(10 points) Dijkstra's single-source shortest path algorithm (a) Run Dijkstra's algorithm on the following directed graph G. Use vertex a as the source. Use the same convention and notation as in the lecture notes to show the values of DI and predf.] for the nodes of G. Show the graph G and the values of D] and pred[1-] after removing and processing each vertex from Q as in the lecture notes. Either color the pointer pred[-] red as in the lecture notes or show the pointer pred[-] as a dashed arrow. A vertex should be shown shaded if it no longer belongs to 3 2 2 10 20 6 50 20 10 (b) Given an example of a graph with negative edge weight and show that Dijkstra's algo- rithm fails to find a shortest path in it