7.22. Programming Exercises¶

Extend the build_parse_tree function to handle mathematical expressions that do not have spaces between every character.
Modify the build_parse_tree 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 find_successor 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 print_exp function so that it does not include an ‘extra’ set of parentheses around each number.
Using the heapify method, write a sorting function that can sort a list 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.

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