Q1: 1. What is the main advantage of using Directed Acyclic Graphs (DAGs) in finding shortest paths?

• A) They are easier to traverse
• B) They guarantee no cycles
• C) They have faster computation time
• D) They have unlimited nodes

Q2: 3. Which algorithm is commonly used to find the shortest paths in Directed Acyclic Graphs?

• A) Dijkstra's algorithm
• B) Bellman-Ford algorithm
• C) Floyd-Warshall algorithm
• D) Topological sorting algorithm

Q3: 4. How does the topological sorting algorithm help in finding the shortest paths in DAGs?

• A) It sorts the vertices based on their weights
• B) It organizes the vertices in a linear ordering
• C) It calculates the total distance between all vertices
• D) It eliminates cycles from the graph

Q4: 5. Which property makes Directed Acyclic Graphs suitable for finding shortest paths efficiently?

• A) Bidirectional edges
• B) Cyclic nature
• C) Unidirectional edges
• D) Weighted vertices

Q5: 6. In a DAG representing a project schedule, what real-life problem statement can be addressed using shortest path algorithms?

• A) Determining the tasks critical for project completion
• B) Finding the longest route for project delays
• C) Identifying non-essential tasks
• D) Planning the project timeline without constraints

Q6: 7. Which step is crucial before applying a shortest path algorithm on a DAG?

• A) Detecting cycles in the graph
• B) Randomly selecting a starting point
• C) Sorting vertices alphabetically
• D) Ignoring edge weights

Q7: 8. What is the time complexity of finding the shortest paths in a DAG using topological sorting?

• A) O(V + E)
• B) O(V log V)
• C) O(E log V)
• D) O(V^2)

Q8: 9. In a transportation network represented by a DAG, which real-life problem statement can be solved using shortest path algorithms?

• A) Optimizing bus routes for minimal travel time
• B) Increasing traffic congestion by choosing longer routes
• C) Randomly selecting routes for diversity
• D) Avoiding main roads for scenic routes

Q9: 10. Which property distinguishes Directed Acyclic Graphs from other graph types in the context of finding shortest paths?

• A) They allow negative weight edges
• B) They contain multiple cycles
• C) They can have bidirectional edges
• D) They have a strict order of vertices

Q10: 11. In a DAG representing a supply chain, what real-life problem statement can be addressed using shortest path algorithms?

• A) Minimizing transportation costs between warehouses
• B) Maximizing warehouse storage capacity
• C) Randomly selecting suppliers for goods
• D) Planning inefficient routes for deliveries

Q11: 12. Which algorithm is efficient for finding shortest paths in DAGs with negative edge weights?

• A) Dijkstra's algorithm
• B) Bellman-Ford algorithm
• C) Floyd-Warshall algorithm
• D) A* algorithm

Q12: 13. In a social network represented by a DAG, what real-life problem statement can be solved using shortest path algorithms?

• A) Finding the quickest way to spread information to all users
• B) Maximizing the number of followers for a user
• C) Randomly connecting users for diversity
• D) Avoiding direct connections between users

Q13: 14. How does the presence of cycles affect the application of shortest path algorithms in graphs?

• A) Cycles ensure faster computation of shortest paths
• B) Cycles introduce ambiguity in determining shortest paths
• C) Cycles simplify path selection in graphs
• D) Cycles have no impact on shortest path algorithms

Q14: 15. Which data structure is commonly used to implement topological sorting for finding shortest paths in DAGs?

• A) Queue
• B) Stack
• C) Heap
• D) Array

Q15: 16. In a DAG representing an internet network, what real-life problem statement can be addressed using shortest path algorithms?

• A) Optimizing data transfer between servers
• B) Maximizing internet downtime for users
• C) Randomly disconnecting servers for testing
• D) Avoiding efficient routing for data packets

Q16: 17. What is the significance of weight assignment in edges when finding shortest paths in DAGs?

• A) Weights do not affect path selection in DAGs
• B) Weight assignment influences the shortest path determination
• C) Equal weights ensure balanced path selection
• D) Heavier weights lead to shorter paths in DAGs

Q17: 18. Which scenario best illustrates the application of shortest path algorithms in a DAG representing a power grid network?

• A) Finding the shortest route for a hiking trail
• B) Optimizing electricity distribution to minimize costs
• C) Randomly connecting power sources for redundancy
• D) Avoiding efficient transmission of electricity

Q18: 19. How does the concept of topological order contribute to finding shortest paths in DAGs?

• A) It ensures a specific order of path selection
• B) It guarantees the absence of cycles in the DAG
• C) It simplifies edge weight calculations
• D) It organizes vertices for efficient path traversal

Q19: 20. Which algorithm is suitable for finding all-pairs shortest paths in a DAG?

• A) Dijkstra's algorithm
• B) Bellman-Ford algorithm
• C) Floyd-Warshall algorithm
• D) Prim's algorithm

Q20: 21. In a financial network represented by a DAG, what real-life problem statement can be solved using shortest path algorithms?

• A) Minimizing transaction costs between banks
• B) Maximizing account balances for customers
• C) Randomly connecting financial institutions for diversity
• D) Avoiding efficient fund transfers

Q21: 22. How does the presence of negative cycles impact the application of shortest path algorithms in graphs?

• A) Negative cycles ensure the shortest path is optimal
• B) Negative cycles may cause the algorithm to loop indefinitely
• C) Negative cycles have no effect on shortest path determination
• D) Negative cycles simplify path selection in graphs

Q22: 23. Which algorithm is more suitable for finding single-source shortest paths in DAGs with positive edge weights?

• A) Dijkstra's algorithm
• B) Bellman-Ford algorithm
• C) Floyd-Warshall algorithm
• D) Kruskal's algorithm

Q23: 24. In a healthcare network represented by a DAG, what real-life problem statement can be addressed using shortest path algorithms?

• A) Minimizing patient transfer times between hospitals
• B) Maximizing patient waiting times for appointments
• C) Randomly connecting healthcare facilities for diversity
• D) Avoiding efficient ambulance routing

Q24: 25. What is the primary advantage of using topological sorting in finding shortest paths in DAGs?

• A) It ensures the shortest path is the longest path
• B) It simplifies the calculation of edge weights
• C) It guarantees the absence of cycles in the graph
• D) It allows for random path selection