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>
#define fastIO ios_base::sync_with_stdio(false); cin.tie(NULL)
#define file(a) freopen(a".inp","r",stdin); freopen(a".out", "w",stdout)
#define fi first
#define se second
#define endl "\n"
#define len(s) int32_t(s.length())
#define MASK(k)(1LL<<(k))
#define TASK "test"
#define int long long
#define double long double
using namespace std;
typedef tuple<int, int, int> tpiii;
typedef pair<double, double> pdd;
typedef pair<int, int> pii;
typedef long long ll;
const long long OO = 1e18;
const int MOD = 1e9 + 7;
const int INF = 1e9;
const int MX = 200005;
int n;
pdd a[MX];
pdd v[MX];
void nhap(){
cin >> n;
for(int i=1; i<=n; i++) cin >> a[i].fi >> a[i].se;
}
double sqr(double x){
return x*x;
}
double euler(pdd a, pdd b){
return sqrt(sqr(a.fi - b.fi) + sqr(a.se - b.se));
}
double dis(pdd ball, double p){
double lo=0, hi=INF;
for(int t=0; t<65; t++){
double mid = (lo+hi)/2;
if(euler(ball, {p, mid}) >= mid + ball.se) lo = mid;
else hi = mid;
}
return (lo + hi)/2;
}
void solve(){
stack<pdd> v;
for(int i=1; i<=n; i++){
double val = a[i].se;
while(v.size()){
val = min({val, dis(v.top(), a[i].fi)});
if(val >= v.top().se) v.pop();
else break;
}
v.push({a[i].fi, val});
cout << fixed << setprecision(3) << val << '\n';
}
}
int32_t main(){
fastIO;
//file(TASK);
nhap();
solve();
return 0;
}
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