This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// Hallelujah, praise the one who set me free
// Hallelujah, death has lost its grip on me
// You have broken every chain, There's salvation in your name
// Jesus Christ, my living hope
#include <bits/stdc++.h>
using namespace std;
#define REP(i, s, e) for (int i = (s); i < (e); i++)
#define RREP(i, s, e) for (int i = (s); i >= (e); i--)
template <class T>
inline bool mnto(T& a, T b) {return a > b ? a = b, 1 : 0;}
template <class T>
inline bool mxto(T& a, T b) {return a < b ? a = b, 1: 0;}
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#define FI first
#define SE second
typedef pair<int, int> ii;
typedef pair<ll, ll> pll;
typedef tuple<int, int, int> iii;
#define ALL(_a) _a.begin(), _a.end()
#define SZ(_a) (int) _a.size()
#define pb push_back
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<ii> vii;
typedef vector<iii> viii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
const int INF = 1000000005;
const ll LINF = 1000000000000000005ll;
const int MAXN = 200005;
int n;
int a[MAXN];
ll psm[MAXN];
ld solve(int l, int r, ld mn, ld mx) {
if (l == r) {
return mx - mn;
}
ld lsm = (ld) (psm[r] - psm[l]) / (r - l);
if (lsm <= mx) {
return solve(l + 1, r, mn, mx);
}
ld rsm = (ld) (psm[r - 1] - psm[l - 1]) / (r - l);
if (mn <= rsm) {
return solve(l, r - 1, mn, mx);
}
return min(solve(l + 1, r, mn, lsm), solve(l, r - 1, rsm, mx));
}
int main() {
#ifndef DEBUG
ios::sync_with_stdio(0), cin.tie(0);
#endif
cin >> n;
REP (i, 1, n + 1) {
cin >> a[i];
psm[i] = a[i] + psm[i - 1];
}
cout << setprecision(15) << solve(1, n, (ld) psm[n] / n, (ld) psm[n] / n) << '\n';
return 0;
}
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