2.3.1(f) Shortest Path Do Now

Imagine you are planning the most efficient route for a delivery truck to reach various destinations in a city. What algorithm would you use to ensure the truck takes the shortest path from its starting location to all other destinations?

• To find the shortest path from one node to every other node in a graph

• To find the longest path in a graph

• To detect cycles in a graph

• To create a minimum spanning tree

Answer explanation

The correct algorithm to ensure the truck takes the shortest path from its starting location to all other destinations is to find the shortest path from one node to every other node in a graph.

Imagine you're planning a road trip starting from your home. Using Dijkstra's algorithm to find the shortest path to your destination, what is the initial distance value assigned to your starting point (home)?

• -1

• 0

• 1

• Infinity

Answer explanation

The initial distance value assigned to the starting point (home) in Dijkstra's algorithm is 0.

Imagine you're navigating through a city using Dijkstra's algorithm. After selecting a particular intersection as your current location, what is the next step?

• Remove the intersection from the map

• Start the navigation process over

• Choose the intersection with the longest distance

• Examine the roads leading out from the intersection and update the navigation chart

Answer explanation

The correct next step after selecting an intersection using Dijkstra's algorithm is to examine the roads leading out from the intersection and update the navigation chart.

Imagine you're planning the most efficient route for a road trip across multiple cities using a GPS app. The app uses Dijkstra's algorithm to calculate the shortest path. What is the time complexity of this algorithm when a Fibonacci heap is used?

• O(v^2)

• O(e + v log v)

• O(n log n)

• O(n^2)

Answer explanation

Provide your explanation here.

Imagine a delivery driver using a navigation system to deliver packages. What does the system do after the driver has visited all the destinations?

• Ends, as the shortest path to all destinations has been found

• Begins the process again with a different starting point

• Calculates the maximum path

• Removes the last destination from consideration

Answer explanation

The system ends as the shortest path to all destinations has been found, indicating the completion of the delivery route.