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 6:****Consider the following graph:**![Graph Image]()``` f / \ b---c /| |\ a | | g \| |/ d---e```1. **Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.)**2. **Starting at vertex \( a \) and resolving ties by the vertex alphabetical order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack).**### Answer:(Note to students: Detailed solutions to these problems should be written below)1. **Adjacency Matrix:**| | a | b | c | d | e | f | g ||----|---|---|---|---|---|---|---|| a | 0 | 1 | 0 | 1 | 0 | 0 | 0 || b | 1 | 0 | 1 | 1 | 0 | 1 | 0 || c | 0 | 1 | 0 | 1 | 0 | 1 | 1 || d | 1 | 1 | 1 | 0 | 1 | 0 | 0 || e | 0 | 0 | 1 | 1 | 0 | 0 | 1 || f | 0 | 1 | 1 | 0 | 0 | 0 | 0 || g | 0 | 0 | 1 | 0 | 1 | 0 | 0 |2. **Adjacency Lists:** - a: {b, d} - b: {a, c, d, f} - c: {b, d, e, f, g} - d: {a, b, c, e} - e: {c, d, g} - f: {b, c} - g: {c, e}3. **Depth-First Search

The answer is given in the below step

Answered: Algorithms in pseudo code MUST be…

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 6:**

**Consider the following graph:**

![Graph Image]()

```
f
/ \
b---c
/| |\
a | | g
\| |/
d---e
```

1. **Write down the adjacency matrix and adjacency lists specifying this graph. (Assume that the matrix rows and columns and vertices in the adjacency lists follow in the alphabetical order of the vertex labels.)**

2. **Starting at vertex \( a \) and resolving ties by the vertex alphabetical order, traverse the graph by depth-first search and construct the corresponding depth-first search tree. Give the order in which the vertices were reached for the first time (pushed onto the traversal stack) and the order in which the vertices became dead ends (popped off the stack).**

### Answer:
(Note to students: Detailed solutions to these problems should be written below)

1. **Adjacency Matrix:**

| | a | b | c | d | e | f | g |
|----|---|---|---|---|---|---|---|
| a | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| b | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| c | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
| d | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
| e | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
| f | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| g | 0 | 0 | 1 | 0 | 1 | 0 | 0 |

2. **Adjacency Lists:**
- a: {b, d}
- b: {a, c, d, f}
- c: {b, d, e, f, g}
- d: {a, b, c, e}
- e: {c, d, g}
- f: {b, c}
- g: {c, e}

3. **Depth-First Search

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