Create main.cpp

Author: JawadSher

23 - Graph Data Structure Problems/16 - Bridge Edge in a Graph/main.cpp

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+class Solution {
+public:
+    // Depth-First Search (DFS) function to explore the graph
+    void dfs(int node, int parent, int timer, int& result, vector<int>& visited, vector<int>& disc, vector<int>& low, vector<vector<int>>& adjacencyList, int c, int d){
+        visited[node] = true;                  // Mark the current node as visited
+        disc[node] = low[node] = timer++;     // Set discovery time and low time of the node
+        
+        // Traverse all adjacent vertices (neighbors) of the current node
+        for(int vertex : adjacencyList[node]){
+            if(vertex == parent) continue;     // Skip the parent node to avoid going backward in the DFS
+
+            if(!visited[vertex]){              // If the neighbor is unvisited, perform DFS on it
+                dfs(vertex, node, timer, result, visited, disc, low, adjacencyList, c, d);
+                low[node] = min(low[node], low[vertex]); // Update the low time of the current node
+                
+                // If low value of the neighbor is greater than the discovery time of the current node
+                // and the edge (node, vertex) is the target edge (c, d), set result to 1 (indicating it's a bridge)
+                if(low[vertex] > disc[node] && ((node == c && vertex == d) || (node == d && vertex == c))) 
+                    result = 1;
+            } else {
+                low[node] = min(low[node], disc[vertex]); // Update the low time if the neighbor is already visited
+            }
+        }
+    }
+    
+    // Function to check if the edge (c, d) is a bridge
+    int isBridge(int V, vector<int> adj[], int c, int d) {
+        vector<int> disc(V, -1); // Discovery time for each vertex (initially -1, indicating unvisited)
+        vector<int> low(V, -1);  // Lowest discovery time reachable from the vertex (initially -1)
+        vector<int> visited(V, false); // To keep track of visited nodes
+        int result = 0; // Variable to store the result (0 means no bridge, 1 means it's a bridge)
+        
+        vector<vector<int>> adjacencyList(V); // Adjacency list to represent the graph
+        
+        // Build the adjacency list from the given edge list
+        for(int i = 0; i < V; i++){
+            for(auto& vertex : adj[i]){
+                adjacencyList[i].push_back(vertex);
+            }
+        }
+        
+        // Perform DFS from every unvisited node
+        for(int i = 0; i < V; i++) 
+            if(!visited[i]) 
+                dfs(i, -1, 0, result, visited, disc, low, adjacencyList, c, d);
+        
+        return result; // Return 1 if the edge (c, d) is a bridge, else return 0
+    }
+};