"""CSC111 Winter 2023 Prep 5: Programming Exercises Instructions (READ THIS FIRST!) =============================== This file contains the BinarySearchTree class you read about in this week's prep, as well a few different methods for you to implement. Each of these methods should be implemented recursively, and you should use the BST property to ensure that you are only making the recursive calls that are required to implement each function--- do not make any unnecessary calls! (The prep readings illustrate this idea in the discussion of how __contains__ is implemented.) Finally, one TIP: don't forget about self._root in the recursive step! This was the most common mistake students made with Prep 4 last week. Even when you are recursing on self._left and/or self._right, you'll often (but not necessarily always) need to do something with self._root as well. NOTE: the doctests access and assign to private attributes directly, which is not good practice (although PythonTA doesn't complain about it in doctests). We'll fix this in lecture when we implement a `BinarySearchTree.insert` method. We have marked each place you need to write code with the word "TODO". As you complete your work in this file, delete each TODO comment. You may add additional doctests, but they will not be graded. You should test your work carefully before submitting it! Copyright and Usage Information =============================== This file is provided solely for the personal and private use of students taking CSC111 at the University of Toronto St. George campus. All forms of distribution of this code, whether as given or with any changes, are expressly prohibited. For more information on copyright for CSC111 materials, please consult our Course Syllabus. This file is Copyright (c) 2023 Mario Badr, David Liu, and Diane Horton. """ from __future__ import annotations from typing import Any, Optional from python_ta.contracts import check_contracts @check_contracts class BinarySearchTree: """Binary Search Tree class. Representation Invariants: - (self._root is None) == (self._left is None) - (self._root is None) == (self._right is None) - (BST Property) if self._root is not None, then all items in self._left are <= self._root, and all items in self._right are >= self._root Note that duplicates of the root can appear in *either* the left or right subtrees. """ # Private Instance Attributes: # - _root: # The item stored at the root of this tree, or None if this tree is empty. # - _left: # The left subtree, or None if this tree is empty. # - _right: # The right subtree, or None if this tree is empty. _root: Optional[Any] _left: Optional[BinarySearchTree] _right: Optional[BinarySearchTree] def __init__(self, root: Optional[Any]) -> None: """Initialize a new BST containing only the given root value. If <root> is None, initialize an empty tree. """ if root is None: self._root = None self._left = None self._right = None else: self._root = root self._left = BinarySearchTree(None) self._right = BinarySearchTree(None) def is_empty(self) -> bool: """Return whether this BST is empty. >>> bst = BinarySearchTree(None) >>> bst.is_empty() True >>> bst = BinarySearchTree(10) >>> bst.is_empty() False """ return self._root is None def __contains__(self, item: Any) -> bool: """Return whether <item> is in this BST. >>> bst = BinarySearchTree(3) >>> bst._left = BinarySearchTree(2) >>> bst._right = BinarySearchTree(5) >>> bst.__contains__(3) # or, 3 in bst True >>> bst.__contains__(5) True >>> bst.__contains__(2) True >>> bst.__contains__(4) False """ if self.is_empty(): return False elif item == self._root: return True elif item < self._root: return self._left.__contains__(item) # or, item in self._left else: return self._right.__contains__(item) # or, item in self._right def __str__(self) -> str: """Return a string representation of this BST. This string uses indentation to show depth. We've provided this method for debugging purposes, if you choose to print a BST. """ return self._str_indented(0) def _str_indented(self, depth: int) -> str: """Return an indented string representation of this BST. The indentation level is specified by the <depth> parameter. Preconditions: - depth >= 0 """ if self.is_empty(): return '' else: return (depth * ' ' + f'{self._root}\n' + self._left._str_indented(depth + 1) + self._right._str_indented(depth + 1)) ############################################################################ # Prep exercises ############################################################################ def maximum(self) -> Optional[int]: """Return the maximum number in this BST, or None if this BST is empty. Hint: Review the BST property to ensure you aren't making unnecessary recursive calls. Preconditions: - all items in this BST are integers >>> BinarySearchTree(None).maximum() is None # Empty BST True >>> BinarySearchTree(10).maximum() 10 >>> bst = BinarySearchTree(7) >>> left = BinarySearchTree(3) >>> left._left = BinarySearchTree(3) >>> left._right = BinarySearchTree(5) >>> right = BinarySearchTree(11) >>> right._left = BinarySearchTree(9) >>> right._right = BinarySearchTree(13) >>> bst._left = left >>> bst._right = right >>> bst.maximum() 13 """ if self.is_empty(): return self._root elif self._right.is_empty() is True: return self._root else: return self._right.maximum() def count(self, item: Any) -> int: """Return the number of occurrences of <item> in this BST. Hint: carefully review the BST property! >>> BinarySearchTree(None).count(148) # An empty BST 0 >>> bst = BinarySearchTree(7) >>> left = BinarySearchTree(3) >>> left._left = BinarySearchTree(3) >>> left._right = BinarySearchTree(5) >>> right = BinarySearchTree(11) >>> right._left = BinarySearchTree(9) >>> right._right = BinarySearchTree(13) >>> bst._left = left >>> bst._right = right >>> bst.count(7) 1 >>> bst.count(3) 2 >>> bst.count(100) 0 """ num = 0 if self.is_empty(): return num elif item == self._root: num += 1 num += self._left.count(item) num += self._right.count(item) return num def items(self) -> list: """Return all of the items in the BST in sorted order. Do not remove duplicates. You should *not* need to sort the list yourself: instead, use the BST property and combine self._left.items(), self._root, and self._right.items() in the correct order! >>> BinarySearchTree(None).items() # An empty BST [] >>> bst = BinarySearchTree(7) >>> left = BinarySearchTree(3) >>> left._left = BinarySearchTree(2) >>> left._right = BinarySearchTree(5) >>> right = BinarySearchTree(11) >>> right._left = BinarySearchTree(9) >>> right._right = BinarySearchTree(13) >>> bst._left = left >>> bst._right = right >>> bst.items() [2, 3, 5, 7, 9, 11, 13] """ num = [] if self.is_empty(): return num num.extend(self._left.items()) num.append(self._root) num.extend(self._right.items()) return num def smaller(self, item: Any) -> list: """Return all of the items in this BST less than <item> in sorted order. Preconditions: - all items in this BST can be compared with <item> using <. As with BinarySearchTree.items, you should *not* need to sort the list yourself! >>> bst = BinarySearchTree(7) >>> left = BinarySearchTree(3) >>> left._left = BinarySearchTree(2) >>> left._right = BinarySearchTree(5) >>> right = BinarySearchTree(11) >>> right._left = BinarySearchTree(9) >>> right._right = BinarySearchTree(13) >>> bst._left = left >>> bst._right = right >>> bst.smaller(6) [2, 3, 5] >>> bst.smaller(13) [2, 3, 5, 7, 9, 11] """ num = [] if self.is_empty(): return num num.extend(self._left.smaller(item)) if item > self._root: num.append(self._root) num.extend(self._right.smaller(item)) return num if __name__ == '__main__': import doctest doctest.testmod(verbose=True) # When you are ready to check your work with python_ta, uncomment the following lines. # (In PyCharm, select the lines below and press Ctrl/Cmd + / to toggle comments.) # You can use "Run file in Python Console" to run PythonTA, # and then also test your methods manually in the console. import python_ta python_ta.check_all(config={ 'max-line-length': 120 })