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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#134695#2440. Valentine's Dayckiseki#AC ✓117ms3948kbC++141.6kb2023-08-04 15:35:162023-08-04 15:35:18

Judging History

This is the latest submission verdict.

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-08-04 15:35:18]
  • Judged
  • Verdict: AC
  • Time: 117ms
  • Memory: 3948kb
  • [2023-08-04 15:35:16]
  • Submitted

answer

#include <bits/stdc++.h>
using namespace std;

#define all(x) begin(x), end(x)
#ifdef CKISEKI
#define safe cerr << __PRETTY_FUNCTION__ << " line " << __LINE__ << " safe\n"
#define debug(a...) debug_(#a, a)
#define orange(a...) orange_(#a, a)
template <typename ...T>
void debug_(const char *s, T ...a) {
    cerr << "\e[1;32m(" << s << ") = (";
    int cnt = sizeof...(T);
    (..., (cerr << a << (--cnt ? ", " : ")\e[0m\n")));
}
template <typename I>
void orange_(const char *s, I L, I R) {
    cerr << "\e[1;32m[ " << s << " ] = [ ";
    for (int f = 0; L != R; L++)
        cerr << (f++ ? ", " : "") << *L;
    cerr << " ]\e[0m\n";
}
#else 
#define safe ((void)0)
#define debug(...) safe
#define orange(...) safe
#endif

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);

    using llf = long double;
    int T;
    cin >> T;
    while (T--) {
        int n;
        cin >> n;
        vector<llf> p(n);
        for (int i = 0; i < n; i++) {
            cin >> p[i];
        }

        sort(p.begin(), p.end());
        if (p.back() == 1) {
            cout << 1 << '\n';
            continue;
        }

        llf ans = p.back();

        llf prod = 1, sum = 0;
        for (int i = 0, r = 0; i < n; i++) {
            while (r < n && prod * sum <= (prod * (1 - p[r]) * (sum + p[r] / (1 - p[r])))) {
                prod *= (1 - p[r]);
                sum += p[r] / (1 - p[r]);
                ++r;
                ans = max(ans, prod * sum);
            }
            prod /= 1 - p[i];
            sum -= p[i] / (1 - p[i]);
            ans = max(ans, prod * sum);
        }

        cout << fixed << setprecision(20) << ans << '\n';
    }
    return 0;
}

Details

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Test #1:

score: 100
Accepted
time: 117ms
memory: 3948kb

input:

100
10
0.020874 0.180969 0.015588 0.043033 0.181293 0.033025 0.163341 0.104341 0.065442 0.129546
10
0.019357 0.210598 0.045487 0.051145 0.014579 0.135566 0.004401 0.008004 0.106695 0.056974
10
0.062679 0.216144 0.010137 0.031823 0.233062 0.042464 0.099544 0.140483 0.201337 0.045349
100
0.116404 0.19...

output:

0.39819007148890732530
0.37368388645907640543
0.41088536275849987464
0.42137404437828100437
0.41987297101569753051
0.42106225701885684700
0.42079685802045167309
0.41989089757572841061
0.41986039320215500813
0.00009999010048508432
0.00000000000000000000
0.00334100000000000000
0.00333600000000000000
0...

result:

ok 100 numbers