From b92284175ec3a6f1ba5f2130c3098633eacf96a2 Mon Sep 17 00:00:00 2001
From: SankalpGupta <sankthegamer@gmail.com>
Date: Thu, 1 Oct 2020 14:42:56 +0530
Subject: [PATCH] added bridges-detection algo in graphs

---
 Graph Algorithms/Bridges-in-graph.cpp | 76 +++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)
 create mode 100644 Graph Algorithms/Bridges-in-graph.cpp

diff --git a/Graph Algorithms/Bridges-in-graph.cpp b/Graph Algorithms/Bridges-in-graph.cpp
new file mode 100644
index 0000000..8e825e8
--- /dev/null
+++ b/Graph Algorithms/Bridges-in-graph.cpp	
@@ -0,0 +1,76 @@
+// Algorithm to find the bridges in graph
+// A bridge is an edge in graph which after removing distribute the graph in connected components
+
+#include<bits/stdc++.h>
+#define ll long long int
+#define vi vector<int>
+#define vll vector<ll>
+#define vvi vector<vi>
+#define vvl vector<vll>
+#define pb push_back
+#define mp make_pair
+#define pii pair<int,int> 
+#define pll pair<ll,ll>
+#define vpii vector<pii >
+#define vpll vector<pll >
+#define ff first
+#define ss second
+#define fastio ios_base::sync_with_stdio(false) , cin.tie(NULL) ,cout.tie(NULL) 
+
+using namespace std;
+
+vi g[100001];// adjacency list
+vector<bool> vis;
+vi tin,low;
+int timer;
+
+void dfs(int v,int p=-1){
+	vis[v]=true;
+	tin[v]=low[v]=timer++;
+	for(int x:g[v]){
+		if(x==p) continue;
+		if(vis[x]){
+			low[v]=min(low[v],tin[x]);
+		}
+		else
+		{
+			dfs(x,v);
+			low[v]=min(low[v],low[x]);
+			if(low[x]>tin[v])
+			{
+				bridge_found(x,v);
+			}
+		}
+	}
+}
+
+void find_bridges(int n){
+	timer=0;
+	tin.assign(n+1,-1);
+	low.assign(n+1,-1);
+	vis.assign(n+1,false);
+	for(int i=1;i<=n;i++){
+		if(!vis[i])
+		dfs(i);
+	}
+}
+
+void bridge_found(int a,int b){
+    cout<<" The Bridge is found between "<<a<<" "<<b<<"\n";
+}
+
+int main(){
+    fastio;
+
+    int n,q; // n is number of nodes ,q is number of edges in a graph
+    cin>>n>>q;
+    while(q--){
+    	int u,v;
+    	cin>>u>>v;
+    	g[u].pb(v);
+    	g[v].pb(u);
+    }
+  
+    find_bridges(n);
+    return 0;
+}
\ No newline at end of file