From 54248a101f3e569eb421f741afed4431f0dc85c1 Mon Sep 17 00:00:00 2001
From: Amit Kumar <offamitkumar@gmail.com>
Date: Sun, 24 May 2020 11:52:29 +0530
Subject: [PATCH] feat : bridge finding with tarjan algorithm

---
 .../bridge_finding_with_tarjan_algorithm.cpp  | 79 +++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 graph/bridge_finding_with_tarjan_algorithm.cpp

diff --git a/graph/bridge_finding_with_tarjan_algorithm.cpp b/graph/bridge_finding_with_tarjan_algorithm.cpp
new file mode 100644
index 000000000..ca124f512
--- /dev/null
+++ b/graph/bridge_finding_with_tarjan_algorithm.cpp
@@ -0,0 +1,79 @@
+/*
+ *  Copyright : 2020 , MIT
+ *  Author : Amit Kumar (offamitkumar)
+ *  Last Modified Date: May 24, 2020
+ *
+ */
+#include <vector>  //  for std::vector
+#include <algorithm>  //  for min & max
+#include <iostream>  //  for cout
+using std::vector;
+using std::cout;
+using std::min;
+class Solution {
+    vector < vector < int > > graph;
+    vector<int>in_time , out_time;
+    int timer;
+    vector < vector < int > > bridge;
+    vector<bool>visited;
+    void dfs(int current_node , int parent) {
+        visited.at(current_node) = true;
+        in_time[current_node] = out_time[current_node] = timer++;
+        for ( auto&itr : graph[current_node] ) {
+            if (itr == parent) {
+                continue;
+            }
+            if (!visited[itr]) {
+                dfs(itr , current_node);
+                if (out_time[itr] > in_time[current_node]) {
+                    bridge.push_back({itr, current_node});
+                }
+            }
+            out_time[current_node] = min(out_time[current_node], out_time[itr]);
+        }
+    }
+
+ public:
+    vector <vector <int> > search_bridges(int n,
+            const vector<vector<int>>& connections) {
+        timer = 0;
+        graph.resize(n);
+        in_time.assign(n, 0);
+        visited.assign(n, false);
+        out_time.assign(n, 0);
+        for (auto&itr : connections) {
+            graph.at(itr[0]).push_back(itr[1]);
+            graph.at(itr[1]).push_back(itr[0]);
+        }
+        dfs(0, -1);
+        return bridge;
+    }
+};
+int main(void) {
+    Solution s1;
+    int number_of_node = 5;
+    vector< vector <int> >node;
+    node.push_back({0, 1});
+    node.push_back({1, 3});
+    node.push_back({1, 2});
+    node.push_back({2, 4});
+    /*
+     *     0 <--> 1 <---> 2
+     *            ^       ^
+     *            |       |
+     *            |       |
+     *            \/     \/
+     *            3       4
+     *
+     *    In this graph there are 4 bridges [0,2] , [2,4] , [3,5] , [1,2]
+     *    
+     *    I assumed that the graph is bi-directional and connected.
+     *
+     */
+    vector< vector <int> > bridges = s1.search_bridges(number_of_node , node);
+    cout << bridges.size() << " bridges found!\n";
+    for (auto&itr : bridges) {
+        cout << itr[0] << " --> " << itr[1] << '\n';
+    }
+    return 0;
+}