// failed/solution-yoshiyuki-incorrect-random-branch-valid-cycle.cpp
// Incorrect attempt of O(N^2) with Monte Carlo
// After remove DAG and handle 2 separate cycles case
// Pick random node with branches, search until 2 valid cycles are found
// It choose a random shortest path between 0 and the start of the cycle
// One counter to this solution is gen_tricky_3.
// This solution MUST be WA and TLE for all values of ATTEMPT.
#include "islands.h"
#include <functional>
#include <queue>
#include <utility>
#include <set>
#include <variant>
#include <vector>
#include <cstring>
#include <cassert>
#include <cstdlib>
#include <ctime>
const int max_n = 1e5;
const int ATTEMPT = 200;
std::vector<int> adj[max_n+10];
std::set<int> u_adj[max_n+10];
int vis[max_n+10]; // 0 = unvisited, 1 = visited, 2 = invalid cycle
bool vis_dag[max_n+10];
bool vis_candidate[max_n+10];
bool vis_path[max_n+10];
std::vector<int> has_cycle;
bool excluded[max_n+10];
std::vector<std::pair<int, int> > candidate;
int prev_path[max_n+10];
// Find cycle from start of branch
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;
}
// Erase DAG / Erase node with 0 outdegree
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;
}
// Find candidates of node with branch
void find_candidate(int cur, int prev) {
if (excluded[cur]) return;
if (vis_candidate[cur]) return;
vis_candidate[cur] = true;
int cnt_branch = 0;
for (auto next: adj[cur]) {
if (next != prev && !excluded[next]) {
cnt_branch++;
find_candidate(next, cur);
}
}
if (cnt_branch >= 2) candidate.push_back({cur, prev});
return;
}
// Find "random" path from 0 to start of branch
void find_path(int start, int finish) {
memset(vis_path, false, sizeof vis_path);
memset(prev_path, -1, sizeof prev_path);
std::queue<int> BFS;
vis_path[start] = true;
BFS.push(start);
while (!BFS.empty()) {
if (vis_path[finish]) break;
int cur = BFS.front();
BFS.pop();
for (auto nex: adj[cur]) {
if (vis_path[nex]) continue;
assert(vis_path[nex] == false);
vis_path[nex] = true;
prev_path[nex] = cur;
BFS.push(nex);
}
}
int cur = finish;
while (cur != start) {
cur = prev_path[cur];
vis[cur] = 2;
}
}
void reset(int start, bool second = false) {
memset(vis, 0, sizeof vis);
if (second) {
find_path(0, start);
}
vis[start] = 1;
}
std::variant<bool, std::vector<int>> find_journey(
int N, int M, std::vector<int> U, std::vector<int> V) {
srand(time(NULL));
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++) {
std::random_shuffle(adj[i].begin(), adj[i].end());
}
erase_dag(0);
// Find 2 cycles with separate outedge from 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;
// If 0 only has 1 outedge with cycle(s)
// 2 cycles must be found here
assert(has_cycle.size() == 1);
find_candidate(has_cycle[0], 0);
random_shuffle(candidate.begin(), candidate.end());
// Find 2 cycles among candidates
int attempt = ATTEMPT;
for (auto [v, prev]: candidate) {
if (v == 0) continue;
cnt = 0;
for (auto start: adj[v]) {
if (start == prev) continue;
if (start == 0) continue;
if (vis[start] == 2) continue;
if (excluded[start]) continue;
attempt--;
reset(start, true);
vis[v] = 1;
if (find_cycle(start, true)) {
cnt++;
}
if (cnt >= 2) {
return true;
}
if (attempt == 0) return false;
}
vis[v] = 0;
if (attempt == 0) return false;
}
return false;
}
