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A and B are sets. Create at set D with properties D (A B)
where D A and D B
Solution
import java.util.*;
import java.lang.*;
import java.io.*;
class Graph
{
int V, E; // V-> no. of vertices & E->no.of edges
Edge edge[]; // /collection of all edges
class Edge
{
int src, dest;
};
// Creates a graph with V vertices and E edges
Graph(int v,int e)
{
V = v;
E = e;
edge = new Edge[E];
for (int i=0; i<e; ++i)
edge[i] = new Edge();
}
// A utility function to find the subset of an element i
int find(int parent[], int i)
{
if (parent[i] == -1)
return i;
return find(parent, parent[i]);
}
// A utility function to do union of two subsets
void Union(int parent[], int x, int y)
{
int xset = find(parent, x);
int yset = find(parent, y);
parent[xset] = yset;
}
// The main function to check whether a given graph
// contains cycle or not
int isCycle( Graph graph)
{
// Allocate memory for creating V subsets
int parent[] = new int[graph.V];
// Initialize all subsets as single element sets
for (int i=0; i<graph.V; ++i)
parent[i]=-1;
// Iterate through all edges of graph, find subset of both
// vertices of every edge, if both subsets are same, then
// there is cycle in graph.
for (int i = 0; i < graph.E; ++i)
{
int x = graph.find(parent, graph.edge[i].src);
int y = graph.find(parent, graph.edge[i].dest);
if (x == y)
return 1;
graph.Union(parent, x, y);
}
return 0;
}
// Driver Method
public static void main (String[] args)
{
/* Let us create following graph
0
| 
| 
1-----2 */
int V = 3, E = 3;
Graph graph = new Graph(V, E);
// add edge 0-1
graph.edge[0].src = 0;
graph.edge[0].dest = 1;
// add edge 1-2
graph.edge[1].src = 1;
graph.edge[1].dest = 2;
// add edge 0-2
graph.edge[2].src = 0;
graph.edge[2].dest = 2;
if (graph.isCycle(graph)==1)
System.out.println( "graph contains cycle" );
else
System.out.println( "graph doesn't contain cycle" );
}
}

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  • 1. A and B are sets. Create at set D with properties D (A B) where D A and D B Solution import java.util.*; import java.lang.*; import java.io.*; class Graph { int V, E; // V-> no. of vertices & E->no.of edges Edge edge[]; // /collection of all edges class Edge { int src, dest; }; // Creates a graph with V vertices and E edges Graph(int v,int e) { V = v; E = e; edge = new Edge[E]; for (int i=0; i<e; ++i)
  • 2. edge[i] = new Edge(); } // A utility function to find the subset of an element i int find(int parent[], int i) { if (parent[i] == -1) return i; return find(parent, parent[i]); } // A utility function to do union of two subsets void Union(int parent[], int x, int y) { int xset = find(parent, x); int yset = find(parent, y); parent[xset] = yset; } // The main function to check whether a given graph // contains cycle or not int isCycle( Graph graph) { // Allocate memory for creating V subsets int parent[] = new int[graph.V]; // Initialize all subsets as single element sets for (int i=0; i<graph.V; ++i) parent[i]=-1;
  • 3. // Iterate through all edges of graph, find subset of both // vertices of every edge, if both subsets are same, then // there is cycle in graph. for (int i = 0; i < graph.E; ++i) { int x = graph.find(parent, graph.edge[i].src); int y = graph.find(parent, graph.edge[i].dest); if (x == y) return 1; graph.Union(parent, x, y); } return 0; } // Driver Method public static void main (String[] args) { /* Let us create following graph 0 | | 1-----2 */ int V = 3, E = 3; Graph graph = new Graph(V, E); // add edge 0-1 graph.edge[0].src = 0;
  • 4. graph.edge[0].dest = 1; // add edge 1-2 graph.edge[1].src = 1; graph.edge[1].dest = 2; // add edge 0-2 graph.edge[2].src = 0; graph.edge[2].dest = 2; if (graph.isCycle(graph)==1) System.out.println( "graph contains cycle" ); else System.out.println( "graph doesn't contain cycle" ); } }