#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<random>
#include<tuple>
#include<chrono>
#include "longesttrip.h"
using namespace std;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//mt19937 rng(89356);
vector<int>ans;
int n;
int cntqueries=0;
bool edge(int u,int v)
{
cntqueries++;
return are_connected({u},{v});
}
void special(vector<int>nodes)
{
if(!are_connected(nodes,ans))return;
if(!edge(ans[0],ans.back()))
{
vector<int>nans;
for(int x:nodes)nans.push_back(x);
for(int i=0;i<ans.size();i++)
{
nans.push_back(ans[i]);
}
ans=nans;
return;
}
int l=0,r=nodes.size()-1;
int pnodes,pans;
while(l<r)
{
int mid=(l+r)/2;
vector<int>tmp;
for(int i=l;i<=mid;i++)
{
tmp.push_back(nodes[i]);
}
if(are_connected(tmp,ans))
{
r=mid;
}
else l=mid+1;
}
pnodes=l;
l=0;r=ans.size()-1;
while(l<r)
{
int mid=(l+r)/2;
vector<int>tmp;
for(int i=l;i<=mid;i++)
{
tmp.push_back(ans[i]);
}
if(are_connected(tmp,{nodes[pnodes]}))
{
r=mid;
}
else l=mid+1;
}
pans=l;
vector<int>nans;
for(int i=pans+1;i<ans.size();i++)
{
nans.push_back(ans[i]);
}
for(int i=0;i<=pans;i++)
{
nans.push_back(ans[i]);
}
for(int i=pnodes;i<nodes.size();i++)
{
nans.push_back(nodes[i]);
}
for(int i=0;i<pnodes;i++)
{
nans.push_back(nodes[i]);
}
ans=nans;
}
void solve(vector<int>nodes,int u)//u=ans.back()
{
if(nodes.size()==0)return;
if(are_connected(nodes,{u})==0){special(nodes);return;}
int l=0,r=nodes.size()-1;
while(l<r)
{
int mid=(l+r)/2;
vector<int>tmp;
for(int i=l;i<=mid;i++)
{
tmp.push_back(nodes[i]);
}
if(are_connected(tmp,{u}))
{
r=mid;
}
else l=mid+1;
}
vector<int>other;
int mid=(nodes.size()-1)/2;
if(l<=mid)
{
for(int i=0;i<l;i++)other.push_back(nodes[i]);
for(int i=l;i<nodes.size();i++)ans.push_back(nodes[i]);
solve(other,ans.back());
}
else
{
for(int i=l;i>=0;i--)
{
ans.push_back(nodes[i]);
}
for(int i=l+1;i<nodes.size();i++)
{
other.push_back(nodes[i]);
}
solve(other,ans.back());
}
}
std::vector<int> longest_trip(int N, int D)
{
cntqueries=0;
n=N;
ans.clear();
///reset eveerything
vector<int>v1,v2;
vector<int>nodes;
for(int i=0;i<n;i++)nodes.push_back(i);
shuffle(nodes.begin(),nodes.end(),rng);
v1.push_back(nodes.back());nodes.pop_back();v2.push_back(nodes.back());nodes.pop_back();
for(int i:nodes)
{
vector<pair<int,int>>tmp;
tmp.push_back({i,v1.back()});
tmp.push_back({v1.back(),v2.back()});
tmp.push_back({v2.back(),i});
shuffle(tmp.begin(),tmp.end(),rng);
for(int j=0;j<3;j++)
{
int x,y;
tie(x,y)=tmp[j];
if(j==2 or edge(x,y))
{
if(x==v1.back() && y==v2.back())
{
vector<int>akka=v1;
reverse(v2.begin(),v2.end());
for(int x:v2)akka.push_back(x);
v1=akka;
v2.clear();v2.push_back(i);
}
else if(x==i)
{
v1.push_back(i);
}
else v2.push_back(i);
break;
}
}
}
if(v1.size()>v2.size())
{
ans=v1;
solve(v2,v1.back());
}
else
{
ans=v2;
solve(v1,v2.back());
}
if(cntqueries>400)while(1);
return ans;
}
