This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pld;
typedef pair<int,int> pii;
typedef tuple<int,int,int> tt;
#define all(a) a.begin(), a.end()
#define filter(a) a.erase(unique(all(a)), a.end())
const ld INF = 1e18;
const ld eps = 1e-9;
const int mn = 2e5 + 5;
ll x[mn], maxR[mn];
ld rad[mn];
bool ok (int j, int i, ld tryR) {
ld tmp = (x[i] - x[j]) * (x[i] - x[j]);
return tmp - 4 * rad[j] * tryR >= -eps;
}
ld calc (int j, int i, ld L = 0, ld R = INF) {
if (abs(L - R) < eps) return L;
ld mid = (L + R) / 2;
if (ok(j, i, mid + eps)) return calc(j, i, mid + eps, R);
return calc(j, i, L, mid);
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
int n; cin >> n;
for (int i = 1; i <= n; i++)
cin >> x[i] >> maxR[i];
rad[1] = maxR[1];
cout << fixed << setprecision(9) << rad[1] << "\n";
vector<int> vec = {1};
for (int i = 2; i <= n; i++) {
rad[i] = INF;
int save = -1;
for (int j = vec.size() - 1; j >= 0; j--) {
ld cur = calc(vec[j], i, 0, maxR[i]);
if (cur <= rad[i]) {
rad[i] = cur;
save = vec[j];
vec.pop_back();
}
else break;
}
vec.push_back(save);
vec.push_back(i);
cout << rad[i] << "\n";
}
return 0;
}
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