, 3, n);
    rep(i, n) if (v[i] == 0) {
      ld cmin = 1;
      rep(j, n) if (v[j] == 0) {
        int x = S + pw3[i];
        int y = S + pw3[j] * 2;
        ld now = p[1][x] * b[i] + p[0][y] * (1-b[i]) * b[j];
        now /= 1 - (1-b[i]) * (1-b[j]);
        chmin(cmin, now);
      }
      chmax(p[0][S], cmin);
    }
    rep(j, n) if (v[j] == 0) {
      ld cmax = 0;
      rep(i, n) if (v[i] == 0) {
        int x = S + pw3[i];
        int y = S + pw3[j] * 2;
        ld now = p[0][y] * b[j] + p[1][x] * (1-b[j]) * b[i];
        now /= 1 - (1-b[i]) * (1-b[j]);
        chmax(cmax, now);
      }
      chmin(p[1][S], cmax);
    }
  }
  cout << p[0][0] << '\n';
  return 0;
}
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