c_cpp 查找关节点和桥梁（未定向）

Posted 2021-05-14

// doesn't matter the value, just different
#define UNVISITED -1

// need these for APB algorithm, initialized in main()
int depth, root, children;
vi lo, num, parent;

// true for index i if i identifies an articulation point
vector<bool> art_points;

// adj list representation of graph
vector<vi> adj_list;

// Find Articulation Points and Bridges
void APB(int u) {
  lo[u] = num[u] = depth++; // lo[u] <= num[u]
  for (auto &v : adj_list[u]) {

    if (num[v] == UNVISITED) {

      // tree edge
      parent[v] = u;
      if (u == root)
        children++;

      // Recurse
      APB(v);

      // articulation point
      if (lo[v] >= num[u])
        art_points[u] = true;

      // bridge
      if (lo[v] > num[u])
        cout << "Edge " << u << " -> " << v << " is a bridge\n";

      // update lo
      lo[u] = min(lo[u], lo[v]);

    } else if (v != parent[u]) {
      // back edge, not a direct cycle
      lo[u] = min(lo[u], num[v]);
    }
  }
}

void SolveForArticulationPointsAndBridges() {
  // setup adjlist
  int V;
  V = 10;

  // find articulation points and bridges
  depth = 0;
  num.assign(V, UNVISITED);
  lo.assign(V, 0);
  parent.assign(V, -1);
  art_points.assign(V, false);

  // first find bridges
  cout << "Bridges:\n";
  FOR(i, V) {
    if (num[i] == UNVISITED) {
      root = i, children = 0;
      APB(i);
      art_points[root] = (children > 1);
    }
  }

  // points
  cout << "Points:\n";
  FOR(i, V) {
    if (art_points[i])
      cout << "Vertex " << i << endl;
  }
}