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by rail for a segment of the Eurail system are shown below with travel times in hours and Paris Amsterdam 1:25 Berlin 5:45 6:10 Lyon 1:55 Frankfurt 3:10 4:00 Bern 3:50 3:55

by rail for a segment of the Eurail system are shown below with travel times in hours and Paris Amsterdam 1:25 Berlin 5:45 6:10 Lyon 1:55 Frankfurt 3:10 4:00 Bern 3:50 3:55

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Eurail Travel Times Table #### Travel times by rail for a segment of the Eurail system are shown below with travel times in hours and minutes. | | Paris | Amsterdam | Berlin | Lyon | Frankfurt | Bern | |-----------|-------|-----------|--------|------|-----------|------| | Munchen | | | 5:45 | | 3:10 | | | Paris | | 1:25 | | 1:55 | | 4:00 | | Amsterdam | | | 6:10 | | | | | Berlin | | | | | | | | Lyon | | | | | 3:50 | | | Frankfurt | | | | | | 3:55 | ### Tasks a. **Create a Weighted Graph**: Represent the rail system using a graph where cities are nodes and travel times are weighted edges. b. **Shortest Travel Path (Bern to Berlin)**: Use any preferred system to find the shortest path in terms of travel time between Bern and Berlin. c. **Shortest Travel Path (Paris to Munchen)**: Use any preferred system to find the shortest path in terms of travel time between Paris and Munchen. In this exercise, students will learn how to convert tabular travel times into a graph structure and apply algorithms to determine the shortest paths between nodes. Understanding the structure and approach is crucial for dealing with real-world transport networks.
Transcribed Image Text:### Eurail Travel Times Table #### Travel times by rail for a segment of the Eurail system are shown below with travel times in hours and minutes. | | Paris | Amsterdam | Berlin | Lyon | Frankfurt | Bern | |-----------|-------|-----------|--------|------|-----------|------| | Munchen | | | 5:45 | | 3:10 | | | Paris | | 1:25 | | 1:55 | | 4:00 | | Amsterdam | | | 6:10 | | | | | Berlin | | | | | | | | Lyon | | | | | 3:50 | | | Frankfurt | | | | | | 3:55 | ### Tasks a. **Create a Weighted Graph**: Represent the rail system using a graph where cities are nodes and travel times are weighted edges. b. **Shortest Travel Path (Bern to Berlin)**: Use any preferred system to find the shortest path in terms of travel time between Bern and Berlin. c. **Shortest Travel Path (Paris to Munchen)**: Use any preferred system to find the shortest path in terms of travel time between Paris and Munchen. In this exercise, students will learn how to convert tabular travel times into a graph structure and apply algorithms to determine the shortest paths between nodes. Understanding the structure and approach is crucial for dealing with real-world transport networks.
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