*Directed Graphs*(G&T Chap 13)**R-12.5**Bob loves foreign languages and wants to plan his course schedule for the following years. He is interested in nine language courses, with prerequisites as follows:- LA15: (none)
- LA16: LA15
- LA22: (none)
- LA31: LA15
- LA32: LA16, LA31
- LA126: LA22, LA32
- LA127: LA16
- LA141: LA22, LA16
- LA169: LA32

a) Use a directed graph to find a sequence of courses that allows Bob to satisfy all the prerequisites.

b) Use the Floyd-Warshall algorithm to compute the transitive closure of the directed graph from part (a). What relationship does this graph represent?*Minimum Spanning Trees*(G&T Chap 13)**R-12.17**There are eight small islands in a lake, and the state wants to build seven bridges to connect them so that each island can be reached from any other one via one or more bridges. The cost of constructing a bridge is proportional to its length. The distances between pairs of islands are given in the following table.2 3 4 5 6 7 8 1 248 210 340 280 200 345 120 2 265 175 215 180 185 155 3 260 115 350 435 195 4 160 330 295 230 5 360 400 170 6 175 205 7 305

Find which bridges to build so that the total construction cost is mimimum, usinga) Kruskal's algorithm

b) the Prim-Jarník algorithmAny Questions about Assignment 3.