1192. Critical Connections in a Network.cpp

1192. Critical Connections in a Network.cpp

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+//Tarjan's algorithm, find bridge
+//https://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/
+//https://www.geeksforgeeks.org/bridge-in-a-graph/
+//https://www.quora.com/q/competitiveprogramming2/Cut-Vertex-Articulation-point
+//Runtime: 1356 ms, faster than 35.79% of C++ online submissions for Critical Connections in a Network.
+//Memory Usage: 167.3 MB, less than 79.16% of C++ online submissions for Critical Connections in a Network.
+class Solution {
+public:
+    void bridgeUtil(int cur, vector<vector<int>>& adj, vector<bool>& visited, vector<int>& disc, vector<int>& low, vector<int>& parent, int& time, vector<vector<int>>& edges){
+        visited[cur] = true;
+        disc[cur] = low[cur] = time++;
+
+        // cout << "discover " << cur << " at " << disc[cur] << endl;
+        // cout << cur << " has " << adj[cur].size() << " neighbors." << endl;
+
+        for(int nei : adj[cur]){
+            if(!visited[nei]){
+                parent[nei] = cur;
+                bridgeUtil(nei, adj, visited, disc, low, parent, time, edges);
+                /*
+                low[cur]: earliest visited vertex reachable 
+                from subtree rooted with cur
+                
+                because nei is a subtree of cur,
+                so we can update low[cur] with low[nei]
+                if low[nei] is smaller
+                */
+                low[cur] = min(low[cur], low[nei]);
+                // if(low[cur] == low[nei]) cout << "through low[" << nei << "], low[" << cur << "]: " << low[cur] << endl;
+
+                /*
+                cur has a subtree rooted at nei,
+                and nei cannot go to cur or 
+                its ancestor through back edge
+                */
+                if(low[nei] > disc[cur]){
+                    edges.push_back({cur, nei});
+                }
+            }else if(nei != parent[cur]){
+                //not understand?
+                low[cur] = min(low[cur], disc[nei]);
+                // if(low[cur] == disc[nei]) cout << "through disc[" << nei << "], low[" << cur << "]: " << low[cur] << endl;
+            }
+        }
+    };
+
+    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
+        //adjacency list
+        vector<vector<int>> adj(n);
+
+        for(vector<int>& conn : connections){
+            //undirected graph
+            adj[conn[0]].push_back(conn[1]);
+            adj[conn[1]].push_back(conn[0]);
+        }
+
+        vector<bool> visited(n, false);
+        vector<int> disc(n);
+        //earliest visited vertex reachable from subtree rooted with v
+        vector<int> low(n);
+        vector<int> parent(n, -1);
+
+        vector<vector<int>> edges;
+
+        for(int i = 0; i < n; ++i){
+            if(!visited[i]){
+                // cout << "visit " << i << endl;
+                int time = 0;
+                bridgeUtil(i, adj, visited, disc, low, parent, time, edges);
+            }
+        }
+
+        return edges;
+    }
+};