REQUIREMENTS: 1. Using Python, you will write a program called dfs-stack.py that implements Algorithm 2.3 (p. 49): Graph depth-first search (DFS) with a stack. 2. 3. You will not use an adjacency list, as indicated in Algorithm 2.3. Instead, you will use an adjacency matrix (i.e., a two-dimensional array, or, in Python, a list of lists). You may use ANY list method you wish (e.g., append, pop, etc.). IMPLEMENTATION DETAILS: 1. Based upon the REQUIREMENTS above, along with the IMPLEMENTATION DETAILS (i.e., this section), you MUST first develop an algorithmic solution using pseudocode. This includes both your logic (in pseudocode) and the logic presented in the pseudocode indicated in Algorithm 2.3. 2. Be sure to include your name, along with the Certificate of Authenticity, as comments at the very beginning of your Python code. Also, if you collaborated with others, be sure to state their names as well. 3. Your program should begin by prompting the user for the number of vertices, V, in the graph, G. 4. Your program will represent the graph G using an adjacency matrix, which is a square matrix with a row and a column for each vertex. Thus, your program will need to create a matrix M that consists of a VxVtwo-dimensional array -- in Python, a list of lists. (I recommend that your program initialize each element of the matrix equal to zero.) 5. Next, your program should prompt the user to indicate which elements in the matrix should be assigned the value of 1 (i.e., information about vertices). Recall that each element in the matrix is the intersection of a row and a column. 6. 7. 8. 9. The result of steps 3, 4, and 5 should be an adjacency matrix representation of a graph, G. At this point, your program should print the newly-created adjacency matrix on the screen. Next, your program should prompt the user to specify node -- i.e., the starting vertex in G. From here, you then proceed with the implementation of Algorithm 2.3, with the following enhancements: Be sure to use the newly-created adjacency matrix, instead of an adjacency list. Immediately following line 5 (but before line 6) of Algorithm 2.3, your program should print the values currently on the stack. At the end of the while block, your program should print the values currently on the stack. In effect, the result of step 9 above should be a display of the stack evolution for your implementation of the DFS algorithm on graph G.

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
icon
Related questions
Question
Python please thank you
**REQUIREMENTS:**

1. Using Python, write a program called `dfs-stack.py` to implement Algorithm 2.3 (p. 49): Graph depth-first search (DFS) with a stack.
2. Do not use an adjacency list, as indicated in Algorithm 2.3. Instead, use an adjacency matrix (i.e., a two-dimensional array or, in Python, a list of lists).
3. You may use any list method you wish (e.g., append, pop, etc.).

**IMPLEMENTATION DETAILS:**

1. Based on the requirements above and the implementation details in this section, first develop an algorithmic solution using pseudocode. This includes both your logic (in pseudocode) and the logic presented in the pseudocode indicated in Algorithm 2.3.
2. Include your name and the Certificate of Authenticity as comments at the very beginning of your Python code. If you collaborated with others, include their names as well.
3. Begin by prompting the user for the number of vertices, \( V \), in the graph, \( G \).
4. Represent the graph \( G \) using an adjacency matrix— a square matrix with a row and a column for each vertex. Create a matrix \( M \) that consists of a \( V \times V \) two-dimensional array (in Python, a list of lists). Initialize each element of the matrix to zero.
5. Prompt the user to indicate which elements in the matrix should be assigned the value of 1 (i.e., information about vertex connections). Each element in the matrix is the intersection of a row and a column.
6. Steps 3, 4, and 5 should create an adjacency matrix representation of the graph, \( G \). Print the newly-created adjacency matrix on the screen.
7. Prompt the user to specify a node—i.e., the starting vertex in \( G \).
8. Proceed with the implementation of Algorithm 2.3, with the following enhancements:
   - Use the newly-created adjacency matrix instead of an adjacency list.
   - Immediately following line 5 (but before line 6) of Algorithm 2.3, print the values currently on the stack.
   - At the end of the while block, print the values currently on the stack.

In effect, the result of step 9 above should display the stack evolution for your implementation of the DFS algorithm on graph \( G \).
Transcribed Image Text:**REQUIREMENTS:** 1. Using Python, write a program called `dfs-stack.py` to implement Algorithm 2.3 (p. 49): Graph depth-first search (DFS) with a stack. 2. Do not use an adjacency list, as indicated in Algorithm 2.3. Instead, use an adjacency matrix (i.e., a two-dimensional array or, in Python, a list of lists). 3. You may use any list method you wish (e.g., append, pop, etc.). **IMPLEMENTATION DETAILS:** 1. Based on the requirements above and the implementation details in this section, first develop an algorithmic solution using pseudocode. This includes both your logic (in pseudocode) and the logic presented in the pseudocode indicated in Algorithm 2.3. 2. Include your name and the Certificate of Authenticity as comments at the very beginning of your Python code. If you collaborated with others, include their names as well. 3. Begin by prompting the user for the number of vertices, \( V \), in the graph, \( G \). 4. Represent the graph \( G \) using an adjacency matrix— a square matrix with a row and a column for each vertex. Create a matrix \( M \) that consists of a \( V \times V \) two-dimensional array (in Python, a list of lists). Initialize each element of the matrix to zero. 5. Prompt the user to indicate which elements in the matrix should be assigned the value of 1 (i.e., information about vertex connections). Each element in the matrix is the intersection of a row and a column. 6. Steps 3, 4, and 5 should create an adjacency matrix representation of the graph, \( G \). Print the newly-created adjacency matrix on the screen. 7. Prompt the user to specify a node—i.e., the starting vertex in \( G \). 8. Proceed with the implementation of Algorithm 2.3, with the following enhancements: - Use the newly-created adjacency matrix instead of an adjacency list. - Immediately following line 5 (but before line 6) of Algorithm 2.3, print the values currently on the stack. - At the end of the while block, print the values currently on the stack. In effect, the result of step 9 above should display the stack evolution for your implementation of the DFS algorithm on graph \( G \).
### Algorithm 2.3: Graph Depth-First Search with a Stack

**StackDFS**(G, node) → visited

**Input**: 
- \( G = (V, E) \), a graph
- *node*, the starting vertex in \( G \)

**Output**: 
- *visited*, an array of size \(|V|\) such that *visited[i]* is true if we have visited node *i*, false otherwise

1. \( S \leftarrow \) CreateStack()
2. *visited* \( \leftarrow \) CreateArray(\(|V|\))
3. for \( i \leftarrow 0 \) to \(|V|\) do
4.   *visited[i]* \( \leftarrow \) false
5. Push(\( S, \) *node*)
6. while not IsStackEmpty(\( S \)) do
7.   \( c \leftarrow \) Pop(\( S \))
8.   *visited[c]* \( \leftarrow \) true
9.   foreach \( v \) in AdjacencyList(\( G, c \)) do
10.    if not *visited[v]* then
11.     Push(\( S, \) *v*)
12. return *visited*

This pseudocode describes a method for performing a Depth-First Search (DFS) on a graph using a stack data structure. The algorithm initializes a stack and a 'visited' array. It then iteratively explores the graph by marking nodes as visited and exploring their adjacent nodes. Expanding the search in this stack-based iterative manner avoids the pitfalls of recursion in environments with limited stack size.
Transcribed Image Text:### Algorithm 2.3: Graph Depth-First Search with a Stack **StackDFS**(G, node) → visited **Input**: - \( G = (V, E) \), a graph - *node*, the starting vertex in \( G \) **Output**: - *visited*, an array of size \(|V|\) such that *visited[i]* is true if we have visited node *i*, false otherwise 1. \( S \leftarrow \) CreateStack() 2. *visited* \( \leftarrow \) CreateArray(\(|V|\)) 3. for \( i \leftarrow 0 \) to \(|V|\) do 4.   *visited[i]* \( \leftarrow \) false 5. Push(\( S, \) *node*) 6. while not IsStackEmpty(\( S \)) do 7.   \( c \leftarrow \) Pop(\( S \)) 8.   *visited[c]* \( \leftarrow \) true 9.   foreach \( v \) in AdjacencyList(\( G, c \)) do 10.    if not *visited[v]* then 11.     Push(\( S, \) *v*) 12. return *visited* This pseudocode describes a method for performing a Depth-First Search (DFS) on a graph using a stack data structure. The algorithm initializes a stack and a 'visited' array. It then iteratively explores the graph by marking nodes as visited and exploring their adjacent nodes. Expanding the search in this stack-based iterative manner avoids the pitfalls of recursion in environments with limited stack size.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Stack
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education