Create main.cpp

Author: JawadSher

23 - Graph Data Structure Problems/17 - Critical Connections in a Network/main.cpp

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+class Solution {
+public:
+    // Helper function to perform DFS traversal and find critical connections
+    void DFS(int server, int timer, int parentServer, vector<int>& low, vector<int>& disc, vector<int>& visited, vector<vector<int>>& criticalEdge, vector<vector<int>>& connections){
+
+        // Mark the current server as visited
+        visited[server] = true;
+
+        // Set discovery time and lowest reachable time for the current server
+        disc[server] = low[server] = timer++; // timer is incremented after setting the discovery time
+        
+        // Explore all neighboring servers (connections)
+        for(int & neighbourServer : connections[server]){
+            
+            // Skip the parent server to avoid going back to the parent in the DFS tree
+            if(neighbourServer == parentServer) continue;
+
+            // If the neighboring server is not visited, explore it
+            if(!visited[neighbourServer]){
+                DFS(neighbourServer, timer, server, low, disc, visited, criticalEdge, connections);
+
+                // After visiting the neighbor, update the low time for the current server
+                low[server] = min(low[server], low[neighbourServer]);
+
+                // If the lowest time of the neighbor is greater than the discovery time of the current server,
+                // it indicates that the edge between current server and the neighbor is a critical connection.
+                if(low[neighbourServer] > disc[server]) 
+                    criticalEdge.push_back({server, neighbourServer});
+            }else {
+                // If the neighboring server was already visited, update the low time
+                low[server] = min(low[server], low[neighbourServer]);
+            }
+        }
+    }
+
+    // Main function to find all critical connections in the network
+    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
+        // Arrays to store the lowest time reachable from a server and the discovery time of each server
+        vector<int> low(n, -1);
+        vector<int> disc(n, -1);
+        
+        // Array to track if a server has been visited
+        vector<int> visited(n, false);
+
+        // To store the critical connections (edges)
+        vector<vector<int>> criticalEdge;
+
+        // Adjacency list to represent the network of servers
+        vector<vector<int>> adjacencyList(n);
+        
+        // Build the adjacency list from the connections
+        for(auto& edge : connections){
+            adjacencyList[edge[0]].push_back(edge[1]);
+            adjacencyList[edge[1]].push_back(edge[0]);
+        }
+
+        // Start DFS from each server that hasn't been visited
+        for(int i = 0; i < n; i++) 
+            if(!visited[i]) 
+                DFS(i, 0, -1, low, disc, visited, criticalEdge, adjacencyList);
+
+        // Return the list of critical connections (edges)
+        return criticalEdge;
+    }
+};