#include "islands.h"
#include <bits/stdc++.h>
using namespace std;
struct Edge
{
size_t u, v, i;
Edge(size_t u_, size_t v_, size_t i_) { u = u_, v = v_, i = i_; }
};
constexpr size_t N = 100000;
vector<Edge> g[N], t[N];
bool visited[N];
size_t preorder[N], postorder[N];
vector<Edge> special_edges;
bool find_tree_path(size_t u, size_t z, vector<int> &path, size_t p = SIZE_MAX)
{
if (u == z)
return 1;
for (auto const &[_, v, i] : t[u])
if (v != p)
{
path.push_back(i);
if (v == z || find_tree_path(v, z, path, u))
return 1;
path.pop_back();
}
return 0;
}
pair<size_t, size_t> find_dfs_tree(size_t u, size_t i1 = 0, size_t i2 = 0)
{
visited[u] = 1;
preorder[u] = i1++;
for (auto const &[_, v, i] : g[u])
if (!visited[v])
{
t[u].emplace_back(u, v, i);
t[v].emplace_back(v, u, i);
tie(i1, i2) = find_dfs_tree(v, i1, i2);
}
postorder[u] = i2++;
return {i1, i2};
}
bool is_ancestor(size_t u, size_t v)
{
return preorder[u] <= preorder[v] && postorder[u] >= postorder[v];
}
void find_special_edges(size_t u)
{
visited[u] = 1;
for (auto const &[_, v, i] : g[u])
{
if (!visited[v])
find_special_edges(v);
else
special_edges.emplace_back(u, v, i);
}
}
variant<bool, vector<int>> find_journey(
int N, int M, vector<int> U, vector<int> V)
{
for (size_t i = 0; i < M; i++)
g[U[i]].emplace_back(U[i], V[i], i);
find_dfs_tree(0);
memset(visited, 0, sizeof visited);
find_special_edges(0);
sort(special_edges.begin(), special_edges.end(),
[](Edge const &a, Edge const &b)
{ return is_ancestor(a.v, a.u) && !is_ancestor(b.v, b.u); });
if (special_edges.empty() ||
!is_ancestor(special_edges[0].v, special_edges[0].u))
return false;
for (size_t i = 1; i < special_edges.size(); i++)
{
auto const u1 = special_edges[0].u, v1 = special_edges[0].v,
u2 = special_edges[i].u, v2 = special_edges[i].v;
if (u1 == u2 && v1 == v2)
continue;
if (is_ancestor(v2, u2) || is_ancestor(v2, u1))
{
vector<int> path;
find_tree_path(0, u1, path);
path.push_back(special_edges[0].i);
find_tree_path(v1, u2, path);
path.push_back(special_edges[i].i);
find_tree_path(v2, v1, path);
path.push_back(special_edges[0].i);
find_tree_path(u1, v2, path);
path.push_back(special_edges[i].i);
find_tree_path(u2, 0, path);
return path;
}
}
return false;
}
