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 <iostream>
#include <iomanip>
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 5e4+5;
const long double eps = 0.000001;
bool visited[MAXN];
//long long test;
int n,k;
pair<pair<long long,long long>,long long> p[MAXN];
struct cmpf{
inline bool operator()(const long long& i, const long long& j)const{
if(p[i].first.second!=p[j].first.second){
return p[i].first.second<p[j].first.second;
}
return i>j;
}
};
set<int,cmpf> s1;
vector<int> v1[MAXN];
vector<int> tempv;
bool dp[MAXN][40];
bool dist(long long i,long long j,long double x){
return (long double)((p[i].first.first-p[j].first.first)*(p[i].first.first-p[j].first.first))+((p[i].first.second-p[j].first.second)*(p[i].first.second-p[j].first.second))<=(long double)x*x;
}
void dfs(int curr){
tempv.push_back(curr);
visited[curr] = true;
for(int x:v1[curr]){
if(!visited[x]){
dfs(x);
}
}
}
int checkmod(int x){
if(x<k){
return x;
}
return x-k;
}
bool findsubset(){
int m = tempv.size();
m--;
if(m>k){
return true;
}
for(int i=0;i<=m+1;i++){
for(int j=0;j<=k+1;j++){
dp[i][j] = false;
}
}
for(int mod = 0;mod<k;mod++){
dp[m+1][mod] = !mod;
}
for(int i=m;i>=1;i--){
for(int mod = 0;mod<k;mod++){
dp[i][mod] = dp[i+1][mod];
if(dp[i+1][(checkmod(mod+p[tempv[i]].second))]){
dp[i][mod] = true;
}
}
if(dp[i+1][p[tempv[i]].second]){
return true;
}
}
return false;
}
bool check(long double x){
for(int i=1;i<=n;i++){
v1[i].clear();
visited[i] = false;
}
s1.clear();
int j = 1;
for(int i=1;i<=n;i++){
while((long double)(p[i].first.first-p[j].first.first)>x){
s1.erase(j);
j++;
}
if(!s1.empty()){
int cnt = 0;
p[n+1] = make_pair(make_pair(p[i].first.first,(long long)(p[i].first.second-(long long)x)),0);
for(auto it = s1.lower_bound(n+1);it!=s1.end();it++){
int idx = *it;
if(p[idx].first.second>p[i].first.second+x){
break;
}
cnt++;
if(cnt>=8*k){
return true;
}
if(dist(i,idx,x)){
v1[i].push_back(idx);
v1[idx].push_back(i);
}
}
}
s1.insert(i);
}
for(int i=1;i<=n;i++){
if(!visited[i]){
tempv.clear();
tempv.push_back(-1);
dfs(i);
if(findsubset()){
return true;
}
}
}
return false;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin>>n>>k;
for(int i=1;i<=n;i++){
cin>>p[i].first.first>>p[i].first.second>>p[i].second;
p[i].second%=k;
}
sort(p+1,p+n+1);
long double l = 0;
long double r = 1e8;
long double ans = -1;
while(r-l>eps){
long double mid = (l+r)/2;
if(check(mid)){
ans = mid;
r = mid-eps;
}else{
l = mid+eps;
}
}
// cout<<check(11163410)<<endl;
if(ans == -1){
printf("No solution!\n");
}else{
printf("%.3lf",(double)ans);
}
}
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