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MODULE 5 PROJECT: BINARY TREES
Learning Objectives:
CLO 1. Identify fundamental data structures in computer science and their use in real-life appli- cations.
CLO 3. Develop problem solving skills by implementing data structures.
CLO 4. Compare advantages and disadvantages of different data structure implementations.
CLO 5. Design and analyze composite data structures.
Data Structure Implementation
- Implement BinaryTree.
Files to Modify: BinaryTree.py Directions: Finish the implementation of the following methods:
- depth(u) - returns the depth of node u
- _height(u) - recursive, helper method that returns the height of node u.
- _size(u) - recursive, helper method that returns the size of the subtree rooted at node u.
- bf_order() - returns the list of nodes that results from traversing the binary tree using breadth-first traversal.
- _in_order(u) - recursive, helper method returns the list of nodes that results from traversing the binary tree rooted at node u using in-order traversal (left, parent, right).
- _post_order(u) - recursive, helper method returns the list of nodes that results from traversing the binary tree rooted at node u using post-order traversal (left, right, parent).
- _pre_order(u) - recursive, helper method returns the list of nodes that results from traversing the binary tree rooted at node u using pre-order traversal (parent, left, right).
- Implement BinarySearchTree which is a specialized BinaryTree data structure. BinarySearchTree will inherit all methods from the BinaryTree class.
Files to Modify: BinarySearchTree.py (new template) Directions: Finish the implementation of the following methods:
- add(key, value) - adds a node with given key and value to the tree, if key does not already exist in the tree (i.e. no duplicate keys are allowed). Returns True if the key- value pair was added successfully, False otherwise.
- find(key) - returns the value corresponding to the given key if the key exists in the tree. Otherwise, it returns None.
- remove(key) - removes the node with given key and returns the value corresponding to the key, if it exists in the tree. Raises a ValueError if the key is not found in the tree.
- _find_eq(key) - helper method; returns the node with given key if the key exists in the tree, None otherwise.
- _find_last(key) - helper method; returns the node with given key if the key exists in the tree. Otherwise, it returns the node that would have been the parent of the node with with the given key, if it existed in the tree.
- _add_child(p, u) - helper method; adds node u as a child of node p, assuming that node p has at most one child. If node p already has two children, a ValueError is raised with message "Parent node already has two children."
- _splice(u) - helper method, links the parent of given node u to the child of node u, assuming u has at most has at most one child. This is equivalent to removing node u from the tree. Returns the node u.
- _remove_node(u) - helper method, removes node u from the binary search tree and returns the node that was removed.
(Optional) Test your data structures:
- Create an empty BinarySearchTree.
- Remove one element from an empty BinarySearchTree. Should result in ValueError
- Attempt to retrieve a value in an empty BinarySearchTree: find(2) should return None
- Add 3 elements: add(3,"third"), add(2, “second"), add(1, “first")
- Check that size() returns 3.
- Access one element, find(2) should return second
- Find an element with a key that does not exist in the tree: - _find_eq(2.5) should return None - find(2.5) should return None - _find_last(2.5).v should return "second"
- Remove one element: remove(3) should return "third". Check that size() returns 2.
- Access the removed element: find(3) should return None
- Add 3 elements: add(3, "third"), add(5,"fifth"), add(4,"fourth").
- Check that size() returns 5.
- Find an element with key that does not exist in the tree: - _find_eq(3.4) should return None - find(3.4).v should return None - _find_last(3.4).v should return "fourth"
- Print the key and values using the list returned by in_order(). The output should be:
1: first 2: second 3: third 4: fourth 5: fifth
Changes to the BookStore System
Files to Modify: (i) BookStore.py (ii) BinarySearchTree.py Directions:
- Modify the constructor in BookStore so that it includes an additional attribute called self.sortedTitleIndices. Initialize it to an empty BinarySearchTree object. This binary search tree will be used to map Book titles to their corresponding index in self.BookCatalogue (i.e. it will allow us to keep track of the index where each Book object is located based on its title).
- Recall that Book objects have attributes key, title, group, rank, and similar. Modify the loadCatalog() method so that when a Book gets loaded into the catalogue, a new element consisting of the book title and the book’s index in the catalogue is stored in the binary search tree. The pseudocode is as follows: For each row i in books.txt b = Book(key, title, group, rank, similar) bookCatalog.append(b) sortedTitleIndices.add(title, bookCatalog.size()-1) The attribute self.bookCatalogue should be an ArrayList.
- Add a method to BinarySearchTree that returns the node containing the given key if it exists; otherwise it returns the node with the smallest key greater than the given key. For example, if a binary search tree has nodes: [(7, 7), (3, 3), (10, 10), (1, 1), (5, 5), (9, 9), (12, 12), (11, 11), (14, 14)], then the node with smallest key greater than or equal to 8 is (9, 9). The node with smallest key greater than or equal to 12 is (12, 12), etc. To motivate the algorithm, you can begin by searching at the root for a node with a key greater than or equal to the given key. If in this process you find a node with key matching the given key, then return the node. Otherwise, once you have found a node, say u, with a key larger than the given key, search the left subtree of node u for a smaller key that is still greater than or equal to the given key. Again, if during this process you happen to find a node matching the given key, return the node. Otherwise, update u to be the newly found node that contains a smaller key than the key in u, but is still larger than the given key. Below is a template of the algorithm to get you started:
Initialize current to be the root. Initialize smallest to be None. While current is not None:
- If key < current.key, then
What should happen?
- Else if key > current.key, then
What should happen?
- Otherwise,
What should happen?
return smallest
- Add a method to BookStore called addBookByPrefix(prefix) that adds the first matched book containing prefix in the title, when the book titles are sorted in alphabetical order. The method should return the title of the book that was added to the cart, if the prefix was matched, None otherwise.
For example, if the catalogue contains books with titles, “World of Borrowed Time" “World of Byzantine Architecture" “World of Cats" “World of Chaos & Darkness" “World of Chocolates" “World of Daisies" Then, addBookByPrefix(“World of C") should add the Book with title “World of Cats", and return the title. Furthermore, addBookByPrefix(“World of Co") should not add any book to the cart, and should return None.
HINTS : I. If the given prefix exists as a title itself, then prefix will match a key in self.sortedTitleIndices. Otherwise, a book with a title that may contain the prefix must be alphabetically greater than prefix, i.e., prefix < book.title. If we want to find the first alphabetically, matched book potentially containing the prefix, then we are looking for the smallest key (i.e. title) in self.sortedTitleIndices that is greater than or equal to prefix. II. Your method from problem 3. of the BookStore System section might come in handy. III. You should make sure that a book title begins with prefix in order for it to be considered a match, i.e. you should be checking if title[0:n] == prefix where n = len(prefix).
Changes to the Calculator System
Files to Modify: Calculator.py.
Directions: Implement the following methods:
- _build_parse_tree(expr) - builds and returns a BinaryTree object representing the parse tree of the given expression expr.
- _evaluate(u) - recursive, helper method; evaluates the given node u. If u holds a variable, it returns the stored value for the variable (if it exists). If u holds an operator, then recursively evaluates the expression value of u.left, operator value of u, value of u.right
- Modify menu_calculator() so that it includes a new option to evaluate an expression. Your new list of options should read as follows:
1 Check mathematical expression 2 Store variable values 3 Print expression with values 4 Evaluate expression 0 Return to main menu
If the user chooses option 4, the system should prompt them for an expression. If all the variables in the expression have been defined, then the system will display the expression with the values substituted in, and the final evaluation. For example, assuming the user has already stored variable values alpha1 = 2, alpha2 = 4, beta1 = 3, beta2 = 5, option 4 would look like the following: Enter the expression: <user enters ((alpha1+beta2)(alpha2-beta1))> Evaluating expression: ((2.0+5.0)(4.0-3.0)) Result: 7. If one or more variables are missing defined values, then the system must display the error message: "Error - Not all variable values are defined." using the following format,
Enter the expression: <user enters ((alpha1+beta2)*(alpha2-beta1)//lambda)> Result: Error - Not all variable values are defined.
SUBMISSION PROCESS
- Submit your project to Repl.it.
- Submit to CodePost:
- BinaryTree.py
- BinarySearchTree.py
- main.py
- BookStore.py
- Calculator.py
RUBRIC
Full Credit Partial Credit No Credit Pts. vary; See Code- Post
0 pts.
BinaryTree implemen- tation
7 pts: Implementation is correct and passes all CodePost tests.
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests. BinarySearchTree im- plementation
11 pts: Implementation is correct and passes all CodePost tests.
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests. _build_parse_tree(e) implementation
2 pts: Implementation is correct and passes all CodePost tests.
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests. _evaluate(u) imple- mentation
2 pts Implementation is correct and passes all CodePost tests.
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests. Bookstore Main Menu implementation
4 pts. Implementation is correct and passes all CodePost tests
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests. Calculator Main Menu implementation
2 pts. Implementation is correct and passes all CodePost tests
Implementation is partially correct; fails one or more CodePost tests.
Implementation is incorrect/incom- plete and fails all CodePost tests.
