This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
//Bismillahirrahmanirrahim...
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
//author: Ahmet Alp Orakci
#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define ONLINE_JUDGE
void solve() {
int n;
cin >> n;
vector <int> vec(n +1);
for(int i = 1; i <= n; i++)
cin >> vec[i];
vector <int> pref = vec;
for(int i = 1; i <= n; i++)
pref[i] += pref[i -1];
function <double(int, int, double, double)> f = [&](int l, int r, double mn, double mx) -> double {
if(l == r) {
return mx - mn;
}
double _l = double(1) * (pref[r] - pref[l]) / (r - l);
if(_l <= mx) {
return f(l +1, r, mn, mx);
}
double _r = double(1) * (pref[r -1] - pref[l -1]) / (r - l);
if(mn <= _r) {
return f(l, r -1, mn, mx);
}
return min(f(l +1, r, mn, _l), f(l, r -1, _r, mx));
};
i64 top = accumulate(vec.begin(), vec.end(), 0LL);
cout << setprecision(15) << f(1, n, top * double(1) / n, top * double(1) / n);
return;
}
signed main() {
#ifndef ONLINE_JUDGE
freopen(".in", "r", stdin);
freopen(".out", "w", stdout);
#endif
ios_base::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
int t = 1; //cin >> t;
for(int i = 1; i <= t; i++) {
solve();
}
return 0;
}
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