Give a topological sort for this graph. F B A D E 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
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Java. Please follow the picture

Transcribed Image Text:**Graph Theory Topic: Topological Sort**
In the image provided, we are asked to give a topological sort for a directed acyclic graph (DAG). The graph contains the following nodes: A, B, C, D, E, F, and G. The directed edges between these nodes indicate dependencies, where an edge from node U to node V signifies that U must come before V in the topological sort.
### Graph Structure
- Node A has outgoing edges to nodes B, D, and G.
- Node B has an outgoing edge to node E.
- Node C has outgoing edges to nodes A and F.
- Node D has no outgoing edges.
- Node E has no outgoing edges.
- Node F has no outgoing edges.
- Node G has an outgoing edge to node E.
### Description of the Topological Sort Process
To find a valid topological ordering of the nodes, follow these steps:
1. **Identify all nodes with no incoming edges** (these nodes have no prerequisites).
2. **Choose one of these nodes** and add it to the topological sort order.
3. **Remove this node and all its outgoing edges** from the graph.
4. If there are still nodes remaining, **repeat the process** with the remaining subgraph.
### Example of Topological Sort for Provided Graph
Using the steps above, we can perform a topological sort on the provided graph:
1. **Identify nodes with no incoming edges**: C (initially).
2. **Select node C**:
- Remove edges: C->A, C->F.
3. **Remaining nodes with no incoming edges**: A, F.
4. **Select node A**:
- Remove edges: A->B, A->D, A->G.
5. **Remaining nodes with no incoming edges**: F, B, D, G.
6. **Select node F** (choice among F, B, D, and G):
- No outgoing edges to remove.
7. **Remaining nodes with no incoming edges**: B, D, G.
8. **Select node B**:
- Remove edge: B->E.
9. **Remaining nodes with no incoming edges**: D, G, E.
10. **Select node D**:
- No outgoing edges to remove.
11. **Remaining nodes with no incoming edges**: G, E.
12. **Select node G**
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