Nit example init (#141)

* nits to example init

* [auto-verifier] verify commit ec84b7f

* update bridge tests

* [auto-verifier] verify commit d5b24be

* fix

* [auto-verifier] verify commit aba5e73

* I like this better

* [auto-verifier] verify commit 97a7ac3

* fix cppcheck

* [auto-verifier] verify commit 5517265

---------

Co-authored-by: GitHub <noreply@github.com>

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -50,10 +50,10 @@
 "tests/library_checker_aizu_tests/flow/dinic_aizu.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/hungarian.test.cpp": "2024-11-17 14:04:03 -0600",
 "tests/library_checker_aizu_tests/flow/min_cost_max_flow.test.cpp": "2024-12-05 10:41:42 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_bcc.test.cpp": "2025-06-23 20:35:49 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp": "2025-06-23 20:35:49 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_bcc.test.cpp": "2025-06-23 20:35:49 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_two_cc.test.cpp": "2025-06-23 20:35:49 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_bcc.test.cpp": "2025-06-24 12:22:14 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp": "2025-06-24 12:25:50 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_bcc.test.cpp": "2025-06-24 12:22:14 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_two_cc.test.cpp": "2025-06-24 12:25:50 -0600",
 "tests/library_checker_aizu_tests/graphs/biconnected_components.test.cpp": "2025-02-10 23:30:47 -0700",
 "tests/library_checker_aizu_tests/graphs/connected_components_of_complement_graph.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/dijkstra_aizu.test.cpp": "2024-12-14 19:50:29 -0600",

library/graphs/bridges_cuts/bcc_callback.hpp

@@ -3,36 +3,39 @@
 //! @code
 //!   {
 //!     vector<vector<int>> adj(n);
-//!     vector<pii> edges(m);
 //!     UF uf(n);
+//!     vector<bool> seen(n);
 //!     bcc_callback(adj, [&](const vi& nodes) {
-//!       if (sz(nodes) == 2) {
+//!       int count_edges = 0;
+//!       rep (i, 0, sz(nodes) - 1) {
+//!         seen[nodes[i]] = 1;
+//!         for (int v : adj[nodes[i]]) if (!seen[v]) {
+//!           // edge nodes[i] <=> v is in current BCC
+//!           count_edges++;
+//!         }
+//!       }
+//!       if (count_edges == 1) {
 //!         // nodes[0] <=> nodes[1] is a bridge
-//!         //   (if no multiple edges)
-//!         // if multiple edges, then join them too in uf
 //!         return;
 //!       }
 //!       for (int v : nodes) uf.join(v, nodes[0]);
 //!     });
 //!     vector<basic_string<int>> bridge_tree(n);
-//!     for (auto [u, v] : edges)
-//!       if (!uf.sameSet(u, v)) {
-//!         u = uf.find(u), v = uf.find(v);
-//!         bridge_tree[u] += v;
-//!         bridge_tree[v] += u;
-//!       }
+//!     rep (i, 0, n)
+//!       for (int v : adj[i])
+//!         if (!uf.sameSet(i, v))
+//!           bridge_tree[uf.find(i)] += uf.find(v);
 //!   }
 //!
 //!   vector<basic_string<int>> adj(n);
-//!   vector<basic_string<array<int, 2>>> adj_edge_ids(n);
-//!   vector<bool> seen(m);
+//!   vector<basic_string<int>> block_vertex_tree(2 * n);
+//!   int bcc_id = n;
 //!   bcc_callback(adj, [&](const vi& nodes) {
-//!     rep (i, 0, sz(nodes) - 1)
-//!       for (auto [v, e_id] : adj_edge_ids[nodes[i]])
-//!         if (!seen[e_id]) {
-//!           seen[e_id] = 1;
-//!           // this edge is in the current BCC
-//!         }
+//!     for (int v : nodes) {
+//!       block_vertex_tree[v] += bcc_id;
+//!       block_vertex_tree[bcc_id] += v;
+//!       bcc_id++;
+//!     }
 //!   });
 //! @endcode
 //! callback not called on components with a single node

tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp

@@ -15,11 +15,23 @@ int main() {
     adj[v] += u;
   }
   vector<pii> bridges;
+  vector<bool> seen(n);
   bcc_callback(adj, [&](const vi& nodes) {
-    assert(sz(nodes) >= 2);
-    if (sz(nodes) == 2)
-      bridges.emplace_back(min(nodes[0], nodes[1]),
-        max(nodes[0], nodes[1]));
+    int count_edges = 0;
+    rep(i, 0, sz(nodes) - 1) {
+      seen[nodes[i]] = 1;
+      count_edges += ranges::count_if(adj[nodes[i]],
+        [&](int v) -> bool { return !seen[v]; });
+    }
+    if (count_edges == 1) {
+      assert(sz(nodes) == 2);
+      pii bridge(nodes[0], nodes[1]);
+      if (bridge.first > bridge.second)
+        swap(bridge.first, bridge.second);
+      bridges.push_back(bridge);
+      // nodes[0] <=> nodes[1] is a bridge
+      return;
+    }
   });
   ranges::sort(bridges);
   for (auto [u, v] : bridges)

tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_two_cc.test.cpp

@@ -8,24 +8,26 @@ int main() {
   int n, m;
   cin >> n >> m;
   vector<basic_string<int>> adj(n);
-  for (int i = 0; i < n; i++) adj[i] += i;
-  vector<array<int, 2>> edges(m);
   for (int i = 0; i < m; i++) {
     int u, v;
     cin >> u >> v;
     adj[u] += v;
     adj[v] += u;
-    if (u > v) swap(u, v);
-    edges[i] = {u, v};
   }
   UF uf(n);
-  ranges::sort(edges);
-  for (int i = 1; i < m; i++)
-    if (edges[i - 1] == edges[i])
-      uf.join(edges[i][0], edges[i][1]);
+  vector<bool> seen(n);
   bcc_callback(adj, [&](const vi& nodes) {
-    assert(sz(nodes) >= 2);
-    if (sz(nodes) == 2) return;
+    int count_edges = 0;
+    rep(i, 0, sz(nodes) - 1) {
+      seen[nodes[i]] = 1;
+      count_edges += ranges::count_if(adj[nodes[i]],
+        [&](int v) -> bool { return !seen[v]; });
+    }
+    if (count_edges == 1) {
+      assert(sz(nodes) == 2);
+      // nodes[0] <=> nodes[1] is a bridge
+      return;
+    }
     for (int v : nodes) uf.join(v, nodes[0]);
   });
   vector<basic_string<int>> two_edge_ccs(n);