# 8.20. Programming Exercises¶

Extend the

`buildParseTree`

function to handle mathematical expressions that do not have spaces between every character.Modify the

`buildParseTree`

and`evaluate`

functions to handle boolean statements (and, or, and not). Remember that “not” is a unary operator, so this will complicate your code somewhat.Using the

`findSuccessor`

method, write a non-recursive inorder traversal for a binary search tree.Modify the code for a binary search tree to make it threaded. Write a non-recursive inorder traversal method for the threaded binary search tree. A threaded binary tree maintains a reference from each node to its successor.

Modify our implementation of the binary search tree so that it handles duplicate keys properly. That is, if a key is already in the tree then the new payload should replace the old rather than add another node with the same key.

Create a binary heap with a limited heap size. In other words, the heap only keeps track of the

`n`

most important items. If the heap grows in size to more than`n`

items the least important item is dropped.Clean up the

`printexp`

function so that it does not include an ‘extra’ set of parentheses around each number.Using the

`buildHeap`

method, write a sorting function that can sort a array in \(O(n\log{n})\) time.Write a function that takes a parse tree for a mathematical expression and calculates the derivative of the expression with respect to some variable.

Implement a binary heap as a max heap.

Using the

`BinaryHeap`

class, implement a new class called`PriorityQueue`

. Your`PriorityQueue`

class should implement the constructor, plus the`enqueue`

and`dequeue`

methods.