Update italiano::remove

algorithm/italiano.h

@@ -38,7 +38,6 @@ private:
   std::map<T, Edges> E;
 };
 
-
 template<typename T>
 void Italiano<T>::init() {
   for (const auto& u : std::views::keys(G.adjMatrix)) {
@@ -62,21 +61,45 @@ bool Italiano<T>::query(const T& u, const T& v) {
 
 template<typename T>
 void Italiano<T>::remove(const T& u, const T& v) {
-  std::map<T, std::set<T>> R;
+  std::map<T, std::forward_list<T>> R;
   for (const auto& w : std::views::keys(G.adjMatrix)) {
-    if (RT[w].contains(u, v)) {
-      R[w].insert(v);
+    if (RT[w].contains(u, v) &&
+        std::distance(E[w].inc.begin(), E[w].inc.end()) > 1) {
+      if (E[v].inc.front() == u) {
+        E[v].inc.pop_front();
+        R[w].push_front(E[v].inc.front());
+        E[v].inc.push_front(u);
+      } else {
+        R[w].push_front(E[v].inc.front());
+      }
     }
-    E[u].inc.remove(v);
-    E[u].out.remove(u);
-    G.remove(u, v);
   }
+  E[u].inc.remove(v);
+  E[u].out.remove(u);
+  G.remove(u, v);
 
-  //for (const auto& w : std::views::keys(G.adjMatrix)) {
-  //  while (R[w].size() > 0) {
-  //    auto pop = R[w].
-  //  }
-  //}
+  for (const auto& w : std::views::keys(G.adjMatrix)) {
+    bool hooked = false;
+    // R contains all vertices that need a hook-parent
+    while (!R[w].empty()) {
+      // z is a candidate hook-parent if it is in RT[w]
+      const auto& toHook = R[w].front();
+      for (const auto& z : E[toHook].inc) {
+        if (RT[w].contains(u, z)) {
+          R[w].remove(toHook);
+          hooked = true;
+          break;
+        }
+      }
+      if (!hooked) {
+        TC[w][toHook] = false;
+        for (const auto& z : E[toHook].out) {
+          if (RT[w].contains(toHook, z))
+            R[w].push_front(z);
+        }
+      }
+    }
+  }
 }
 
 } // namespace algo