Add more example usages (#137)

* add better example usages

* [auto-verifier] verify commit c67f8d7

* format and golf

* [auto-verifier] verify commit 6580c6f

* more golf and format

---------

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

Author: lrvideckis

.verify-helper/timestamps.remote.json

@@ -52,7 +52,7 @@
 "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/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/cuts_callback.test.cpp": "2025-06-23 04:33:28 -0600",
+"tests/library_checker_aizu_tests/graphs/cuts_callback.test.cpp": "2025-06-23 18:22:23 -0600",
 "tests/library_checker_aizu_tests/graphs/dijkstra_aizu.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/dijkstra_lib_checker.test.cpp": "2024-12-14 19:50:29 -0600",
 "tests/library_checker_aizu_tests/graphs/directed_cycle.test.cpp": "2025-02-10 23:30:47 -0700",

library/graphs/bridges_cuts/cuts_callback.hpp

@@ -3,10 +3,31 @@
 //! @code
 //!   {
 //!     vector<vector<int>> adj(n);
-//!     cuts_callback(adj, [&](const vi& nodes) {});
+//!     vector<pii> edges(m);
+//!     UF uf(n);
+//!     cuts_callback(adj, [&](const vi& nodes) {
+//!       if (sz(nodes) > 2)
+//!         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;
+//!       }
 //!   }
+//!
 //!   vector<basic_string<int>> adj(n);
+//!   vector<basic_string<array<int, 2>>> adj_edge_ids(n);
+//!   vector<bool> seen(m);
 //!   cuts_callback(adj, [&](const vi& nodes) {
+//!     rep (i, 0, sz(nodes) - 1)
+//!       for (auto [u, e_id] : adj_edge_ids[nodes[i]])
+//!         if (!seen[e_id]) {
+//!           seen[e_id] = 1;
+//!           // this edge is in the current BCC
+//!         }
 //!   });
 //! @endcode
 //! callback not called on components with a single node