do this assignment as soon as possible and draw the diagrams where needed and do it in a proper sequence

Consider the following search graph in which A is the start state and F is the goal state. Assume that for each search method, the details are such that a state's children will be visted in alphabetical order when possible; a) In what order will the states be expanded by a depth-first tree search? b) In what order will the states be expanded by a breadth-first graph search? c) In what order will the states be expanded by a uniform-cost graph search? Properties of Search Techniques a) Show that breadth first search, depth-first search, and uniform-cost search are special cases of best-first search. b) Show that uniform-cost search is a special case of A search. The Traveling Salesperson Problem (TSP) is a frequently studied route planning problem. In a TSP, one has a set C of cities connected by roads. The length of the direct roads between cities x and y is given by d(x,y); if two cities are not directly connected by a road, d(x,y) will be infinite. A tour is a list of cities that starts and ends at the same city and visits each city exactly once. The task is to find a tour of minimum total length. It is impractical to enumerate all tours, so one must devise better, often approximate, algorithms to solve TSPs. a) Give a formulation which casts the TSP as a single agent search problem in which optimal solutions correspond to TSP solutions. What are the states and successor functions? What is the start state and what is the goal test? What is the cost of a single action? (Hint: without loss of generality, you may assume that some city s in C is to be the beginning of the tour.) b) If all cities are connected with roads of length 1, compare briefly the behavior of DFS and BFS. Under these circumstances, is DFS complete? Optimal? Is BFS complete? Optimal? Which is better and why? c) If roads have arbitrary length, which of the following will be optimal: DFS, BFS, uniform cost search, greedy search, and/or A search