$(20$ points$)$ Give an example of a weighted directed graph for which Dijkstra's algorithm

produces an incorrect solution. Draw the graph. Identify the source vertex $s$ and a vertex $v$

for which the algorithm produces and incorrect shortest path. Write both the path obtained

by the algorithm and the correct path.

Identify why the textbook's statement of the theorem "Correctness of Dijkstra's algorithm"

does not apply to your example, and identify where the textbook's proof fails for it$.$