Submission #485101

#TimeUsernameProblemLanguageResultExecution timeMemory
485101dz001Balloons (CEOI11_bal)C++11
10 / 100
407 ms6580 KiB
#include <bits/stdc++.h>
using namespace std;

#define sqr(x) (x)*(x)

const double eps=1e-3;
const int N=2e5+10;
double ans[N];
long long x[N],R[N];
int n;

double get(int i,int j){
    double l=0,r=R[i],kq=-1;
    for(int k=0;k<32;++k){
        double m=(l+r)/2.;
        double dist=sqr(m-ans[j])+sqr(x[j]-x[i]);
        if(sqr(m+ans[j])-dist<eps)kq=m,l=m;
        else r=m;
    }

    return kq;
}

signed main()
{
    ios::sync_with_stdio(NULL);
    cin.tie(nullptr);
    cout.precision(3);
    cout<<fixed;

    cin>>n;
    for(int i=0;i<n;++i)cin>>x[i]>>R[i];

    ans[0]=R[0];
    for(int i=1;i<n;++i){
        for(int j=max(0,i-10);j<i;++j){
            double tmp=get(i,j);
            // cout<<tmp<<endl;
            if(ans[i]>=tmp||ans[i]==0)ans[i]=tmp;
        }
    }

    for(int i=0;i<n;++i)cout<<ans[i]<<'\n';
}
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