// failed/solution-yoshiyuki-incorrect-cycle-finding.cpp
// Incorrect attempt of O(N^2) with pruning
// Counter of this solution:
// * gen_dag: WA
// * gen_tricky2: TLE
// A fix to this incorrect solution is to remove DAG,
// which lead to the lemma 1 (remove nodes with 0 out-degree)
#include "islands.h"
#include <functional>
#include <utility>
#include <set>
#include <variant>
#include <vector>
#include <cstring>
#include <cassert>
const int max_n = 1e5;
std::vector<int> adj[max_n+10];
std::set<int> u_adj[max_n+10];
int vis[max_n+10];
bool vis_one_deg[max_n+10];
std::vector<int> visited, to_start;
std::vector<int> has_cycle;
bool find_cycle(int cur, bool init = true) {
if (!init && vis[cur] == 1) return true;
if (vis[cur] == 2) return false;
vis[cur] = 1;
visited.push_back(cur);
for (auto nex: u_adj[cur]) {
if (find_cycle(nex, false)) return true;
}
return false;
}
void reset(int start) {
for (auto u: visited) vis[u] = 0;
visited.clear();
for (auto u: to_start) vis[u] = 2;
vis[start] = 1;
}
std::variant<bool, std::vector<int>> find_journey(
int N, int M, std::vector<int> U, std::vector<int> V) {
memset(vis, 0, sizeof vis);
for (int i = 0; i < M; i++) {
adj[U[i]].push_back(V[i]);
u_adj[U[i]].insert(V[i]);
}
for (int i = 0; i < N; i++) {
random_shuffle(adj[i].begin(), adj[i].end());
}
int cnt = 0;
for (auto start: adj[0]) {
reset(start);
vis[0] = 1;
if (find_cycle(start)) {
cnt++;
has_cycle.push_back(start);
}
if (cnt >= 2) return true;
}
if (has_cycle.empty()) return false;
assert(has_cycle.size() == 1);
for (auto u: has_cycle) {
int v = u, prev = 0;
to_start.clear();
to_start.push_back(0);
vis_one_deg[0] = true;
while (true) {
if (vis_one_deg[v]) return false;
to_start.push_back(v);
int cnt_branch = 0;
vis_one_deg[v] = true;
for (auto nex: adj[v]) {
if (nex != prev) cnt_branch++;
if (cnt_branch >= 2) break;
}
if (cnt_branch >= 2) break;
if (cnt_branch != 1) return false;
for (auto nex: adj[v]) {
if (nex != prev) {
prev = v;
v = nex;
break;
}
}
}
if (adj[v].empty() || to_start.empty()) continue;
cnt = 0;
for (auto start: adj[v]) {
if (start == prev) continue;
reset(start);
vis[v] = 1;
cnt += find_cycle(start);
if (cnt >= 2) return true;
}
vis[v] = 0;
}
return false;
}
