
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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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](https://content.bartleby.com/qna-images/question/4cd5838b-3f34-487e-9642-7770197fe05c/8a199797-f76a-4e42-b87e-81327550e68b/if0rav9_thumbnail.png)
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.](https://content.bartleby.com/qna-images/question/4cd5838b-3f34-487e-9642-7770197fe05c/8a199797-f76a-4e42-b87e-81327550e68b/u34y0w_thumbnail.png)
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.
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