Added Detect Cycle in Directed Graph using DFS with clear comments

Algorithms/DetectCycleInDirectedGraph.cpp

@@ -0,0 +1,63 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// Function to check if a cycle exists using DFS
+bool dfs(int node, vector<int> adj[], vector<int> &visited, vector<int> &recStack) {
+    visited[node] = 1;      // Mark the current node as visited
+    recStack[node] = 1;     // Add this node to the recursion stack
+
+    // Visit all adjacent vertices
+    for (auto neighbor : adj[node]) {
+        // If the neighbor is not visited, do a DFS on it
+        if (!visited[neighbor]) {
+            if (dfs(neighbor, adj, visited, recStack)) {
+                return true; // Found a cycle
+            }
+        }
+        // If the neighbor is already in recursion stack → cycle found
+        else if (recStack[neighbor]) {
+            return true;
+        }
+    }
+
+    // Remove the node from recursion stack before returning
+    recStack[node] = 0;
+    return false;
+}
+
+// Function to check if the directed graph has a cycle
+bool isCyclic(int V, vector<int> adj[]) {
+    vector<int> visited(V, 0);
+    vector<int> recStack(V, 0);
+
+    // Check each node (for disconnected graphs)
+    for (int i = 0; i < V; i++) {
+        if (!visited[i]) {
+            if (dfs(i, adj, visited, recStack)) {
+                return true; // If cycle found
+            }
+        }
+    }
+    return false; // No cycle
+}
+
+int main() {
+    int V, E;
+    cout << "Enter number of vertices and edges: ";
+    cin >> V >> E;
+
+    vector<int> adj[V];
+    cout << "Enter edges (u -> v):\n";
+    for (int i = 0; i < E; i++) {
+        int u, v;
+        cin >> u >> v;
+        adj[u].push_back(v); // Directed edge
+    }
+
+    if (isCyclic(V, adj))
+        cout << "Cycle detected in the graph.\n";
+    else
+        cout << "No cycle found in the graph.\n";
+
+    return 0;
+}

Algorithms/Quick_sort.cpp

@@ -1,4 +1,4 @@
-#include <iostream>
+TT#include <iostream>
 #include <vector>
 #include <algorithm> // Required for std::swap