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QUIREMENTS: 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. 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). 3. You may use ANY list method you wish (e.g., append, pop, etc.).

QUIREMENTS: 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. 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). 3. You may use ANY list method you wish (e.g., append, pop, etc.).

Database System Concepts
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
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## Educational Text: Implementing Depth-First Search with a Stack ### Requirements 1. **Python Implementation**: Write a program named `dfs-stack.py` that executes Algorithm 2.3 for graph depth-first search (DFS) utilizing a stack. 2. **Adjacency Matrix Usage**: Do not employ an adjacency list as per Algorithm 2.3 instructions. Use an adjacency matrix instead (a two-dimensional array, or a list of lists in Python). 3. **Flexible List Methods**: Use any list method suitable for your needs (e.g., append, pop). ### Implementation Details 1. **Algorithmic Solution**: Develop an algorithmic solution using pseudocode, based on the requirements and detailed implementation steps. Include your logic and any pseudocode from Algorithm 2.3. Add a Certificate of Authenticity as comments at the start of your Python code. If you collaborated, include their names. 2. **User Input for Vertices**: Prompt the user to input the number of vertices, \( V \), for the graph, \( G \). 3. **Adjacency Matrix Representation**: Construct a square matrix for the adjacency representation—each row and column corresponds to a vertex. Initiate the matrix with zeroes. 4. **User Input for Matrix Values**: Prompt the user to assign values of 1 to specific matrix elements, indicating vertex connections. 5. **Matrix Display**: Steps 3, 4, and 5 collectively result in an adjacency matrix that represents the graph \( G \). Display this matrix. 6. **Specify Starting Vertex**: Prompt the user to determine the starting vertex in \( G \). 7. **Implement Algorithm 2.3 with Enhancements**: - Use the adjacency matrix instead of an adjacency list. - After line 5 (prior to line 6) in Algorithm 2.3, program the display of current stack values. - The while block should conclude with printing the stack’s current status. By following these steps, your application should effectively showcase the stack's evolution as the DFS algorithm is applied to graph \( G \).
Transcribed Image Text:## Educational Text: Implementing Depth-First Search with a Stack ### Requirements 1. **Python Implementation**: Write a program named `dfs-stack.py` that executes Algorithm 2.3 for graph depth-first search (DFS) utilizing a stack. 2. **Adjacency Matrix Usage**: Do not employ an adjacency list as per Algorithm 2.3 instructions. Use an adjacency matrix instead (a two-dimensional array, or a list of lists in Python). 3. **Flexible List Methods**: Use any list method suitable for your needs (e.g., append, pop). ### Implementation Details 1. **Algorithmic Solution**: Develop an algorithmic solution using pseudocode, based on the requirements and detailed implementation steps. Include your logic and any pseudocode from Algorithm 2.3. Add a Certificate of Authenticity as comments at the start of your Python code. If you collaborated, include their names. 2. **User Input for Vertices**: Prompt the user to input the number of vertices, \( V \), for the graph, \( G \). 3. **Adjacency Matrix Representation**: Construct a square matrix for the adjacency representation—each row and column corresponds to a vertex. Initiate the matrix with zeroes. 4. **User Input for Matrix Values**: Prompt the user to assign values of 1 to specific matrix elements, indicating vertex connections. 5. **Matrix Display**: Steps 3, 4, and 5 collectively result in an adjacency matrix that represents the graph \( G \). Display this matrix. 6. **Specify Starting Vertex**: Prompt the user to determine the starting vertex in \( G \). 7. **Implement Algorithm 2.3 with Enhancements**: - Use the adjacency matrix instead of an adjacency list. - After line 5 (prior to line 6) in Algorithm 2.3, program the display of current stack values. - The while block should conclude with printing the stack’s current status. By following these steps, your application should effectively showcase the stack's evolution as the DFS algorithm is applied to graph \( G \).
**Algorithm 2.3: Graph Depth-First Search with a Stack** **StackDFS(G, node) → visited** - **Input:** - \( G = (V, E) \), a graph - \( \text{node} \), the starting vertex in \( G \) - **Output:** - \( \text{visited} \), an array of size \(|V|\) such that \( \text{visited}[i] \) is TRUE if we have visited node \( i \), FALSE otherwise **Algorithm Steps:** 1. \( S \leftarrow \text{CreateStack()} \) 2. \( \text{visited} \leftarrow \text{CreateArray}(|V|) \) 3. **for** \( i = 0 \) to \(|V| - 1\) **do** 4.   \( \text{visited}[i] \leftarrow \text{FALSE} \) 5. \(\text{Push}(S, \text{node})\) 6. **while** not \(\text{IsStackEmpty}(S)\) **do** 7.   \( c \leftarrow \text{Pop}(S) \) 8.   \( \text{visited}[c] \leftarrow \text{TRUE} \) 9.   **foreach** \( v \) in \(\text{AdjacencyList}(G, c)\) **do** 10.    **if** not \( \text{visited}[v] \) **then** 11.     \(\text{Push}(S, v)\) 12. **return** \( \text{visited} \)
Transcribed Image Text:**Algorithm 2.3: Graph Depth-First Search with a Stack** **StackDFS(G, node) → visited** - **Input:** - \( G = (V, E) \), a graph - \( \text{node} \), the starting vertex in \( G \) - **Output:** - \( \text{visited} \), an array of size \(|V|\) such that \( \text{visited}[i] \) is TRUE if we have visited node \( i \), FALSE otherwise **Algorithm Steps:** 1. \( S \leftarrow \text{CreateStack()} \) 2. \( \text{visited} \leftarrow \text{CreateArray}(|V|) \) 3. **for** \( i = 0 \) to \(|V| - 1\) **do** 4.   \( \text{visited}[i] \leftarrow \text{FALSE} \) 5. \(\text{Push}(S, \text{node})\) 6. **while** not \(\text{IsStackEmpty}(S)\) **do** 7.   \( c \leftarrow \text{Pop}(S) \) 8.   \( \text{visited}[c] \leftarrow \text{TRUE} \) 9.   **foreach** \( v \) in \(\text{AdjacencyList}(G, c)\) **do** 10.    **if** not \( \text{visited}[v] \) **then** 11.     \(\text{Push}(S, v)\) 12. **return** \( \text{visited} \)
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