// failed/solution-yoshiyuki-incorrect-exclude-dag.cpp
// Incorrect attempt of O(N^2) with pruning and removing DAG
// Time Complexity might be O(N) (unproven) due to DAG removal
// Has incorrect cycle finding
// Counter of this solution (already generalized in some of gen_solution)
/*
6 8
0 1
1 2
2 3
3 2
2 4
4 2
1 5
5 0
*/
#include "islands.h"
#include <functional>
#include <queue>
#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];
bool vis_dag[max_n+10];
std::vector<int> to_start;
std::vector<int> has_cycle;
bool excluded[max_n+10];
bool find_cycle(int cur, bool init = true) {
if (excluded[cur]) return false;
if (!init && vis[cur] == 1) return true;
if (vis[cur] == 2) return false;
vis[cur] = 1;
for (auto nex: u_adj[cur]) {
if (find_cycle(nex, false)) return true;
}
return false;
}
void erase_dag(int cur) {
if (vis_dag[cur]) return;
vis_dag[cur] = true;
bool has_outdegree = false;
for (auto nex: adj[cur]) {
erase_dag(nex);
if (excluded[nex]) continue;
has_outdegree = true;
}
if (!has_outdegree) excluded[cur] = true;
return;
}
void reset(int start) {
memset(vis, 0, sizeof vis);
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());
}
erase_dag(0);
int cnt = 0;
for (auto start: adj[0]) {
if (excluded[start]) continue;
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);
// Find the first node with branches
int u = has_cycle[0];
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()) return false;
// 2 cycles must be found here -> incorrect assumption
cnt = 0;
for (auto start: adj[v]) {
if (start == prev) continue;
if (excluded[start]) continue;
reset(start);
vis[v] = 1;
if (find_cycle(start)) {
cnt++;
}
if (cnt >= 2) return true;
}
vis[v] = 0;
return false;
}
