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Question 2: Binary Search Trees et al. (24 marks) Consider the binary tree T below which was created using only insertions 30 20 60 10 40 70 50 e Suppose T is a binary search tree (as it is) a. (4 marks) Delete 30 from T and show the two resultant binary search trees. b. ( mark) Show the binary search tree immediately before 30 was inserted Suppose T is an AVL tree. a. (3 marks) Label each node of T with its balancing factor. b. (3 marks) Delete 10 from T and show the resultant tree g Suppose T is a splay tree a. (4 marks) Show and justify the splay tree immediately before the last value was inserted b. ( mark) Using the big-Oh notation, state the amortized cost of splay tree methods h) Suppose T is a red-black tree a. (3 marks) Label each node of T with its colour. b. (3 marks) Show the two possible red-black trees immediately before 50 was inserted i) (2 marks) Give two reasons why T cannot be a 2-3 tree