The time complexity of the Best-first search depends on..........................................a)the number of nodes in the graph.b)the branching factor of the graph.c)the depth of the solution.d)the heuristic function used.

When is breadth first search is optimal?

Discuss the time complexity of searching for a node in a binary search give the answer for 5 marks

Give the time and space complexity of the Tree Search version of Depth-First Search (DFS), in terms of the branching factor b and the maximum depth m of the search tree.Write your answer using big-O notation, and if you need to use powers then write them in TeX notation. For example, n squared would be written as n^2. If the algorithm has worst-case complexity n squared, it would be written as O(n^2).

(a) You will investigate various search algorithms for the graph in figure 1. Edges arelabeled with their costs, and heuristic values h for states are labeled next to thestates. S is the start state, and G is the goal state. For each of the following graphsearch strategies, work out the order in which states are expanded, the path returnedby graph search, the path cost, as well as the states that are not expanded. In allsearch algorithms, assume ties are broken in alphabetical order. Draw search tree foreach search strategy to illustrate your answer.Figure 1: Search graph 12 of 5(i) Depth first search [ 3 marks](ii) Breadth First search [ 3 marks](iii) Uniform cost Search [ 4 marks](iv) A* search [4 marks](v) Greedy Search [ 2 marks](b) The heuristic values for the graph in figure 2 are not correct. For which single state (S,A, B, C, D, or G) could you change the heuristic value to make everything admissibleand consistent? What range of values are possible to make this correction? [ 4marks]Figure 2: Search graph 2Question 3(a) Explain the role probability play in Artificial Intelligence. [2 marks](b) Covid-19, Maleria and Paralysis diseases cases have been reported in Makerere Uni-versity. The Ministry of Healthy has sent a team of experts to perform a diseasediagnosis to patients suspected being suffering from the diseases within Makerereand report on their rampage as soon as possible. But as they try to perform thedisease diagnostics, they discover that these diseases exhibit similar symptoms whichmakes the diagnosis process much more complicated, thus delaying the results. Inorder to reduce on the time delay in the provision of diagnostics results in the nearfuture, they have proposed using a machine learning diagnosis system and you havebeen approached to assist in the development of such systems. Using the knowledgeof Artificial intelligence and probability theory, discuss the steps you would followin developing such a system. You should clearly state the assumptions and relevantexamples for full marks. [18 marks]

Suppose you were applying the Graph Search version of A* Search to a search problem. Using an admissible heuristic would guarantee that:Group of answer choicesAll nodes expanded by the search algorithm will have the same value of f(n).The first solution found is an optimal solution.The heuristic is also consistent.None of the above.