2. Black-Height (6 points) Write pseudocode for a function int computeBH (RBnode root) that takes the root node of a candidate red-black tree and returns the black-height of the tree if the tree is a valid red-black tree, or -1 otherwise. Assume that the class RBnode stores the key, the color, and references left and right to its two childrein What is the runtime of your function? Hint:You can assume all null 's are black and that each node's color is either RED or BLACK. Check the blackness of the root separately using a wrapper-function, and write a recursive function to compute the black-height while checking the remaining red-black tree properties 4 and 5.) 3. B-tree-search using binary search (4 points) Consider changing B-TrEe-SeArCH to use binary search instead of linear search on the key (a) What is the number of disk accesses? Justify your answer. (b) Show that the CPU time is O(logn), which is independent of k