Re-adding Tarjan's SCC algorithm in correct path

graph/strongly_connected_components.cpp

@@ -0,0 +1,89 @@
+/**
+ * @file strongly_connected_components.cpp
+ * @author Kia Pousti
+ * @brief Tarjan’s Algorithm to find Strongly Connected Components (SCC) in a directed graph
+ * @date 2025-07-29
+ */
+
+#include <iostream>
+#include <vector>
+#include <stack>
+#include <algorithm>
+#include <cassert>
+
+using namespace std;
+
+class TarjanSCC {
+private:
+    int V, time;
+    vector<vector<int> > adj;
+    vector<int> disc, low;
+    vector<bool> inStack;
+    stack<int> stk;
+    vector<vector<int> > components;
+
+    void dfs(int u) {
+        disc[u] = low[u] = time++;
+        stk.push(u);
+        inStack[u] = true;
+
+        for (int v : adj[u]) {
+            if (disc[v] == -1) {
+                dfs(v);
+                low[u] = min(low[u], low[v]);
+            } else if (inStack[v]) {
+                low[u] = min(low[u], disc[v]);
+            }
+        }
+
+        if (disc[u] == low[u]) {
+            vector<int> scc;
+            int v;
+            do {
+                v = stk.top(); stk.pop();
+                inStack[v] = false;
+                scc.push_back(v);
+            } while (u != v);
+            components.push_back(scc);
+        }
+    }
+
+public:
+    TarjanSCC(int V) : V(V), time(0), adj(V), disc(V, -1), low(V, -1), inStack(V, false) {}
+
+    void addEdge(int u, int v) {
+        adj[u].push_back(v);
+    }
+
+    vector<vector<int> > getSCCs() {
+        for (int i = 0; i < V; ++i) {
+            if (disc[i] == -1)
+                dfs(i);
+        }
+        return components;
+    }
+};
+
+int main() {
+    TarjanSCC g(5);
+    g.addEdge(1, 0);
+    g.addEdge(0, 2);
+    g.addEdge(2, 1);
+    g.addEdge(0, 3);
+    g.addEdge(3, 4);
+
+    auto sccs = g.getSCCs();
+
+    // Assert the expected number of SCCs
+    assert(sccs.size() == 3);
+
+    // Print SCCs
+    cout << "Strongly Connected Components:\n";
+    for (const auto& scc : sccs) {
+        for (int node : scc)
+            cout << node << " ";
+        cout << "\n";
+    }
+
+    return 0;
+}