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;
#define pr pair<double, int>
#define ll long long
#define pb push_back
#define f first
#define s second
vector<double> x, r;
set<pr> xr;
bool check(double mid, set<pr>::iterator it1, set<pr>::iterator it2, int be){
bool judge=false;
for (auto it=it1; it!=it2; it++){
int pos=it->s;
double rr=(mid+r[pos])*(mid+r[pos]);
double dist1=(mid-r[pos])*(mid-r[pos])+(x[be]-x[pos])*(x[be]-x[pos]);
if(rr>=dist1){
judge=true; break;
}
}
return judge;
}
int main(){
int n; cin>>n;
x.resize(n); r.resize(n);
for (int i=0; i<n; i++) {
cin>>x[i]>>r[i];
pr node={x[i]+r[i], i};
xr.insert(node); // r value changes and this need to be update
}
vector<double> ans(n);
for (int i=0; i<n; i++){
if(i==0) {
ans[i]=r[i];
continue;
}
//
pr node={x[i]-r[i], i};
set<pr>::iterator it1=xr.lower_bound(node); // pos can only be less than or equal to i;
node={x[i]+r[i], i};
set<pr>::iterator it2=xr.find(node);
if(it1==it2) {ans[i]=r[i]; continue;}
double lft=0; double rht=r[i];
while(rht-lft>0.00001){
double mid=lft+(rht-lft)/2;
if(check(mid, it1, it2, i)) {
rht=mid;
}
else lft=mid;
}
ans[i]=lft;
xr.erase(node);
node={x[i]+lft, i};
xr.insert(node);
}
cout << fixed <<setprecision(3);
for (int i=0; i<n; i++) cout<<ans[i]<<endl;
}
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