#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; template<class T> using ordered_set =tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update> ; #define debug(x) cout << "[" << #x << " " << x << "] "; #define ar array #define ll long long #define ld long double #define sz(x) ((int)x.size()) #define all(a) (a).begin(), (a).end() typedef vector<int> vi; typedef pair<int,int> pi; const int MAX_N = 5e5 + 5; const ll MOD = 1e9 + 7; const ll INF = 1e9; const ld EPS = 1e-9; void solve() { int n,t; cin >> n >> t; vector<double> p(n); for (int i = 0; i < n; i++) { cin >> p[i]; } sort(p.rbegin(), p.rend()); queue<pair<int,int>> point_to_eval; for (int i=t, j=0; i+2*j<=n; j++){ point_to_eval.push({i+2*j,j}); } // dp[i][j] = probability of fucking up i answers after choosing first j questions double ans = 0.0; vector<double> prev_dp(n+1,0.0); prev_dp[0] = 1.0; for (int i=1; i<=n; i++) { vector<double> dp(n+1,0.0); dp[0] = prev_dp[0] * p[i-1]; for (int j=1; j<=i; j++) { dp[j] = prev_dp[j] * p[i-1] + prev_dp[j-1] * (1.0 - p[i-1]); } if (point_to_eval.front().first == i) { double cdf = 0.0; for (int j=0; j<=point_to_eval.front().second; j++){ cdf += dp[j]; } ans = max(ans,cdf); point_to_eval.pop(); } prev_dp = dp; } cout << std::fixed << std::setprecision(20) << ans << "\n"; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int tc = 1; for (int t = 1; t <= tc; t++) { // cout << "Case #" << t << ": "; solve(); } }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 | #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace __gnu_pbds; using namespace std; template<class T> using ordered_set =tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update> ; #define debug(x) cout << "[" << #x << " " << x << "] "; #define ar array #define ll long long #define ld long double #define sz(x) ((int)x.size()) #define all(a) (a).begin(), (a).end() typedef vector<int> vi; typedef pair<int,int> pi; const int MAX_N = 5e5 + 5; const ll MOD = 1e9 + 7; const ll INF = 1e9; const ld EPS = 1e-9; void solve() { int n,t; cin >> n >> t; vector<double> p(n); for (int i = 0; i < n; i++) { cin >> p[i]; } sort(p.rbegin(), p.rend()); queue<pair<int,int>> point_to_eval; for (int i=t, j=0; i+2*j<=n; j++){ point_to_eval.push({i+2*j,j}); } // dp[i][j] = probability of fucking up i answers after choosing first j questions double ans = 0.0; vector<double> prev_dp(n+1,0.0); prev_dp[0] = 1.0; for (int i=1; i<=n; i++) { vector<double> dp(n+1,0.0); dp[0] = prev_dp[0] * p[i-1]; for (int j=1; j<=i; j++) { dp[j] = prev_dp[j] * p[i-1] + prev_dp[j-1] * (1.0 - p[i-1]); } if (point_to_eval.front().first == i) { double cdf = 0.0; for (int j=0; j<=point_to_eval.front().second; j++){ cdf += dp[j]; } ans = max(ans,cdf); point_to_eval.pop(); } prev_dp = dp; } cout << std::fixed << std::setprecision(20) << ans << "\n"; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int tc = 1; for (int t = 1; t <= tc; t++) { // cout << "Case #" << t << ": "; solve(); } } |