Question

Professor Gaedel has written a program that he claims implements Dijkstra's algorithm. The program produces v: d and v: for each vertex v in V. Give an O(V + E)-time algorithm to check the output of the professor's program. It should determine whether the d and attributes match those of some shortest-paths tree. You may assume that all edge weights are nonnegative.

A) Perform a depth-first search (DFS) on the output to check for matching attributes.
B) Use Breadth-First Search (BFS) to compare d attributes and validate the output.
C) Implement a Bellman-Ford algorithm to verify the correctness of the output.
D) Apply Dijkstra's algorithm again to confirm the accuracy of the professor's program.

Answer 1

The correct way to verify the output of a program implementing Dijkstra's algorithm is to apply Dijkstra's algorithm again and compare the results. The correct option is d.

Step-by-step explanation:

To verify the output of Professor Gaedel's program which claims to implement Dijkstra's algorithm, we should apply an algorithm that checks if the d attributes and \(\pi\) attributes match a shortest-paths tree, given all edge weights are nonnegative. The most efficient verification strategy, considering the constraints of the question, would be:

• D) Apply Dijkstra's algorithm again to confirm the accuracy of the professor's program by comparing the computed shortest path and predecessor attributes with the output provided by the program.

For the one-word answers to the given descriptions:

1. a. Optimal path
2. b. Vector
3. c. Acceleration
4. d. Reference point
5. e. Distance
6. f. Instantaneous velocity