From cf6ec9d9231fdbc667a8ba4bef60335bb8922a7f Mon Sep 17 00:00:00 2001
From: Karan <karandeepbatra@gmail.com>
Date: Tue, 16 Oct 2018 10:20:43 +0530
Subject: [PATCH] Add Bridge Tree

---
 Graph/BridgeTree/bridge-tree.cpp | 80 ++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100644 Graph/BridgeTree/bridge-tree.cpp

diff --git a/Graph/BridgeTree/bridge-tree.cpp b/Graph/BridgeTree/bridge-tree.cpp
new file mode 100644
index 00000000..89ab19ce
--- /dev/null
+++ b/Graph/BridgeTree/bridge-tree.cpp
@@ -0,0 +1,80 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+ 
+#define MOD                 1000000007LL
+#define EPS                 1e-9
+#define io                  ios_base::sync_with_stdio(false);cin.tie(NULL);
+#define M_PI                3.14159265358979323846
+
+const int MAXN = 1e5+5;
+vector<int> adj[MAXN], tree[MAXN];     // The bridge edge tree formed from the given graph.
+int disc[MAXN], low[MAXN], vis[MAXN];
+queue<int> Q[MAXN];
+int currTime, n, m, cmpno = 1;
+map<pair<int, int>, int> bridge;
+
+void dfs0(int u, int parent){
+    vis[u] = true;
+    disc[u] = low[u] = currTime++;
+    for(auto v : adj[u]){
+        if(v == parent)     continue;
+        if(!vis[v]){
+            dfs0(v, u);
+            low[u] = min(low[u], low[v]);
+            if(low[v] > disc[u]){
+                bridge[{u, v}] = 1;
+                bridge[{v, u}] = 1;
+            }
+        }else{
+            low[u] = min(low[u], disc[v]);
+        }
+    }
+    return;
+}
+
+bool isBridge(int u, int v){
+    return (bridge[{u, v}] == 1 && bridge[{v, u}] == 1);
+}
+
+void dfs1(int u){
+    int currcmp = cmpno;
+    Q[currcmp].push(u);
+    vis[u] = true;
+    while(!Q[currcmp].empty()){
+        int u = Q[currcmp].front();
+        Q[currcmp].pop();
+        for(auto v : adj[u]){
+            if(vis[v])  continue;
+            if(isBridge(u, v)){
+                cmpno++;
+                tree[currcmp].push_back(cmpno);
+                tree[cmpno].push_back(currcmp);
+                dfs1(v);
+            }else{
+                Q[currcmp].push(v);
+                vis[v] = true;
+            }
+        }
+    }
+    return;
+}
+
+int main(){
+    io;
+    cin >> n >> m;
+    for(int i = 0;i < m; i++){
+        int a, b;
+        cin >> a >> b;
+        adj[a].push_back(b);
+        adj[b].push_back(a);
+    }
+    dfs0(1, -1);    // To find bridges  
+    memset(vis, false, sizeof vis);
+    dfs1(1);    // To build bridge tree
+    for(int i = 1;i <= cmpno; i++){
+        for(int j = 0;j < tree[i].size(); j++)
+            cout << i << " " << tree[i][j] << endl;
+    }
+    return 0;
+}
\ No newline at end of file