#include "parks.h"
#include<bits/stdc++.h>
using namespace std;
vector<int>parent(2e5);
vector<int>siz(2e5);
void makesets(int v){
parent[v]=v;
siz[v]=1;
}
int findsets (int v){
if (v==parent[v])return v;
parent[v]=findsets(parent[v]);
return parent[v];
}
void unionset(int a,int b){
a = findsets(a);
b =findsets(b);
if (a==b)return;
if (siz[a]<siz[b])swap(a,b);
siz[a]+=siz[b];
parent[b]=a;
}
void build(vector<int> u, vector<int> v, vector<int> a, vector<int> b);
struct point {
int x,y,index;
};
bool dist(point x,point y){
if (((x.x - y.x)*(x.x - y.x)+(x.y-y.y)*(x.y-y.y))!=4)return false;
return true;
}
int binarysearch(int seg,int eq,int n,vector<point>arr){
int left = 0;
int right = n-1;
while(left<=right){
int mid = (left + right) >> 1;
if (arr[mid].x<seg)left= mid + 1;
else if (arr[mid].x>seg)right = mid-1;
else {
if (arr[mid].y<eq){
left=mid+1;
}
else if (arr[mid].y>eq){
right = mid-1;
}
else return mid;
}
}
if (left>=0&&left<n)return left;
return 0;
}
int construct_roads(std::vector<int> x, std::vector<int> y) {
vector<point>arr;
vector<vector<bool>>p(10,vector<bool>(2e5+10 ,false));
int n = x.size();
bool ok=true;
for (int i = 0 ;i<n;++i){
if (x[i]!=x[0])ok=false;
arr.push_back({x[i],y[i],i});
}
vector<int>ansx,ansy,ansxi,ansyi;
if (ok){
sort(arr.begin(),arr.end(),[&](point a,point b){
return a.y<b.y;
});
for (int i = 1;i<n;++i){
if (dist(arr[i],arr[i-1])){
ansx.push_back(min(arr[i].x,arr[i-1].x) + 1);
ansy.push_back(min(arr[i].y,arr[i-1].y)+1);
ansxi.push_back(arr[i].index);
ansyi.push_back(arr[i-1].index);
}
else return 0;
}
build(ansxi,ansyi,ansx,ansy);
return 1;}
else{
for (int i =0;i<n;++i){
makesets(i);
}
sort(arr.begin(),arr.end(),[&](point a,point b){
if (a.x==b.x)return a.y<b.y;
return a.x<b.x;
});
stack<int>check;
int i =1;
for (;i<n;++i){
if (arr[i].x!=2)break;
if (dist(arr[i],arr[i-1])){
ansx.push_back(min(arr[i].x,arr[i-1].x) - 1);
ansy.push_back(min(arr[i].y,arr[i-1].y) + 1);
ansxi.push_back(arr[i].index);
ansyi.push_back(arr[i-1].index);
unionset(i-1,i);
p[ansx.back()][ansy.back()]=true;
}
else {
check.push(i);
check.push(i-1);
}
}
check.push(i);
check.push(i-1);
for (;i<n;++i){
if (arr[i-1].x==2)continue;
if (dist(arr[i],arr[i-1])){
ansx.push_back(min(arr[i].x,arr[i-1].x) + 1);
ansy.push_back(min(arr[i].y,arr[i-1].y) + 1);
ansxi.push_back(arr[i].index);
ansyi.push_back(arr[i-1].index);
unionset(i-1,i);
p[ansx.back()][ansy.back()]=true;
}
else {
check.push(i);
check.push(i-1);
}
}
while(!check.empty()){
int k = check.top();
check.pop();
for (auto j:{max(k-1,0),min(k+1,n-1),binarysearch(arr[k].x+2,arr[k].y,n,arr),binarysearch(arr[k].x-2,arr[k].y,n,arr)}){
if (dist(arr[j],arr[k])&&findsets(j)!=findsets(k)){
int first1=min(arr[k].x,arr[j].x) + 1;
int second1=min(arr[k].y,arr[j].y) + 1;
int second2 = min(arr[k].y,arr[j].y) - 1;
if (!p[first1][second1]){
ok=true;
ansx.push_back(first1);
ansy.push_back(second1);
ansxi.push_back(arr[j].index);
ansyi.push_back(arr[k].index);
unionset(j,k);
p[ansx.back()][ansy.back()]=true;
break;
}
if (!p[first1][second2]){
ok=true;
ansx.push_back(first1);
ansy.push_back(second2);
ansxi.push_back(arr[j].index);
ansyi.push_back(arr[k].index);
unionset(j,k);
p[ansx.back()][ansy.back()]=true;
break;
}
}
}
}
if (siz[findsets(0)]!=n)return 0;
build(ansxi,ansyi,ansx,ansy);
return 1;
}
}
