Write a JAVA program of A Data File Structure for a connected graph that produces a tree. There is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that is joining a node to itself (self-loop) or one of its ancestor in the tree produced by Data File Structure. To find the back edge to any of its ancestor keep a visited array and if there is a back edge to any visited node then there is a loop and return true. Algorithm: 1. Create the graph using the given number of edges and vertices. 2. Create a recursive function that that current index or vertex, visited and recursion stack. 3. Mark the current node as visited and also mark the index in recursion stack. 4. Find all the vertices which are not visited and are adjacent to the current node. Recursively call the function for those vertices, if the recursive function returns true return true. 5. If the adjacent vertices are already marked in the recursion stack then return true. 6. Create a wrapper class, that calls the recursive function for all the vertices and if any function returns true, return true. 7. Else if for all vertices the function returns false return false. Adja cent list (g) 0-1,2,3 1-0, 2 2-0, 1 3- 0,4 4-3 3 v[ 0 ] is already visited and *i= parent isCyclicUtil( 0,-1), vis[0] = true isCyclicUtil(1,0), vis[ 1 ] = true 2 iscyclicutil(2,1), vis[2] = true v[ 0 ] is already visited and *i!= parent cycle found
Write a JAVA program of A Data File Structure for a connected graph that produces a tree. There is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that is joining a node to itself (self-loop) or one of its ancestor in the tree produced by Data File Structure. To find the back edge to any of its ancestor keep a visited array and if there is a back edge to any visited node then there is a loop and return true. Algorithm: 1. Create the graph using the given number of edges and vertices. 2. Create a recursive function that that current index or vertex, visited and recursion stack. 3. Mark the current node as visited and also mark the index in recursion stack. 4. Find all the vertices which are not visited and are adjacent to the current node. Recursively call the function for those vertices, if the recursive function returns true return true. 5. If the adjacent vertices are already marked in the recursion stack then return true. 6. Create a wrapper class, that calls the recursive function for all the vertices and if any function returns true, return true. 7. Else if for all vertices the function returns false return false. Adja cent list (g) 0-1,2,3 1-0, 2 2-0, 1 3- 0,4 4-3 3 v[ 0 ] is already visited and *i= parent isCyclicUtil( 0,-1), vis[0] = true isCyclicUtil(1,0), vis[ 1 ] = true 2 iscyclicutil(2,1), vis[2] = true v[ 0 ] is already visited and *i!= parent cycle found
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
Java - implement an actual graph that can be outputted using the program requirements shown in the picture. Include both comments and explanations.
![import java.io.*;
import java.util. *;
// This class represents a
// directed graph using adjacent list Representation.
class Graph
{
// No. of vertices
private int V;
// Adjacency List Representation
private LinkedList<Integer> adj [];
// Constructor
Graph (int v)
{
}
V = v;
adj = new LinkedList [v];
for (int i=0; i<v; ++i)
adj [i] new LinkedList ();
=
Your code continues below](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cd5838b-3f34-487e-9642-7770197fe05c%2F3806c04f-0099-4cad-8a50-40ed6dd95c28%2F3a6a4yp_processed.png&w=3840&q=75)
Transcribed Image Text:import java.io.*;
import java.util. *;
// This class represents a
// directed graph using adjacent list Representation.
class Graph
{
// No. of vertices
private int V;
// Adjacency List Representation
private LinkedList<Integer> adj [];
// Constructor
Graph (int v)
{
}
V = v;
adj = new LinkedList [v];
for (int i=0; i<v; ++i)
adj [i] new LinkedList ();
=
Your code continues below
![Write a JAVA program of A Data File Structure for a connected graph that produces a tree. There
is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that
is joining a node to itself (self-loop) or one of its ancestor in the tree produced by Data File
Structure.
To find the back edge to any of its ancestor keep a visited array and if there is a back edge to any
visited node then there is a loop and return true.
Algorithm:
1. Create the graph using the given number of edges and vertices.
2. Create a recursive function that that current index or vertex, visited and recursion
stack.
3. Mark the current node as visited and also mark the index in recursion stack.
4. Find all the vertices which are not visited and are adjacent to the current node.
Recursively call the function for those vertices, if the recursive function returns true
return true.
5. If the adjacent vertices are already marked in the recursion stack then return true.
6. Create a wrapper class, that calls the recursive function for all the vertices and if any
function returns true, return true.
7. Else if for all vertices the function returns false return false.
2
0
Adja cent list (g) 01, 2, 3
1-0, 2
2-0, 1
3- 0,4
4-3
3
v[ 0 ] is already
visited and *i= parent
4
isCyclicUtil( 0,-1), vis[ 0 ] = true
isCyclicUtil(1,0), vis[ 1 ] = true
2
iscyclicutil(2,1), vis[ 2 ] = true
v[ 0 ] is already visited and *i!= parent
cycle found](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cd5838b-3f34-487e-9642-7770197fe05c%2F3806c04f-0099-4cad-8a50-40ed6dd95c28%2Fpidbdk_processed.png&w=3840&q=75)
Transcribed Image Text:Write a JAVA program of A Data File Structure for a connected graph that produces a tree. There
is a cycle in a graph only if there is a back edge present in the graph. A back edge is an edge that
is joining a node to itself (self-loop) or one of its ancestor in the tree produced by Data File
Structure.
To find the back edge to any of its ancestor keep a visited array and if there is a back edge to any
visited node then there is a loop and return true.
Algorithm:
1. Create the graph using the given number of edges and vertices.
2. Create a recursive function that that current index or vertex, visited and recursion
stack.
3. Mark the current node as visited and also mark the index in recursion stack.
4. Find all the vertices which are not visited and are adjacent to the current node.
Recursively call the function for those vertices, if the recursive function returns true
return true.
5. If the adjacent vertices are already marked in the recursion stack then return true.
6. Create a wrapper class, that calls the recursive function for all the vertices and if any
function returns true, return true.
7. Else if for all vertices the function returns false return false.
2
0
Adja cent list (g) 01, 2, 3
1-0, 2
2-0, 1
3- 0,4
4-3
3
v[ 0 ] is already
visited and *i= parent
4
isCyclicUtil( 0,-1), vis[ 0 ] = true
isCyclicUtil(1,0), vis[ 1 ] = true
2
iscyclicutil(2,1), vis[ 2 ] = true
v[ 0 ] is already visited and *i!= parent
cycle found
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