Format RequirementAlgorithms in pseudo code MUST be placed in code blocks/fences, and use either the cpp or java syntax highlighter.Algorithms should follow the pseudo code standard described in handout 1. Your pseudo code should be placed in a code block, for exampleAlgorithm alg_name(a, b) { // A description of the algorithm // input: a - a positive decimal integer; b - an integer // ouput: the sum of a and b c = a + b // or, c <- a + b return c }Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmath.pdfWays enter into the math mode in Notion: https://www.notion.so/help/math-equations **Problem 1**A network topology specifies how computers, printers, and other devices are connected over a network. The figure below illustrates three common topologies of networks: the ring, the star, and the fully connected mesh.You are given a boolean matrix A[0..n-1, 0..n-1], where \( n > 3 \), which is supposed to be the adjacency matrix of a graph modeling a network with one of these topologies. Your task is to determine which of these three topologies, if any, the matrix represents. Design a brute-force algorithm for this task and indicate its time efficiency class.**Diagram Descriptions:**1. **Ring Topology:** - This diagram shows six nodes connected in a circular arrangement. Each node is connected to two other nodes, forming a closed loop.2. **Star Topology:** - This diagram depicts six nodes where one central node is directly connected to the five outer nodes. The outer nodes are not connected to each other.3. **Fully Connected Mesh Topology:** - This diagram illustrates six nodes where each node is connected to every other node. There are no isolated nodes; every node has a direct link to all other nodes in the network. ### Answer:#### Algorithm to Detect a Ring```cpp// algorithm to detect ring// input: matrix A// output: true - it is a ring, or false otherwise```#### Algorithm to Detect a Star```cpp// algorithm to detect star```#### Algorithm to Detect a Fully Connected Mesh```cpp// algorithm to detect a fully connected mesh```---### Explanation:In this exercise, we have three distinct sections, each discussing an algorithm to detect different types of network topologies based on an input matrix `A`. Below, we briefly describe the purpose of each algorithm.1. **Algorithm to Detect Ring**: - **Input**: The algorithm takes a matrix `A` as its input. This matrix likely represents the adjacency matrix of a graph. - **Output**: The output is a boolean value, where `true` indicates that the input matrix represents a ring topology, and `false` otherwise.2. **Algorithm to Detect Star**: - This section is reserved for an algorithm to detect a star topology. In a star topology, one central node is directly connected to all other nodes, and there are no other connections between the nodes. The specific details of the implementation are not provided in the text.3. **Algorithm to Detect a Fully Connected Mesh**: - This section is meant for an algorithm to determine if the input matrix represents a fully connected mesh topology. In a fully connected mesh, each node is directly connected to every other node in the network.### SummaryThese algorithms are crucial for network topology detection, an essential task in fields like computer networking and graph theory. Understanding and implementing these algorithms helps in recognizing different network structures, which can be applied for various optimizations and analyses in network management and graph-based computations.

Answered: Problem 1 A network topology specifies…

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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Format Requirement

Algorithms in pseudo code MUST be placed in code blocks/fences, and use either the cpp or java syntax highlighter.
Algorithms should follow the pseudo code standard described in handout 1.
- Your pseudo code should be placed in a code block, for example
Algorithm alg_name(a, b) { // A description of the algorithm // input: a - a positive decimal integer; b - an integer // ouput: the sum of a and b c = a + b // or, c <- a + b return c }
Do NOT change the template except the answer portion.
Formulas and equations should be in math mode using Latex math symbols.
- Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmath.pdf
- Ways enter into the math mode in Notion: https://www.notion.so/help/math-equations

**Problem 1**

A network topology specifies how computers, printers, and other devices are connected over a network. The figure below illustrates three common topologies of networks: the ring, the star, and the fully connected mesh.

You are given a boolean matrix A[0..n-1, 0..n-1], where \( n > 3 \), which is supposed to be the adjacency matrix of a graph modeling a network with one of these topologies. Your task is to determine which of these three topologies, if any, the matrix represents. Design a brute-force algorithm for this task and indicate its time efficiency class.

**Diagram Descriptions:**

1. **Ring Topology:**
- This diagram shows six nodes connected in a circular arrangement. Each node is connected to two other nodes, forming a closed loop.

2. **Star Topology:**
- This diagram depicts six nodes where one central node is directly connected to the five outer nodes. The outer nodes are not connected to each other.

3. **Fully Connected Mesh Topology:**
- This diagram illustrates six nodes where each node is connected to every other node. There are no isolated nodes; every node has a direct link to all other nodes in the network.

### Answer:

#### Algorithm to Detect a Ring
```cpp
// algorithm to detect ring
// input: matrix A
// output: true - it is a ring, or false otherwise
```

#### Algorithm to Detect a Star
```cpp
// algorithm to detect star
```

#### Algorithm to Detect a Fully Connected Mesh
```cpp
// algorithm to detect a fully connected mesh
```

---

### Explanation:

In this exercise, we have three distinct sections, each discussing an algorithm to detect different types of network topologies based on an input matrix `A`. Below, we briefly describe the purpose of each algorithm.

1. **Algorithm to Detect Ring**:
- **Input**: The algorithm takes a matrix `A` as its input. This matrix likely represents the adjacency matrix of a graph.
- **Output**: The output is a boolean value, where `true` indicates that the input matrix represents a ring topology, and `false` otherwise.

2. **Algorithm to Detect Star**:
- This section is reserved for an algorithm to detect a star topology. In a star topology, one central node is directly connected to all other nodes, and there are no other connections between the nodes. The specific details of the implementation are not provided in the text.

3. **Algorithm to Detect a Fully Connected Mesh**:
- This section is meant for an algorithm to determine if the input matrix represents a fully connected mesh topology. In a fully connected mesh, each node is directly connected to every other node in the network.

### Summary

These algorithms are crucial for network topology detection, an essential task in fields like computer networking and graph theory. Understanding and implementing these algorithms helps in recognizing different network structures, which can be applied for various optimizations and analyses in network management and graph-based computations.

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