feat: bridge support

src/code/graph/v_bcc.hpp

@@ -5,38 +5,52 @@
 
 namespace tifa_libs::graph {
 
-template <bool get_cut = false, bool get_belongs = true>
+template <bool get_vcut = false, bool get_ecut = false, bool get_belongs = true>
 struct v_bcc {
+  static_assert(!get_ecut || (!get_vcut && !get_belongs));
   vecu dfn, low;
   vvecu belongs;
-  vecb cut;
+  vecb vcut;
+  vecptu ecut;
 
   //! g should be undirect
   template <bool with_deg>
   CEXP v_bcc(alist<with_deg> CR g) NE : dfn(g.size()), low(g.size()) {
-    if CEXP (get_cut) cut = vecb(g.size());
+    if CEXP (get_vcut) vcut = vecb(g.size());
+    if CEXP (get_ecut) ecut.reserve(g.size());
     vecu stk;
     u32 cnt = 0, start;
     auto tarjan = [&](auto&& f, u32 u, u32 fa) -> void {
       u32 son = 0;
+      bool ecut_flag = false;
       low[u] = dfn[u] = ++cnt;
       if CEXP (get_belongs) stk.push_back(u);
       for (auto v : g[u])
         if (!dfn[v]) {
           ++son, f(f, v, u), low[u] = min(low[u], low[v]);
-          if (low[v] >= dfn[u]) {
-            if CEXP (get_cut)
-              if (u != start) cut[u] = true;
-            if CEXP (get_belongs) {
-              vecu now;
-              now.reserve(stk.size() + 1);
-              while (!stk.empty() && (now.empty() || now.back() != v)) now.push_back(stk.back()), stk.pop_back();
-              now.push_back(u), now.shrink_to_fit(), belongs.push_back(now);
+          if CEXP (get_ecut) {
+            if (low[v] > dfn[u]) ecut.emplace_back(v, u);
+          } else {
+            if (low[v] >= dfn[u]) {
+              if CEXP (get_vcut)
+                if (u != start) vcut[u] = true;
+              if CEXP (get_belongs) {
+                vecu res;
+                u32 p;
+                do res.push_back(p = stk.back()), stk.pop_back();
+                while (v != p);
+                res.push_back(u), belongs.emplace_back(std::move(res));
+              }
             }
           }
-        } else if (v != fa) low[u] = min(low[u], dfn[v]);
-      if CEXP (get_cut)
-        if (u == start && son >= 2) cut[u] = true;
+        } else {
+          if CEXP (get_ecut) {
+            if (v != fa || ecut_flag) low[u] = min(low[u], dfn[v]);
+            else ecut_flag = true;
+          } else if (v != fa) low[u] = min(low[u], dfn[v]);
+        }
+      if CEXP (get_vcut)
+        if (u == start && son >= 2) vcut[u] = true;
       if CEXP (get_belongs)
         if (!~fa && !son) belongs.push_back({u});
     };

src/test_cpverifier/aizu-grl/grl_3_a.test.cpp

@@ -11,8 +11,8 @@ int main() {
     std::cin >> u >> v;
     g.add_arc(u, v), g.add_arc(v, u);
   }
-  tifa_libs::graph::v_bcc<true, false> bcc(g);
+  tifa_libs::graph::v_bcc<true, false, false> bcc(g);
   flt_ (u32, i, 0, n)
-    if (bcc.cut[i]) std::cout << i << '\n';
+    if (bcc.vcut[i]) std::cout << i << '\n';
   return 0;
 }

src/test_cpverifier/aizu-grl/grl_3_b.test.cpp

@@ -0,0 +1,17 @@
+#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/all/GRL_3_B"
+
+#include "../../code/graph/v_bcc.hpp"
+
+int main() {
+  std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
+  u32 n, m;
+  std::cin >> n >> m;
+  tifa_libs::graph::alist g(n);
+  for (u32 i = 0, u, v; i < m; ++i) {
+    std::cin >> u >> v;
+    g.add_arc(u, v), g.add_arc(v, u);
+  }
+  tifa_libs::graph::v_bcc<false, true, false> bcc(g);
+  for (auto [v, u] : bcc.ecut) std::cout << v << ' ' << u << '\n';
+  return 0;
+}