#include "longesttrip.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
template <typename T1, typename T2>
using indexed_map = tree<T1, T2, less<T1>, rb_tree_tag, tree_order_statistics_node_update>;
template <typename T>
using indexed_set = indexed_map<T, null_type>;
#define loop(x, i) for (int i = 0; i < (x); i++)
#define loop1(x, i) for (int i = 1; i <= (x); i++)
#define rev(x, i) for (int i = (int)(x) - 1; i >= 0; i--)
#define itloop(x) for (auto it = begin(x); x != end(x); it++)
#define itrev(x) for (auto it = rbegin(x); x != rend(x); it++)
#define INF32 ((int32_t)(2e9 + 1))
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
#define removeIn(x, l) l.erase(find(ALL(l), x))
#define pb push_back
#define sz(x) (int)(x).size()
#define F first
#define S second
#define var const auto &
#define foreach(l) for (var e : l)
typedef int8_t i8;
typedef int16_t i16;
typedef int32_t i32;
typedef int64_t i64;
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
typedef tuple<int, int, int, int> iiii;
typedef vector<int> vi;
typedef vector<i32> vi32;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vi32> vvi32;
typedef vector<ii> vii;
typedef vector<iii> viii;
typedef vector<vii> vvii;
typedef vector<viii> vviii;
typedef set<int> si;
typedef set<ii> sii;
typedef set<iii> siii;
typedef vector<si> vsi;
typedef vector<sii> vsii;
typedef vector<vsi> vvsi;
typedef vector<string> vstr;
typedef vector<vector<string>> vvstr;
typedef vector<bool> vb;
typedef vector<vb> vvb;
vi longest_trip(int N, int D)
{
if (D >= 2)
{
vi res(N);
iota(ALL(res), 0);
if (D == 3)
{
return res;
}
si resterend;
loop1(N - 1, i) resterend.insert(res[i]);
loop1(N - 1, i)
{
auto it = resterend.begin();
if (are_connected({res[i - 1]}, {*it}))
{
res[i] = *it;
resterend.erase(it);
}
else
{
if (resterend.size() == 1)
{
res.insert(res.begin(), *it);
res.pop_back();
return res;
}
res[i] = *next(it);
resterend.erase(next(it));
}
}
return res;
}
else
{
vvi adj(N);
bitset<256> con[256];
for (int i = 0; i < N; i++)
{
for (int j = i + 1; j < N; j++)
{
if (are_connected({i}, {j}))
{
// cerr << i << ' ' << j << endl;
adj[i].pb(j);
adj[j].pb(i);
con[i][j] = 1;
con[j][i] = 1;
}
}
}
vb vis(N);
int cnt = 0;
auto dfs = [&](auto &&self, int i) -> void
{
vis[i] = 1;
cnt++;
for (int j : adj[i])
{
if (!vis[j])
self(self, j);
}
};
dfs(dfs, 0);
vi res;
if (cnt != N)
{
int mx = max(cnt, N - cnt);
loop(N, i)
{
if (vis[i] == cnt == mx)
res.pb(i);
}
loop(sz(res) - 1, i) assert(con[res[i]][res[i + 1]]);
return res;
}
deque<int> path;
path.pb(0);
int i2 = *adj[0].begin();
path.pb(i2);
int i3 = -1;
for (int j : adj[i2])
{
if (j != 0)
{
i3 = j;
path.pb(i3);
break;
}
}
if (i3 == -1)
{
for (int j : adj[0])
{
if (j != i2)
{
i3 = j;
path.push_front(i3);
break;
}
}
}
deque<int> left;
for (int i = 1; i < N; i++)
if (i != i2 && i != i3)
left.pb(i);
while (!left.empty())
{
int i = left.back();
left.pop_back();
if (con[i][path[0]])
{
path.push_front(i);
}
else if (con[i][path.back()])
{
path.push_back(i);
}
else
{
assert(con[path[0]][path.back()]);
int newBegin = -1;
for (int j = 1; j < sz(path) - 1; j++)
{
if (con[i][path[j]])
{
newBegin = j;
break;
}
}
if (newBegin == -1)
{
left.push_front(i);
continue;
}
deque<int> newPath;
newPath.pb(i);
for (int j = newBegin; j < sz(path); j++)
{
newPath.pb(path[j]);
}
for (int j = 0; j < newBegin; j++)
{
newPath.pb(path[j]);
}
path = newPath;
}
}
for (int v : path)
res.pb(v);
assert(sz(res) == N);
loop(sz(res) - 1, i) assert(con[res[i]][res[i + 1]]);
return res;
}
throw;
return {};
}
