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. 1 2 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. 1 2 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
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
Related questions
Question
Please use Java, include comments in the code, and explain what the code is doing. Problem is in the photos.
![**Title: Detecting Cycles in a Graph Using Java**
**Objective:**
This tutorial guides you through writing a Java program to detect cycles in a graph using a data file structure. This approach is particularly useful for examining connected graphs that can be represented as trees.
**Definitions:**
- **Cycle in a Graph:** This occurs if there is a back edge present. A back edge connects a node to itself (self-loop) or to one of its ancestors in the graph structure.
- **Back Edge:** An edge linking a node to an ancestor node in the tree, indicating a cycle.
**Algorithm:**
1. **Graph Creation:**
- Begin by constructing the graph using a specified number of edges and vertices.
2. **Recursive Function:**
- Implement a recursive function that accepts the current index (vertex), a visited tracker, and a recursion stack.
3. **Mark Visited Nodes:**
- As you traverse, mark the current node as visited.
- Additionally, record the node in the recursion stack.
4. **Explore Adjacent Vertices:**
- Identify all unvisited vertices adjacent to the current node.
- Recursively call the function on these vertices.
- If a recursive call detects a cycle, return `true`.
5. **Check for Back Edges:**
- If adjacent vertices are already in the recursion stack, a cycle exists. Return `true`.
6. **Wrapper Class:**
- Design a wrapper class to execute the recursive function for all vertices.
- If any vertex function returns `true`, confirm a cycle and return `true`.
7. **Cycle Absence:**
- If the function finishes and no cycles are found, return `false`.
**Graph Explanation:**
- **Adjacency List Representation:**
- Node 0: 1, 2, 3
- Node 1: 0, 2
- Node 2: 0, 1
- Node 3: 0, 4
- Node 4: 3
- **Cycle Detection Flowchart:**
- Start with `isCyclicUtil(0, -1)`, marking `vis[0] = true`.
- Move to `isCyclicUtil(1, 0)`, marking `vis[1] = true`.
- No cycle if moving back to `vis[0]` as it](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cd5838b-3f34-487e-9642-7770197fe05c%2F8a199797-f76a-4e42-b87e-81327550e68b%2Fif0rav9_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Detecting Cycles in a Graph Using Java**
**Objective:**
This tutorial guides you through writing a Java program to detect cycles in a graph using a data file structure. This approach is particularly useful for examining connected graphs that can be represented as trees.
**Definitions:**
- **Cycle in a Graph:** This occurs if there is a back edge present. A back edge connects a node to itself (self-loop) or to one of its ancestors in the graph structure.
- **Back Edge:** An edge linking a node to an ancestor node in the tree, indicating a cycle.
**Algorithm:**
1. **Graph Creation:**
- Begin by constructing the graph using a specified number of edges and vertices.
2. **Recursive Function:**
- Implement a recursive function that accepts the current index (vertex), a visited tracker, and a recursion stack.
3. **Mark Visited Nodes:**
- As you traverse, mark the current node as visited.
- Additionally, record the node in the recursion stack.
4. **Explore Adjacent Vertices:**
- Identify all unvisited vertices adjacent to the current node.
- Recursively call the function on these vertices.
- If a recursive call detects a cycle, return `true`.
5. **Check for Back Edges:**
- If adjacent vertices are already in the recursion stack, a cycle exists. Return `true`.
6. **Wrapper Class:**
- Design a wrapper class to execute the recursive function for all vertices.
- If any vertex function returns `true`, confirm a cycle and return `true`.
7. **Cycle Absence:**
- If the function finishes and no cycles are found, return `false`.
**Graph Explanation:**
- **Adjacency List Representation:**
- Node 0: 1, 2, 3
- Node 1: 0, 2
- Node 2: 0, 1
- Node 3: 0, 4
- Node 4: 3
- **Cycle Detection Flowchart:**
- Start with `isCyclicUtil(0, -1)`, marking `vis[0] = true`.
- Move to `isCyclicUtil(1, 0)`, marking `vis[1] = true`.
- No cycle if moving back to `vis[0]` as it
![```java
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
}
```
### Explanation:
This Java code is part of a program to create a directed graph using an adjacency list representation:
- **Imports**:
- `import java.io.*;`
- `import java.util.*;`
- These imports bring in I/O and utility libraries required for various operations.
- **Class Definition**: `class Graph`
- Represents a graph structure.
- **Attributes**:
- `private int V;`: Stores the number of vertices in the graph.
- `private LinkedList<Integer> adj[];`: An array of linked lists to store the adjacency list of the graph.
- **Constructor**:
- `Graph(int v)`: Initializes a new graph with `v` vertices.
- `V = v;`: Sets the number of vertices.
- `adj = new LinkedList[v];`: Initializes the adjacency list array.
- The `for` loop initializes each element of the adjacency list as a new linked list for storing neighboring vertices.
This is a foundational setup commonly used for graph data structures in computer science education, particularly for illustrating graph algorithms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cd5838b-3f34-487e-9642-7770197fe05c%2F8a199797-f76a-4e42-b87e-81327550e68b%2Fu34y0w_processed.png&w=3840&q=75)
Transcribed Image Text:```java
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
}
```
### Explanation:
This Java code is part of a program to create a directed graph using an adjacency list representation:
- **Imports**:
- `import java.io.*;`
- `import java.util.*;`
- These imports bring in I/O and utility libraries required for various operations.
- **Class Definition**: `class Graph`
- Represents a graph structure.
- **Attributes**:
- `private int V;`: Stores the number of vertices in the graph.
- `private LinkedList<Integer> adj[];`: An array of linked lists to store the adjacency list of the graph.
- **Constructor**:
- `Graph(int v)`: Initializes a new graph with `v` vertices.
- `V = v;`: Sets the number of vertices.
- `adj = new LinkedList[v];`: Initializes the adjacency list array.
- The `for` loop initializes each element of the adjacency list as a new linked list for storing neighboring vertices.
This is a foundational setup commonly used for graph data structures in computer science education, particularly for illustrating graph algorithms.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 5 images
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY