Adding Articulation Point in this AlgoHub

graph/articulation_point.cpp

@@ -0,0 +1,82 @@
+/**
+ * Articulation Point in a Graph is a point
+ * that if we remove that then our graph is divided into more
+ * than one component.
+ * In other words, it is a point that if we remove it
+ * then the graph becomes disconnected.
+ *
+ * This algorithm is based on DFS and it is similar
+ * to finding bridges in a graph.
+ *
+ * Where is this concept used?
+ * 1. In network design, to find critical nodes in a network.
+ * 2. In social networks, to find influential people.
+ * 3. In transportation, to find critical junctions in a road network.
+ * 4. In software engineering, to find critical modules in a software system.
+ */
+
+#include <iostream>
+#include <set>
+#include <vector>
+
+using namespace std;
+
+vector<vector<int>> adj;
+vector<int> dist, low;
+vector<bool> visited;
+set<int> articulationPoints;
+int timer;
+void dfs(int u, int parent);
+
+int main() {
+    int n, m;
+    cin >> n >> m;
+    adj.resize(n);
+    dist.resize(n);
+    low.resize(n);
+    visited.resize(n, false);
+    for (int i = 0; i < m; i++) {
+        int u, v;
+        cin >> u >> v;
+        adj[u].push_back(v);
+        adj[v].push_back(u);
+    }
+    timer = 0;
+    for (int i = 0; i < n; i++) {
+        if (!visited[i]) {
+            dfs(i, -1);
+        }
+    }
+    cout << "Articulation Points:" << endl;
+    for (auto x : articulationPoints) {
+        cout << x << " ";
+    }
+    cout << endl;
+    return 0;
+}
+
+void dfs(int u, int parent) {
+    visited[u] = true;
+    dist[u] = low[u] = timer++;
+    int children = 0;
+    for (int v : adj[u]) {
+        if (v == parent)  // if v is parent of u then ignore it
+            continue;
+        if (visited[v]) {  // if v is already visited then it is a back edge
+            // back edge
+            low[u] = min(low[u], dist[v]);
+        } else {  // else it is a tree edge
+            dfs(v, u);
+            low[u] = min(low[u], low[v]);
+            // this is articulation point in case of non root node
+            if (low[v] >= dist[u] && parent != -1) {
+                articulationPoints.insert(u);
+            }
+            children++;
+        }
+    }
+    // root case
+    if (parent == -1 && children > 1) {
+        articulationPoints.insert(u);
+    }
+}