add another example (#144)

* add another example

* [auto-verifier] verify commit e473ecc

* nits

* nit

---------

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": "2025-06-25 15:06:18 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp": "2025-06-25 15:06:18 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_bcc.test.cpp": "2025-06-25 15:06:18 -0600",
-"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_two_cc.test.cpp": "2025-06-25 15:06:18 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_bcc.test.cpp": "2025-07-08 18:30:57 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp": "2025-07-08 18:30:57 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_bcc.test.cpp": "2025-07-08 18:30:57 -0600",
+"tests/library_checker_aizu_tests/graphs/bcc_callback_lib_checker_two_cc.test.cpp": "2025-07-08 18:30:57 -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

@@ -27,6 +27,19 @@
 //!           bridge_tree[uf.find(i)] += uf.find(v);
 //!   }
 //!
+//!   {
+//!     // ********* IF NO MULTIPLE EDGES *********
+//!     vector<vi> adj(n);
+//!     vi cc_id(n);
+//!     bcc_callback(adj, [&](const vi& nodes) {
+//!       if (sz(nodes) == 2) {
+//!         // nodes[0] <=> nodes[1] is a bridge
+//!         return;
+//!       }
+//!       for (int v : nodes) cc_id[v] = nodes.back();
+//!     });
+//!   }
+//!
 //!   vector<basic_string<int>> adj(n);
 //!   vector<basic_string<int>> block_vertex_tree(2 * n);
 //!   int bcc_id = n;

tests/library_checker_aizu_tests/graphs/bcc_callback_aizu_two_edge_cc.test.cpp

@@ -15,16 +15,8 @@ int main() {
     adj[v] += u;
   }
   vector<pii> bridges;
-  vector<bool> seen(n);
   bcc_callback(adj, [&](const vi& nodes) {
-    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);
+    if (sz(nodes) == 2) {
       pii bridge(nodes[0], nodes[1]);
       if (bridge.first > bridge.second)
         swap(bridge.first, bridge.second);