// Witold Milewski
// PA 2025
#include <bits/stdc++.h>
#define int long long
using namespace std;
#define FOR(i, a, b) for(int i=a; i<=b; ++i)
#define FORB(i, b, a) for(int i=b; i>=a; --i)
#define sz(A) (int)(A.size())
#define ll long long
#define ld long double
#define eb emplace_back
#define pb push_back
#define pi pair<int, int>
#define f first
#define s second
#define rs resize
#define V vector
const int maxn=50007, offset=50000;
ld dp[2][2*maxn];
int n, t;
signed main() {
cin >> n >> t;
V<ld> praw;
ld x;
FOR(i, 1, n) {
cin >> x;
praw.eb(x);
}
sort(praw.begin(), praw.end(), greater<ld>());
FOR(i, 0, 1) FOR(j, 0, maxn-1) dp[i][j]=0;
dp[0][offset+0]=1;
ld wyn=0;
FOR(i, 0, sz(praw)-1) {
ld p = praw[i];
int a = i%2;
int b = 1-a;
FOR(j, 0, 2*maxn-1) dp[b][j]=0;
FOR(j, 1, 2*maxn-2) {
dp[b][j+1]+=dp[a][j]*p;
dp[b][j-1]+=dp[a][j]*(1.0-p);
}
ld praw = 0;
FOR(j, t, maxn-1) praw+=dp[b][offset+j];
// if(i%2==0) cout << fixed << setprecision(7) << praw << '\n';
wyn=max(wyn, praw);
}
cout << fixed << setprecision(7) << wyn << '\n';
}
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 | // Witold Milewski // PA 2025 #include <bits/stdc++.h> #define int long long using namespace std; #define FOR(i, a, b) for(int i=a; i<=b; ++i) #define FORB(i, b, a) for(int i=b; i>=a; --i) #define sz(A) (int)(A.size()) #define ll long long #define ld long double #define eb emplace_back #define pb push_back #define pi pair<int, int> #define f first #define s second #define rs resize #define V vector const int maxn=50007, offset=50000; ld dp[2][2*maxn]; int n, t; signed main() { cin >> n >> t; V<ld> praw; ld x; FOR(i, 1, n) { cin >> x; praw.eb(x); } sort(praw.begin(), praw.end(), greater<ld>()); FOR(i, 0, 1) FOR(j, 0, maxn-1) dp[i][j]=0; dp[0][offset+0]=1; ld wyn=0; FOR(i, 0, sz(praw)-1) { ld p = praw[i]; int a = i%2; int b = 1-a; FOR(j, 0, 2*maxn-1) dp[b][j]=0; FOR(j, 1, 2*maxn-2) { dp[b][j+1]+=dp[a][j]*p; dp[b][j-1]+=dp[a][j]*(1.0-p); } ld praw = 0; FOR(j, t, maxn-1) praw+=dp[b][offset+j]; // if(i%2==0) cout << fixed << setprecision(7) << praw << '\n'; wyn=max(wyn, praw); } cout << fixed << setprecision(7) << wyn << '\n'; } |
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