//Detect if there is odd cycle in an undirected graph. We can do this easily by maintaining 2-color information while doing
//a DFS search. Every new node gets the opposite color of its predecessor. Then any non-tree edge with both endpoints with
//the same color will prove the existance of an odd cycle.
import java.util.*;
import java.io.*;
class Graph{
LinkedList adj[]; //adjacency list representation
int V; //number of vertices in the graph
boolean oddCycle;
int[] color;
Graph(int v){
this.V = v;
adj = new LinkedList[v];
for(int i=0; i < v; i++){
adj[i] = new LinkedList();
}
color = new int[v];
Arrays.fill(color, 0);
}
void addEdge(int u, int v){
adj[u].add(v);
adj[v].add(u);
}
boolean hasOddCycle(){
return oddCycle;
}
void dfs(int u, int vcolor){
if(color[u] != 0){
if(color[u] != vcolor){
oddCycle = true;
}
return;
}
color[u] = vcolor; //mark vertex with designated color
for(int v : adj[u]){
dfs(v, 3-vcolor); //call dfs with alternate color to paint adjacent vertices with different colors
}
}
void detectOddCycle(){
for(int i=0; i < V; i++){
if(color[i] == 0) //dfs on every unvisited vertices
dfs(i,1);
}
}
}
public class OddCycle{
public static void main(String[] args){
Graph g = new Graph(5);
g.addEdge(0,4);
g.addEdge(0,1);
g.addEdge(1,2);
g.addEdge(2,3);
g.addEdge(0,3);
g.addEdge(1,3);
g.detectOddCycle();
System.out.println("Graph has odd cycle: " + g.hasOddCycle());
}
}