File size: 6,054 Bytes
1fd0050 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 | #include <iostream>
#include <vector>
#include <algorithm>
#include <stack>
#include <random>
#include <chrono>
#include <queue>
using namespace std;
const int MAXN = 500005;
const int INF = 1e9;
vector<int> adj[MAXN];
vector<int> rev_adj[MAXN]; // Reverse edges for BFS
int n, m;
int a_scores[10];
// SCC
int dfn[MAXN], low[MAXN], timer;
int scc[MAXN], scc_cnt;
bool in_stack[MAXN];
stack<int> st;
int scc_size[MAXN];
// Topological sort
int scc_rank[MAXN];
// DFS
bool visited[MAXN];
vector<int> path;
vector<int> best_path;
int cnt_visited_in_scc[MAXN];
// Heuristics
bool is_exit[MAXN];
int dist_to_exit[MAXN];
// Random
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
void tarjan(int u) {
dfn[u] = low[u] = ++timer;
st.push(u);
in_stack[u] = true;
for (int v : adj[u]) {
if (!dfn[v]) {
tarjan(v);
low[u] = min(low[u], low[v]);
} else if (in_stack[v]) {
low[u] = min(low[u], dfn[v]);
}
}
if (low[u] == dfn[u]) {
scc_cnt++;
while (true) {
int v = st.top();
st.pop();
in_stack[v] = false;
scc[v] = scc_cnt;
scc_size[scc_cnt]++;
if (u == v) break;
}
}
}
auto start_time = chrono::steady_clock::now();
bool time_limit_exceeded() {
auto curr = chrono::steady_clock::now();
return chrono::duration_cast<chrono::milliseconds>(curr - start_time).count() > 3800;
}
bool solve_dfs(int u) {
if (time_limit_exceeded()) return false;
visited[u] = true;
path.push_back(u);
int u_scc = scc[u];
cnt_visited_in_scc[u_scc]++;
if (path.size() > best_path.size()) {
best_path = path;
}
if (best_path.size() == n) return true;
int u_rank = scc_rank[u_scc];
for (int v : adj[u]) {
if (visited[v]) continue;
int v_scc = scc[v];
int v_rank = scc_rank[v_scc];
if (v_rank == u_rank) {
if (solve_dfs(v)) return true;
} else if (v_rank == u_rank + 1) {
if (cnt_visited_in_scc[u_scc] == scc_size[u_scc]) {
if (solve_dfs(v)) return true;
}
}
if (time_limit_exceeded()) break;
}
visited[u] = false;
path.pop_back();
cnt_visited_in_scc[u_scc]--;
return false;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
if (!(cin >> n >> m)) return 0;
for (int i = 0; i < 10; ++i) cin >> a_scores[i];
for (int i = 0; i < m; ++i) {
int u, v;
cin >> u >> v;
adj[u].push_back(v);
rev_adj[v].push_back(u);
}
for (int i = 1; i <= n; ++i) {
if (!dfn[i]) tarjan(i);
}
for (int i = 1; i <= scc_cnt; ++i) {
scc_rank[i] = scc_cnt - i;
}
// Identify exit nodes and compute distances
for (int u = 1; u <= n; ++u) {
dist_to_exit[u] = INF;
int r = scc_rank[scc[u]];
for (int v : adj[u]) {
if (scc_rank[scc[v]] == r + 1) {
is_exit[u] = true;
break;
}
}
}
// BFS for distances within each SCC
// We can do one global BFS if we are careful, but doing it per SCC is safer/clearer.
// Actually, we can just iterate all nodes, if is_exit push to queue.
// Then run BFS on reverse edges, but ONLY traversing edges within same SCC.
queue<int> q;
for (int u = 1; u <= n; ++u) {
if (is_exit[u]) {
dist_to_exit[u] = 0;
q.push(u);
}
}
while (!q.empty()) {
int u = q.front();
q.pop();
int u_scc = scc[u];
for (int v : rev_adj[u]) {
if (scc[v] == u_scc) { // Internal edges only
if (dist_to_exit[v] == INF) {
dist_to_exit[v] = dist_to_exit[u] + 1;
q.push(v);
}
}
}
}
// Sort adjacency lists
for (int i = 1; i <= n; ++i) {
shuffle(adj[i].begin(), adj[i].end(), rng); // Randomize initially
sort(adj[i].begin(), adj[i].end(), [&](int a, int b) {
int r_a = scc_rank[scc[a]];
int r_b = scc_rank[scc[b]];
int r_u = scc_rank[scc[i]];
// Priority 1: Rank. Prefer same rank.
bool same_rank_a = (r_a == r_u);
bool same_rank_b = (r_b == r_u);
if (same_rank_a != same_rank_b) {
return same_rank_a; // Same rank first
}
if (same_rank_a) {
// Both same rank. Prefer larger dist_to_exit.
// If dists are equal (e.g. INF), order doesn't matter.
// Note: non-exit nodes have dist > 0 (or INF). Exit nodes have dist 0.
// So sorting by dist desc puts non-exits first.
return dist_to_exit[a] > dist_to_exit[b];
} else {
// Both next rank. Prefer larger dist_to_exit in NEXT component.
// This helps choosing the best entry point for the next SCC.
return dist_to_exit[a] > dist_to_exit[b];
}
});
}
// Select start nodes
int first_scc_id = scc_cnt; // Rank 0
vector<int> starts;
for (int i = 1; i <= n; ++i) {
if (scc[i] == first_scc_id) {
starts.push_back(i);
}
}
// Sort starts by dist_to_exit descending
sort(starts.begin(), starts.end(), [&](int a, int b) {
return dist_to_exit[a] > dist_to_exit[b];
});
// Run DFS
for (int start_node : starts) {
if (solve_dfs(start_node)) break;
if (time_limit_exceeded()) break;
}
cout << best_path.size() << "\n";
for (size_t i = 0; i < best_path.size(); ++i) {
cout << best_path[i] << (i == best_path.size() - 1 ? "" : " ");
}
cout << "\n";
return 0;
} |