File size: 4,929 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 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int n, m;
cin >> n >> m;
vector<int> a(10);
for (int i = 0; i < 10; i++) cin >> a[i]; // scoring parameters, not used in algorithm
vector<vector<int>> adj(n + 1), radj(n + 1);
vector<int> indeg(n + 1, 0), outdeg(n + 1, 0);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
adj[u].push_back(v);
radj[v].push_back(u);
outdeg[u]++;
indeg[v]++;
}
// Attempt topological sort to check if the graph is a DAG
vector<int> indeg_kahn = indeg;
queue<int> q;
for (int i = 1; i <= n; i++) {
if (indeg_kahn[i] == 0) q.push(i);
}
vector<int> topo;
while (!q.empty()) {
int u = q.front(); q.pop();
topo.push_back(u);
for (int v : adj[u]) {
if (--indeg_kahn[v] == 0) q.push(v);
}
}
// If topological sort succeeded (n vertices processed), graph is a DAG
if ((int)topo.size() == n) {
// Longest path in DAG via DP on topological order
vector<int> dp(n + 1, 1), prev(n + 1, -1);
for (int u : topo) {
for (int v : adj[u]) {
if (dp[u] + 1 > dp[v]) {
dp[v] = dp[u] + 1;
prev[v] = u;
}
}
}
// Find vertex with maximum dp value
int last = 1;
for (int i = 2; i <= n; i++) {
if (dp[i] > dp[last]) last = i;
}
// Reconstruct the path
vector<int> path;
while (last != -1) {
path.push_back(last);
last = prev[last];
}
reverse(path.begin(), path.end());
// Output
cout << path.size() << "\n";
for (size_t i = 0; i < path.size(); i++) {
if (i > 0) cout << " ";
cout << path[i];
}
cout << "\n";
return 0;
}
// Non‑DAG case: greedy heuristic with multiple starting points
// Select up to 10 candidate starting vertices
vector<bool> in_candidate(n + 1, false);
vector<int> candidates;
// 1. vertices with indegree 0 (sources)
for (int i = 1; i <= n && candidates.size() < 10; i++) {
if (indeg[i] == 0) {
candidates.push_back(i);
in_candidate[i] = true;
}
}
// 2. vertices with outdegree 0 (sinks) not already chosen
if (candidates.size() < 10) {
for (int i = 1; i <= n && candidates.size() < 10; i++) {
if (!in_candidate[i] && outdeg[i] == 0) {
candidates.push_back(i);
in_candidate[i] = true;
}
}
}
// 3. fill remaining with vertices having highest outdegree
if (candidates.size() < 10) {
vector<pair<int, int>> tmp;
for (int i = 1; i <= n; i++) {
if (!in_candidate[i]) {
tmp.emplace_back(outdeg[i], i);
}
}
sort(tmp.begin(), tmp.end(), greater<pair<int, int>>());
int need = 10 - candidates.size();
for (int i = 0; i < need && i < (int)tmp.size(); i++) {
candidates.push_back(tmp[i].second);
in_candidate[tmp[i].second] = true;
}
}
vector<int> best_path;
vector<int> last_visited(n + 1, 0);
int cur_time = 0;
// Greedy extension from both ends
auto extend = [&](int start) -> vector<int> {
cur_time++;
deque<int> path;
path.push_back(start);
last_visited[start] = cur_time;
bool extended = true;
while (extended) {
extended = false;
// Try to prepend a vertex to the front
int front = path.front();
for (int v : radj[front]) {
if (last_visited[v] != cur_time) {
path.push_front(v);
last_visited[v] = cur_time;
extended = true;
break;
}
}
if (extended) continue;
// Try to append a vertex to the back
int back = path.back();
for (int v : adj[back]) {
if (last_visited[v] != cur_time) {
path.push_back(v);
last_visited[v] = cur_time;
extended = true;
break;
}
}
}
return vector<int>(path.begin(), path.end());
};
for (int start : candidates) {
vector<int> path = extend(start);
if (path.size() > best_path.size()) {
best_path = move(path);
}
}
// Output the best path found
cout << best_path.size() << "\n";
for (size_t i = 0; i < best_path.size(); i++) {
if (i > 0) cout << " ";
cout << best_path[i];
}
cout << "\n";
return 0;
} |