What is the appropriate data structure and algorithms to use in different situations and why? $(10$pts$)$ a$.$ You have to maintain a large list of names. You need fast searching on the order of log $($n$),$ efficient insertions and deletions and be able to quickly sort the list. Which data structure would you use. b$.$ You have an airline reservation system with hundreds of inquiries every minute. You need to perform searches extremely quickly. What searching algorithm would you use and how would the information be stored. c$.$ The road structure in Virginia has become too expensive to maintain, since it possesses too many redundant paths. Governor Northam has tasked you with creating a road structure that connects each Virginia city so that you can reach each city from every other city. How could you create such a structure so that the sum of the distances on the road is as small as possible