Update italiano's query and remove methods

algorithm/italiano.h

@@ -3,12 +3,11 @@
 
 #include "algorithm/roditty_zwick.h"
 #include "algorithm/tarjan.h"
-#include "tree/breadth_first_tree.h"
+#include "graph/breadth_first_tree.h"
 
 #include <forward_list>
 
 using namespace graph;
-using namespace tree;
 
 namespace algo {
 
@@ -25,60 +24,59 @@ public:
 private:
   Digraph<T> G;
 
-  // Connect each vertex with its representative SCC
-  std::map<T, SCC<T>> TC;
+  // Transitive closure matrix, used to answer reachability queries in O(1)
+  std::map<T, std::map<T, bool>> TC;
 
-  // Reachability trees
-  std::map<T, std::set<T>> RT;
+  // Each vertex's reachability tree
+  std::map<T, BreadthFirstTree<T>> RT;
 
   // Incoming / Outgoing edges
   struct Edges {
-    std::forward_list<T> Ein;
-    std::forward_list<T> Eout;
+    std::forward_list<T> inc;
+    std::forward_list<T> out;
   };
-  std::map<SCC<T>, Edges> E;
+  std::map<T, Edges> E;
 };
 
 
 template<typename T>
 void Italiano<T>::init() {
-
+  for (const auto& u : std::views::keys(G.adjMatrix)) {
+    for (const auto& v : G.adjMatrix[u]) {
+      E[v].inc.push_front(u);
+      E[u].out.push_front(v);
+      TC[u][v] = false;
+    }
+    RT[u] = BreadthFirstTree(G, u);
+    TC[u][u] = true;
+    for (const auto& v : std::views::keys(RT[u].adjMatrix)) {
+      TC[u][v] = true;
+    }
+  }
 }
 
 template<typename T>
 bool Italiano<T>::query(const T& u, const T& v) {
-  return TC[u] == TC[v];
+  return TC[u][v];
 }
 
 template<typename T>
 void Italiano<T>::remove(const T& u, const T& v) {
-
-  for (const auto& w : G.adjMatrix) {
-    // Check if (u,v) edge of T(w) || p(w,v) points to (u,v)
-
-    // If yes => set p(w, v) to point to the next edge (u',v) in Ein(v)
-    // If (u,v) the last edge, then set it to point to null
-
-    // If T(w) contains u' then the new edge reconnects v to T(w)
-    // As this needs to be checked, we set R(w) <- {v}
-
-    // If (u,v) is not edge of T(w) or is the last edge in Ein(v), R(w) <- phi
-
-    // Remove (u,v) from Eout(u) and Ein(v)
+  std::map<T, std::set<T>> R;
+  for (const auto& w : std::views::keys(G.adjMatrix)) {
+    if (RT[w].contains(u, v)) {
+      R[w].insert(v);
+    }
+    E[u].inc.remove(v);
+    E[u].out.remove(u);
+    G.remove(u, v);
   }
 
-  for (const auto& w : G.adjMatrix) {
-
-    // Check tentative pointers of the vertices in R(w).
-    // While there is a vertex x in R(w), scan the edges in Ein(x), starting
-    // from the edge pointed to by p(w,x), until an edge (u',x) for which
-    // p(w,u') != null is found or Ein(x) is exhausted.
-
-    // If such edge is found, x is removed from R(w).
-    // If the list is exhausted, set p(w,x) to null and M(w,x) to 0
-
-    // Then scan all Eout(x). If (x,x') is tree edge, add x' to R(w)
-  }
+  //for (const auto& w : std::views::keys(G.adjMatrix)) {
+  //  while (R[w].size() > 0) {
+  //    auto pop = R[w].
+  //  }
+  //}
 }
 
 } // namespace algo