#include <bits/stdc++.h>
#include "longesttrip.h"
using namespace std;
using ll = long long;
int n;
vector<int> longest_trip(int N, int D) {
n = N;
vector<int> p1, p2;
p1.push_back(0);
int st = 0;
for (int i = 1;i < n;i++) {
if (p2.empty()) {
if (are_connected({ p1.back() }, { i })) p1.push_back(i);
else p2.push_back(i), st = 0;
}
else {
if (st == 0) {
if (!are_connected({ p1.back(), i }, { p2.back() })) p1.push_back(i);
else p2.push_back(i), st = 1;
}
else if (st == 1) {
if (are_connected({ p2.back() }, { i })) p2.push_back(i);
else {
if (are_connected({ p1.back() }, { i })) {
p1.push_back(i), st = 0;
reverse(p2.begin(), p2.end());
}
else {
reverse(p2.begin(), p2.end());
for (auto& x : p2) p1.push_back(x);
p1.push_back(i);
p2.clear();
}
}
}
}
}
if (p1.size() > p2.size()) swap(p1, p2);
if ((int)p2.size() == n) return p2;
int l = 0, r = p1.size();
while (l < r) {
int mid = (l + r) / 2;
vector<int> t;
for (int j = 0;j <= mid;j++) t.push_back(p1[j]);
if (are_connected(t, p2)) r = mid;
else l = mid + 1;
}
if (l == (int)p1.size()) return p2;
if (are_connected({ p1.back() }, p2)) {
reverse(p1.begin(), p1.end());
}
else {
vector<int> p3;
for (int i = 0;i < (int)p1.size();i++) {
p3.push_back(p1[(i + l) % ((int)p1.size())]);
}
swap(p1, p3);
}
l = 0, r = p2.size() - 2;
while (l < r) {
int mid = (l + r) / 2;
vector<int> t;
for (int j = 0;j <= mid;j++) t.push_back(p2[j]);
if (are_connected(t, { p1.front() })) r = mid;
else l = mid + 1;
}
if (are_connected({ p1.front() }, { p2.back() })) {
vector<int> ans;
for (auto& x : p2) ans.push_back(x);
for (auto& x : p1) ans.push_back(x);
return ans;
}
else {
vector<int> p3;
for (int i = 0;i < (int)p2.size();i++) {
p3.push_back(p2[(i + l) % ((int)p2.size())]);
}
swap(p2, p3);
}
reverse(p2.begin(), p2.end());
vector<int> ans;
for (auto& x : p2) ans.push_back(x);
for (auto& x : p1) ans.push_back(x);
return ans;
}
