For the 8-puzzle problem in Figure 1, given this initial starting state: 2 8 7 3 1 4 5 6 Figure 1 a) Using breadth first search, show the search tree that would be built down to level 2 (assume level zero is the root of the tree). (5 marks) b) Using depth first search, show the state of the search tree down the level 3 (stop once you have expanded one node that goes to level 3). (5 marks) c) What is the worst-case time and space complexity of the above two algorithms? (5 marks) Describe the terms complete and optimal with regards to evaluating search strategies. (4 marks) e) Are either depth-first-search or breadth-first-search complete or optimal? Justify your answer. (6 marks)