Add base paper and tarjan's SCC algorithm

algorithm/tarjan.h

@@ -0,0 +1,74 @@
+#ifndef TARJAN_H_
+#define TARJAN_H_
+
+#include "graph/graph.h"
+using namespace graph;
+
+#include <stack>
+#include <iostream>
+#include <ranges>
+#include <iterator>
+#include <algorithm>
+
+namespace algorithm {
+
+template<typename T>
+class Tarjan {
+public:
+  Tarjan(Graph<T> G) : G(G) {}
+
+  void findSCC();
+
+  void strongConnect(Vertex<T>& v);
+
+  std::uint16_t index = 0;
+  std::stack<Vertex<T>> S;
+private:
+  Graph<T> G;
+};
+
+template<typename T>
+void Tarjan<T>::strongConnect(Vertex<T>& v) {
+  v.index, v.lowlink = index++;
+  v.onStack = true;
+  S.push(v);
+
+  for (auto& w : v.edges) {
+    if (w.index == -1) {
+      // successor w has not yet been visited, recurse on it
+      strongConnect(w);
+      v.lowlink = std::min(v.lowlink, w.lowlink);
+    } else if (w.onStack) {
+      // successor w is in stack S and hence in the current SCC
+      // if w is not on stack, then (v, w) is an edge pointing to an SCC
+      // already found and must be ignored
+      v.lowlink = std::min(v.lowlink, w.index);
+    }
+  }
+
+  // if v is a root node, pop the stack and generate an SCC
+  if (v.lowlink = v.index) {
+    // start a new SCC
+    Vertex<T> w;
+    do {
+      w = S.top();
+      S.pop();
+      // add w to current SCC
+
+    } while (w != v);
+  }
+}
+
+template<typename T>
+void Tarjan<T>::findSCC() {
+
+  for (auto& vertex : G.vertices) {
+    if (vertex.index == -1) {
+      strongConnect(vertex);
+    }
+  }
+}
+
+} // namespace algorithm
+
+#endif