Suppose we (1) have a directed graph as, and (2) allow negative weights of edges in the input to Dijsktra’s algorithm.

Question part 1: Demonstrate a graph with these two properties, such as Dijkstra’s algorithm from class returns an incorrect output. Explain what the correct output is, what output Dijkstra’s algorithm produces, and why.

Question part 2: Which of the above two properties causes the algorithm to fail?

Question part 3: Show exactly where our proof of correctness of Dijkstra’s algorithm fails if we allow the property in your previous answer.