Hibbard deletion degradation. Write a program that takes an integer Nfrom the command line, builds a random BST of size N, then enters into a loop where it deletes a random key (using the code de1ete(se1ect(StdRandom.uniform(N)))) and then inserts a random key, iterating the loop N2 times. After the loop, measure and print the average length of a path in the tree (the internal path length divided by N, plus 1). Run your program for N = 102, 103, and 104 to test the somewhat counterintuitive hypothesis that this process increases the average path length of the tree to be proportional to the square root of N. Run the same experiments for a de1ete() implementation that makes a random choice whether to use the predecessor or the successor node.
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