Please respond to the following Discussion Questions (Covers Chapter 9&10): Ques

Question

Please respond to the following Discussion Questions (Covers Chapter 9&10): Question 1: In chapter 9 we discuss several common problems in graph theory Not only are these algorithms useful in practice, they are also interesting because in many real-life applications they are too slow unless careful attention is paid to the choice of data structures. Show several real-life problems, which can be converted to problems on graphs. Question 2: In chapter 9 we discuss several common problems in graph theory. Not only are these algorithms useful in practice, they are also interesting because in many real- life applications they are too slow unless careful attention is paid to the choice of data structures. Give algorithms to solve several common graph problems. Show how the proper choice of data structures can drastically reduce the running time of these algorithms.

Explanation / Answer

Answer :

1) one of the most common application of the graphs in real life is the connection management on the social media website, all the people who sign up there would get a node created in the graph with there name, whenever a friend request comes or sent, a request edge is drawn between them and once conformed this would get transformed into permanent graph edge, after un friending, the edge can be deleted. The use of graphs ahad made the representation of problem so much simpler that it becomes daily understandable.

2) there are many graph algorithms like for reaching of a node in graph we have depth first search, breadth first search, iterated search, A* search,etc. We have algorithms related to graph coloring problems that can be used to allocated different colors or resources to the adjacent nodes, no two adjacent nodes will have the same color, this is used in real life quite often, all there algorithms play a small or large role in the big problems like connection management on social media website as explained above.

The proper choice of data structure is always the key to solve the problem, it enables us to better represent and organise the data as per problem needs, suppose we use arrays for connection management that we need to create a different profile for all the users, send requests receive requests but there was no structure for representations the whole process becomes Cumbersome also the time complexity increases if we doesn't chose a right data structure for solving a particular problem

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