From 97d0b71f9acbb85ac669d17643ec627deb48a7f4 Mon Sep 17 00:00:00 2001
From: MAYANK JAIN <makjn10@gmail.com>
Date: Sat, 12 Oct 2019 00:56:32 +0530
Subject: [PATCH] Added Articulation Points finding Algorithm in C++

This adds an algorithm that can be used to find the articulation points in a Graph.
---
 .../C++/articulationpoints.cpp                | 69 +++++++++++++++++++
 1 file changed, 69 insertions(+)
 create mode 100644 Graphs/Articulation_Point/C++/articulationpoints.cpp

diff --git a/Graphs/Articulation_Point/C++/articulationpoints.cpp b/Graphs/Articulation_Point/C++/articulationpoints.cpp
new file mode 100644
index 00000000..cf6d772b
--- /dev/null
+++ b/Graphs/Articulation_Point/C++/articulationpoints.cpp
@@ -0,0 +1,69 @@
+//this code can be used to find Articulation points in a Graph
+#include <bits/stdc++.h>
+using namespace std;
+
+int timee;// a variable to keep track of the time at which a particular vertex is encounterd
+
+vector<int> graph[100];//adjacency list for the graph (100 is the max number of vertices.. you can change as per your needs)
+bool visited[100] , AP[100];
+//visited - bool array used in DFS to know whether the node is visited or not
+//AP - bool array to tell whether ith vertex is a AP or NOT
+
+int disc[100] , low[100] , parent[100];
+//disc - discovery time of a vertex
+//low - exit time of a source
+//parent - array to tell the parent of ith vertex
+
+//finding all APs
+void printAP2(int source){
+	visited[source] = true;
+	disc[source] = timee++;
+	low[source] = disc[source];
+	int child = 0;
+	for(auto i : graph[source]){
+		if(!visited[i]){
+			child++;
+			parent[i] = source;
+			printAP2(i);
+			low[source] = min(low[i] , low[source]);
+			
+			if(parent[source] == source){
+				if(child > 1)	AP[source] = true;
+			}
+			else{
+				if(low[i] >= disc[source])	AP[source] = true; // IMP
+			}
+		}
+		else if(i != parent[source])	low[source] = min(low[i] , low[source]);
+	}
+}
+
+//find and print all APs
+void printAP(int n , int source){
+	for(int i = 0 ; i < n ; i++)	low[i] = INT_MAX;
+	parent[source] = source; //initializing source os source vertex to itself
+	printAP2(source);
+	for(int i = 0 ; i < n ; i++){
+		if(!visited[i]){
+			parent[i] = i;
+			printAP2(i);
+		}	
+	}
+	for(int i = 0 ; i < n ; i++){
+		if(AP[i])	cout << i << " ";
+	}
+	cout << endl;
+}
+
+int main(){
+	//n - no. of vertices , e - no. of edges
+	int n , e , u , v;
+	cin >> n >> e;
+	//inputting e edges
+	for(int i = 0 ; i < e ; i++){
+		cin >> u >> v;
+		graph[u].push_back(v);
+		graph[v].push_back(u);
+	}
+	printAP(n , 0);
+}