Write a function randomTree(h) that
builds a complete binary tree of height h. Every value in the tree
should be a random integer in the range 0 .. 999.
Write a function completeTree(h) that
builds a complete binary tree of height h. Every node's value should
be that node's depth.
Write a function
mirror(t) that modifies
a binary tree, flipping it from left to right so that it looks
like a mirror image of the original tree.
a) Write a function max_in_tree(t) that returns the maximum value in a binary tree.
b) Modify the function to be more efficient if the input tree is known to be a binary search tree.
Write a function isAncestor(p, q)
that takes pointers to two nodes p and q in a binary tree and returns
true if p is an ancestor of q.
Write a function that takes an integer N and inserts N random values in the range from 0 .. N – 1 into a binary search tree. Let r be the ratio of the tree's height to the minimum possible height of any tree that holds N values. The function should compute and return r.
Write a class TreeSet that implements a set of values using a binary search tree, with methods add() and contains(). Implement these methods using recursion, with no loops. Hint: write recursive helper functions outside your TreeSet class that work with Node objects.
Write a program that reads a text file and prints the most common word in the file, along with its count of occurrences. Assume that words are sequences of Latin letters (A .. Z, a .. z), and ignore case. Do not use a Python dictionary. Instead, use a binary search tree to store the word counts.
Write a method that determines how many values v in a binary search tree of unique integers fall in the range a ≤ v ≤ b, where a and b are function parameters. The function should run in time O(h + n), where h is the tree height and n is the number of integers in the range.
Write a function that returns the greatest difference between any two consecutive values in a binary search tree.
Write a method which, given a binary search tree of non-negative integers and an integer i, returns the next highest value in the tree, i.e. the smallest value in the tree that is greater than i. Return -1 if there are no values greater than i. Assume that all integers in the tree are unique. The value i may or may not be present in the tree. Your function should run in time O(h), where h is the height of the tree.