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"""CSC111 Winter 2022 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 need to do something with
self._root as well, at least in some cases.
NOTE: the doctests access and assign to private attributes directly, which is
not good practice (although python_ta doesn't complain about it in doctests).
We'll fix this in this week 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) 2022 Mario Badr, David Liu, and Diane Horton.
"""
from __future__ import annotations
from typing import Any, Optional
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._right is None or self._right.is_empty():
return self._root
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
"""
if self.is_empty():
return 0
s = int(self._root == item)
if self._root <= item:
s += self._right.count(item)
if self._root >= item:
s += self._left.count(item)
return s
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]
"""
if self.is_empty():
return []
return self._left.items() + [self._root] + self._right.items()
def smaller(self, item: Any) -> list:
"""Return all 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]
"""
if self.is_empty():
return []
if self._root < item:
return self._left.smaller(item) + [self._root] + self._right.smaller(item)
else:
return self._left.smaller(item)
if __name__ == '__main__':
import python_ta.contracts
python_ta.contracts.check_all_contracts()
import doctest
doctest.testmod()
import python_ta
python_ta.check_all(config={
'max-line-length': 100,
'disable': ['E1136']
})