Cycle Detection in Graphs

Graphs/cycleDetectionInUndirectedGraph.cpp

@@ -0,0 +1,113 @@
+/*
+
+Detect cycle in a Un Directed Graph :
+
+What you do in DFS ?
+
+Look for back edge.
+
+Can you use the same method here ?
+
+No.
+
+Why ?
+
+When you are looking foe a back-edge in a undirected graph , obviously the parent will be counted
+i.e the node where it came from.
+But that does not contribute to a cycle in a Undirected graph.
+
+
+Approach :
+
+It's simple.Just keep checking for already visited nodes , Provided it is not the parent of the current 
+node.Then cycle exists :)
+
+*/
+
+#include<bits/stdc++.h>
+using namespace std; 
+
+bool iscyclic(int s,vector<vector<int> > &adj,vector<bool> &visited,int parent) 
+{ 
+
+    if(visited[s]==false){
+    //Mark the current node as visited and  print it 
+     visited[s]=true;
+     vector<int> :: iterator i;
+    // Recur for all the vertices adjacent  to this vertex 
+        for (i = adj[s].begin(); i != adj[s].end(); i++) 
+        { 
+            if (!visited[*i] && iscyclic(*i,adj,visited,s)) 
+            { 
+               return true;
+            } 
+            //If you find any other node other than parent that is already visited
+            else if(*i!=parent)
+            {
+                return true;
+            }
+        } 
+
+    }
+    return false;
+
+
+
+
+} 
+
+int main() 
+{ 
+    // Create a graph given in the above diagram 
+    int vertices=7;
+    //Adjacency list representation  of the graph is represented using 2-D vector
+    vector<vector<int> > adj(vertices);
+    adj[0].push_back(1);
+    adj[0].push_back(2);
+    adj[0].push_back(3);
+    adj[1].push_back(4);
+    adj[2].push_back(6);
+    adj[4].push_back(6);
+    adj[3].push_back(5);
+    vector<bool> visited(vertices,false) ;
+
+    int start=0;
+    bool cyclic=false;
+
+    //Looping if in case the graph is not connected
+    for(int i=0;i<vertices;i++){
+        if(iscyclic(i,adj,visited,-1)){
+            cyclic=true;
+            break;
+
+        }
+    }
+
+
+
+    if(cyclic==true)
+        cout<<"Cycle is present";
+    else
+        cout<<"Cycle is not present"; 
+
+    return 0; 
+} 
+/*
+
+INPUT :
+
+      1 - 4
+     /     \
+    0 -2 - 6
+     \
+      3- 5
+
+
+OUTPUT:
+
+Cycle is present
+
+
+Time Complexity: O(V+E). 
+Space Complexity : O(V).
+*/

Graphs/cycleDetectioninDirectedGraph.cpp

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+/*
+Detect cycle in a Directed Graph:
+
+When do you say a graph has a cycle ?
+
+When there is a edge(back-edge) from any of it's children to ancestors.
+
+Approach :
+
+Use a another boolean array to keep track of the nodes visited during recursion.
+While traversing if any of it's chidren is already in the recursion stack and is visited
+then the graph contains a cycle.
+
+Using DFS.
+
+
+*/
+
+#include<bits/stdc++.h>
+
+using namespace std; 
+
+bool iscyclic(int s,vector<vector<int> > &adj,vector<bool> &visited,vector<bool> &rec) 
+{ 
+
+    if(visited[s]==false){
+    //Mark the current node as visited and  print it 
+     visited[s]=true;
+     rec[s]=true;
+
+     vector<int> :: iterator i;
+    // Recur for all the vertices adjacent  to this vertex 
+        for (i = adj[s].begin(); i != adj[s].end(); i++) 
+        { 
+            if (!visited[*i] && iscyclic(*i,adj,visited,rec)) 
+            { 
+               return true;
+            } 
+            //The node is in the recursion stack
+            else if(rec[*i]==true)
+            {
+                return true;
+            }
+        } 
+
+    }
+
+    //Mark the current node in recursionn false as it has come out of the recursion stack
+    rec[s]=false;
+    return false;
+
+
+
+
+} 
+
+int main() 
+{ 
+    // Create a graph given in the above diagram 
+    int vertices=4;
+    //Adjacency list representation  of the graph is represented using 2-D vector
+    vector<vector<int> > adj(vertices);
+    adj[0].push_back(1);
+    adj[0].push_back(2);
+    adj[1].push_back(2);
+    adj[2].push_back(3);
+    adj[2].push_back(0);
+    adj[3].push_back(3);
+
+    vector<bool> visited(vertices,false) ;
+    vector<bool> rec(vertices,false) ;
+
+
+
+    int start=0;
+    bool cyclic=false;
+
+    for(int i=0;i<vertices;i++){
+        if(iscyclic(i,adj,visited,rec)){
+            cyclic=true;
+            break;
+
+        }
+    }
+
+
+
+    if(cyclic==true)
+        cout<<"Cycle is present";
+    else
+        cout<<"Cycle is not present"; 
+
+    return 0; 
+} 
+
+/*
+
+
+INPUT:
+
+
+0---->1
+
+0---->2 
+2---->0 //While you are checking for 2's (i.e from 0) neighours you will find 0 in the rec stack
+
+
+1---->2
+
+3---->3 //Self loop
+
+2---->3
+
+OUTPUT:
+
+Cycle is present
+
+
+Time Complexity: O(V+E). 
+Space Complexity : O(V).
+
+*/
+