Write a program that takes an integer N from the command line, builds a random BST of size N, then enters into a loop where it deletes a random key (using the code delete(select(StdRandom.uniform(N)))) and then inserts a random key, iterating the loop N 2 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 10 4 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 delete() implementation that makes a random choice whether to use the predecessor or the successor node.

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Merge sort

Merge Sort recursively sorts a given collection of numbers or elements by using the divide and conquer strategy in less time. It is one of the most used algorithms, with the worst-case time complexity of O (n log n). It was invented by John Von Neumann. The algorithm continuously divides an array into sub-arrays until each sub-array consists of a single element. It then merges those sub-arrays to produce a sorted array.