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1. 5 marks) Illustrate that the nodes of any AVL tree T can be colored "red" and "black so that T becomes a red-black tree. 2. (5 + 10 transformed into another search tree T2 (with the same items) (5 marks). Give an algorithm to perform this transformation using O(N log N) rotation on average (10 marks) 15 marks) Illustrate that via AVL single rotation, any binary search tree TI can be