#include "longesttrip.h"
#include <bits/stdc++.h>
using namespace std;
int n;
std::vector<int> longest_trip(int N, int D)
{
n = N;
vector<int> path;
vector<bool> used(n, false);
path.push_back(0);
used[0] = true;
while (path.size() != n) {
int lst = path.back();
vector<int> cands;
for (int i = 0; i < n; i++) {
if (!used[i]) cands.push_back(i);
}
bool conn = are_connected({path.back()}, {cands});
if (!conn) {
break;
}
int nxt = -1;
int lo = 0, hi = cands.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
vector<int> qr;
for (int j = 0; j <= mid; j++) {
qr.push_back(cands[j]);
}
bool conn = are_connected({path.back()}, qr);
if (conn) {
nxt = qr.back();
hi = mid-1;
}
else lo = mid+1;
}
assert(are_connected({path.back()}, {nxt}));
path.push_back(nxt);
used[nxt] = true;
}
if (path.size() == n) return path;
vector<int> comp2;
for (int i = 0; i < n; i++) {
if (!used[i]) {
comp2.push_back(i);
}
}
if (!are_connected(path, comp2)) {
if (path.size() > comp2.size()) return path;
return comp2;
}
if (are_connected({path[0]}, {comp2})) {
int nxt = -1;
int lo = 0, hi = comp2.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
vector<int> qr;
for (int j = 0; j <= mid; j++) {
qr.push_back(comp2[j]);
}
bool conn = are_connected({path[0]}, qr);
if (conn) {
nxt = qr.back();
hi = mid-1;
}
else lo = mid+1;
}
vector<int> ans;
for (auto x: comp2) {
if (x != nxt) ans.push_back(x);
}
ans.push_back(nxt);
for (auto x: path) ans.push_back(x);
return ans;
}
else { // path is actually a big cycle
int u = -1;
int lo = 0, hi = path.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
vector<int> qr;
for (int j = 0; j <= mid; j++) {
qr.push_back(path[j]);
}
bool conn = are_connected(qr, comp2);
if (conn) {
u = mid;
hi = mid-1;
}
else lo = mid+1;
}
int v = -1;
lo = 0, hi = comp2.size() - 1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
vector<int> qr;
for (int j = 0; j <= mid; j++) {
qr.push_back(comp2[j]);
}
bool conn = are_connected({path[u]}, qr);
if (conn) {
v = qr.back();
hi = mid-1;
}
else lo = mid+1;
}
vector<int> ans;
for (int i = u+1; i < path.size(); i++) ans.push_back(path[i]);
for (int i = 0; i <= u; i++) ans.push_back(path[i]);
ans.push_back(v);
for (auto x: comp2) {
if (x != v) ans.push_back(x);
}
return ans;
}
return {};
}
