UVA 10301 / DSU

/***
 created: 2022-06-12-14.38.54
***/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename U> using ordered_set=tree<U, null_type,less<U>,rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define test int tt; cin>>tt; for(int cs=1;cs<=tt;cs++)
#define get_lost_idiot return 0
#define nl '\n'

ll mx=0;

vector<ll>parent(200005),rankk(200005);

void make_set(ll n)
{
    for(ll i=0; i<n; i++)
    {
        parent[i] = i;
        rankk[i] = 1;
    }
}

ll find_set(ll v)
{
    if (v == parent[v])
    {
        return v;
    }
    return parent[v] = find_set(parent[v]);
}

void union_sets(ll a, ll b)
{
    a = find_set(a);
    b = find_set(b);

    if (a == b) return;

    parent[b]=a;

    rankk[a]+=rankk[b];

    rankk[b]=0;

}


double distnc(double x,double y,double x1,double y1)
{
    return (x-x1)*(x-x1)+(y-y1)*(y-y1);
}


int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    ll n;

    while(cin>>n && n!=-1)
    {
        parent.resize(n);
        rankk.resize(n);


        make_set(n);

        double x[n+4],y[n+4],r[n+4];

        ll m,i,j,k,l;

        for(i=0;i<n;i++)
        {
            cin>>x[i]>>y[i]>>r[i];

            for(j=0;j<i;j++)
            {
                double diss=distnc(x[i],y[i],x[j],y[j]);

                if((diss-(1e-8))<=((r[i]+r[j])*(r[i]+r[j])))
                {
                    if((diss+(1e-8))>=((r[i]-r[j])*(r[i]-r[j])))
                    {
                        union_sets(i,j);
                    }
                }
            }

        }

        m=0;

        if(rankk.empty()==false) m=*max_element(rankk.begin(),rankk.end());


        cout<<"The largest component contains "<<m<<" ring";
        if(m!=1) cout<<"s";
        cout<<"."<<nl;

    }


    get_lost_idiot;
}