Add operator<< for graph types, add contains query for digraph types and normalize scc

graph/scc.h

@@ -3,8 +3,6 @@
 
 #include "digraph.h"
 
-#include <ranges>
-
 namespace graph {
 
 template<typename T>
@@ -12,22 +10,34 @@ class SCC : public Digraph<T> {
 public:
   SCC() = default;
 
-  SCC(std::map<T, std::set<T>> scc)
-    : Digraph<T>::Digraph(scc) { proxy = scc.begin()->first; }
+  SCC(std::map<T, std::set<T>> G, T id) : Digraph<T>(G), id(id) { normalize(); }
 
-  //
-  T representative() { return proxy; };
+  SCC(Digraph<T> G, T id) : id(id) { normalize(); }
+
+  T id;
 
   bool operator==(const SCC& o) const;
 private:
-  // Each SCC has a representative vertex that helps
-  // answer strong connectivity queries in O(1) time
-  T proxy;
+  // For every vertex in the SCC, if there is an edge between an in-scc vertex
+  // and an out-scc vertex erase the edge between them and the out-scc vertex
+  void normalize();
 };
 
+template<typename T>
+void SCC<T>::normalize() {
+  for (const auto& u : this->adjMatrix) {
+    for (const auto& v : u.second) {
+      if (!this->adjMatrix.count(v)) {
+        this->adjMatrix[u.first].erase(v);
+        this->adjMatrix.erase(v);
+      }
+    }
+  }
+}
+
 template<typename T>
 bool SCC<T>::operator==(const SCC& o) const{
-  return proxy == o.proxy;
+  return id == o.id;
 }
 
 }; // namespace graph