From 354fd0c745c6719744c0ea388c62739b10af40d4 Mon Sep 17 00:00:00 2001
From: puneet1747 <puneet807dhanuka@gmail.com>
Date: Fri, 8 Oct 2021 11:17:49 +0530
Subject: [PATCH] Added bridges code

---
 Graphs Algos/Bridges.cpp | 59 ++++++++++++++++++++++++++++++++++++++++
 Graphs Algos/README.md   |  2 +-
 README.md                |  1 +
 3 files changed, 61 insertions(+), 1 deletion(-)
 create mode 100644 Graphs Algos/Bridges.cpp

diff --git a/Graphs Algos/Bridges.cpp b/Graphs Algos/Bridges.cpp
new file mode 100644
index 0000000..8befbbb
--- /dev/null
+++ b/Graphs Algos/Bridges.cpp	
@@ -0,0 +1,59 @@
+// Find bridges in an undirected graph
+vector<pair<int, int>> bridge;
+vector<int> low(n, 0), disc(n, 0);
+int timer = 1;
+
+void dfs_bridge(int cur, int prev) // Run this for each connected component
+{
+    disc[cur] = low[cur] = timer++;
+    for (int next : adj[cur])
+    {
+        if (disc[next] == 0)
+        {
+            dfs_bridge(next, cur);
+            low[curr] = min(low[curr], low[next]);
+        }
+        else if (next != prev) // Back edges can never be bridges, so we have to check only tree edges
+        {
+            low[curr] = min(low[curr], disc[next]); //checking backedge with its ancestor node, and not parent node bcz we are considering parent child as current edge
+        }
+
+        if (low[next] > disc[cur])
+            bridge.push_back({cur, next});
+    }
+}
+/*
+Example :
+Problem - https://leetcode.com/problems/critical-connections-in-a-network/
+Solution : 
+class Solution {
+public:
+    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
+        disc = vector<int>(n);
+        low = vector<int>(n);
+        for (auto conn : connections) {
+            edgeMap[conn[0]].push_back(conn[1]);
+            edgeMap[conn[1]].push_back(conn[0]);
+        }
+        dfs(0, -1);
+        return ans;
+    }
+    void dfs(int curr, int prev) {
+        disc[curr] = low[curr] = time++;
+        for (int next : edgeMap[curr]) {
+            if (disc[next] == 0) {
+                dfs(next, curr);
+                low[curr] = min(low[curr], low[next]);
+            } else if (next != prev)    //if visited, but not parent, can be ancestor (back edge)
+                low[curr] = min(low[curr], disc[next]); //min of ancestoe in time(or discovery)
+            if (low[next] > disc[curr]) //if child ka low time should be greater than in time of parent , tabhi cycle mai nahe rahenga
+                ans.push_back({curr, next});
+        }
+    }
+private:
+    vector<int> disc{0}, low{0};
+    int time = 1;
+    vector<vector<int>> ans;
+    unordered_map<int, vector<int>> edgeMap;
+};
+*/
\ No newline at end of file
diff --git a/Graphs Algos/README.md b/Graphs Algos/README.md
index a91981f..ea7d733 100644
--- a/Graphs Algos/README.md	
+++ b/Graphs Algos/README.md	
@@ -28,7 +28,7 @@
 - Branch and bound
 - and many approxiation algorithms
 
-### 6) Bridges 
+### 6) Bridges ✔️
 - DFS No of Components ✔️
 
 ### 7) Articulation points
diff --git a/README.md b/README.md
index 3fbf12c..dc1f17c 100644
--- a/README.md
+++ b/README.md
@@ -112,6 +112,7 @@ This Repo is For those who want to contribute in an open Source Repo for Hacktob
     ├── bfs-shorteat-path-grid.cpp
     ├── bfs-shortest-path-list.cpp
     ├── bipartite-graph-dfs.cpp
+    ├── bridges.cpp
     ├── cycles-one-dfs.cpp
     ├── dfs-recursion-list.cpp
     ├── dijkstra-shortest-path-dfs.cpp