binary_search_tree.py

r"""
A binary search Tree

Example
 8
 / \
 3 10
 / \ \
 1 6 14
 / \ /
 4 7 13

>>> t = BinarySearchTree().insert(8, 3, 6, 1, 10, 14, 13, 4, 7)
>>> print(" ".join(repr(i.value) for i in t.traversal_tree()))
8 3 1 6 4 7 10 14 13

>>> tuple(i.value for i in t.traversal_tree(inorder))
(1, 3, 4, 6, 7, 8, 10, 13, 14)
>>> tuple(t)
(1, 3, 4, 6, 7, 8, 10, 13, 14)
>>> t.find_kth_smallest(3, t.root)
4
>>> tuple(t)[3-1]
4

>>> print(" ".join(repr(i.value) for i in t.traversal_tree(postorder)))
1 4 7 6 3 13 14 10 8
>>> t.remove(20)
Traceback (most recent call last):
 ...
ValueError: Value 20 not found
>>> BinarySearchTree().search(6)
Traceback (most recent call last):
 ...
IndexError: Warning: Tree is empty! please use another.

Other example:

>>> testlist = (8, 3, 6, 1, 10, 14, 13, 4, 7)
>>> t = BinarySearchTree()
>>> for i in testlist:
... t.insert(i) # doctest: +ELLIPSIS
BinarySearchTree(root=8)
BinarySearchTree(root={'8': (3, None)})
BinarySearchTree(root={'8': ({'3': (None, 6)}, None)})
BinarySearchTree(root={'8': ({'3': (1, 6)}, None)})
BinarySearchTree(root={'8': ({'3': (1, 6)}, 10)})
BinarySearchTree(root={'8': ({'3': (1, 6)}, {'10': (None, 14)})})
BinarySearchTree(root={'8': ({'3': (1, 6)}, {'10': (None, {'14': (13, None)})})})
BinarySearchTree(root={'8': ({'3': (1, {'6': (4, None)})}, {'10': (None, {'14': ...
BinarySearchTree(root={'8': ({'3': (1, {'6': (4, 7)})}, {'10': (None, {'14': (13, ...

Prints all the elements of the list in order traversal
>>> print(t)
{'8': ({'3': (1, {'6': (4, 7)})}, {'10': (None, {'14': (13, None)})})}

Test existence
>>> t.search(6) is not None
True
>>> 6 in t
True
>>> t.search(-1) is not None
False
>>> -1 in t
False

>>> t.search(6).is_right
True
>>> t.search(1).is_right
False

>>> t.get_max().value
14
>>> max(t)
14
>>> t.get_min().value
1
>>> min(t)
1
>>> t.empty()
False
>>> not t
False
>>> for i in testlist:
... t.remove(i)
>>> t.empty()
True
>>> not t
True
"""

from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass
from typing import Any, Self


@dataclass
class Node:
 value: int
 left: Node | None = None
 right: Node | None = None
 parent: Node | None = None # Added in order to delete a node easier

 def __iter__(self) -> Iterator[int]:
 """
 >>> list(Node(0))
 [0]
 >>> list(Node(0, Node(-1), Node(1), None))
 [-1, 0, 1]
 """
 yield from self.left or []
 yield self.value
 yield from self.right or []

 def __repr__(self) -> str:
 from pprint import pformat

 if self.left is None and self.right is None:
 return str(self.value)
 return pformat({f"{self.value}": (self.left, self.right)}, indent=1)

 @property
 def is_right(self) -> bool:
 return bool(self.parent and self is self.parent.right)


@dataclass
class BinarySearchTree:
 root: Node | None = None

 def __bool__(self) -> bool:
 return bool(self.root)

 def __iter__(self) -> Iterator[int]:
 yield from self.root or []

 def __str__(self) -> str:
 """
 Return a string of all the Nodes using in order traversal
 """
 return str(self.root)

 def __reassign_nodes(self, node: Node, new_children: Node | None) -> None:
 if new_children is not None: # reset its kids
 new_children.parent = node.parent
 if node.parent is not None: # reset its parent
 if node.is_right: # If it is the right child
 node.parent.right = new_children
 else:
 node.parent.left = new_children
 else:
 self.root = new_children

 def empty(self) -> bool:
 """
 Returns True if the tree does not have any element(s).
 False if the tree has element(s).

 >>> BinarySearchTree().empty()
 True
 >>> BinarySearchTree().insert(1).empty()
 False
 >>> BinarySearchTree().insert(8, 3, 6, 1, 10, 14, 13, 4, 7).empty()
 False
 """
 return not self.root

 def __insert(self, value) -> None:
 """
 Insert a new node in Binary Search Tree with value label
 """
 new_node = Node(value) # create a new Node
 if self.empty(): # if Tree is empty
 self.root = new_node # set its root
 else: # Tree is not empty
 parent_node = self.root # from root
 if parent_node is None:
 return
 while True: # While we don't get to a leaf
 if value < parent_node.value: # We go left
 if parent_node.left is None:
 parent_node.left = new_node # We insert the new node in a leaf
 break
 else:
 parent_node = parent_node.left
 elif parent_node.right is None:
 parent_node.right = new_node
 break
 else:
 parent_node = parent_node.right
 new_node.parent = parent_node

 def insert(self, *values) -> Self:
 for value in values:
 self.__insert(value)
 return self

 def search(self, value) -> Node | None:
 """
 >>> tree = BinarySearchTree().insert(10, 20, 30, 40, 50)
 >>> tree.search(10)
 {'10': (None, {'20': (None, {'30': (None, {'40': (None, 50)})})})}
 >>> tree.search(20)
 {'20': (None, {'30': (None, {'40': (None, 50)})})}
 >>> tree.search(30)
 {'30': (None, {'40': (None, 50)})}
 >>> tree.search(40)
 {'40': (None, 50)}
 >>> tree.search(50)
 50
 >>> tree.search(5) is None # element not present
 True
 >>> tree.search(0) is None # element not present
 True
 >>> tree.search(-5) is None # element not present
 True
 >>> BinarySearchTree().search(10)
 Traceback (most recent call last):
 ...
 IndexError: Warning: Tree is empty! please use another.
 """

 if self.empty():
 raise IndexError("Warning: Tree is empty! please use another.")
 else:
 node = self.root
 # use lazy evaluation here to avoid NoneType Attribute error
 while node is not None and node.value is not value:
 node = node.left if value < node.value else node.right
 return node

 def get_max(self, node: Node | None = None) -> Node | None:
 """
 We go deep on the right branch

 >>> BinarySearchTree().insert(10, 20, 30, 40, 50).get_max()
 50
 >>> BinarySearchTree().insert(-5, -1, 0.1, -0.3, -4.5).get_max()
 {'0.1': (-0.3, None)}
 >>> BinarySearchTree().insert(1, 78.3, 30, 74.0, 1).get_max()
 {'78.3': ({'30': (1, 74.0)}, None)}
 >>> BinarySearchTree().insert(1, 783, 30, 740, 1).get_max()
 {'783': ({'30': (1, 740)}, None)}
 """
 if node is None:
 if self.root is None:
 return None
 node = self.root

 if not self.empty():
 while node.right is not None:
 node = node.right
 return node

 def get_min(self, node: Node | None = None) -> Node | None:
 """
 We go deep on the left branch

 >>> BinarySearchTree().insert(10, 20, 30, 40, 50).get_min()
 {'10': (None, {'20': (None, {'30': (None, {'40': (None, 50)})})})}
 >>> BinarySearchTree().insert(-5, -1, 0, -0.3, -4.5).get_min()
 {'-5': (None, {'-1': (-4.5, {'0': (-0.3, None)})})}
 >>> BinarySearchTree().insert(1, 78.3, 30, 74.0, 1).get_min()
 {'1': (None, {'78.3': ({'30': (1, 74.0)}, None)})}
 >>> BinarySearchTree().insert(1, 783, 30, 740, 1).get_min()
 {'1': (None, {'783': ({'30': (1, 740)}, None)})}
 """
 if node is None:
 node = self.root
 if self.root is None:
 return None
 if not self.empty():
 node = self.root
 while node.left is not None:
 node = node.left
 return node

 def remove(self, value: int) -> None:
 # Look for the node with that label
 node = self.search(value)
 if node is None:
 msg = f"Value {value} not found"
 raise ValueError(msg)

 if node.left is None and node.right is None: # If it has no children
 self.__reassign_nodes(node, None)
 elif node.left is None: # Has only right children
 self.__reassign_nodes(node, node.right)
 elif node.right is None: # Has only left children
 self.__reassign_nodes(node, node.left)
 else:
 predecessor = self.get_max(
 node.left
 ) # Gets the max value of the left branch
 self.remove(predecessor.value) # type: ignore[union-attr]
 node.value = (
 predecessor.value # type: ignore[union-attr]
 ) # Assigns the value to the node to delete and keep tree structure

 def preorder_traverse(self, node: Node | None) -> Iterable:
 if node is not None:
 yield node # Preorder Traversal
 yield from self.preorder_traverse(node.left)
 yield from self.preorder_traverse(node.right)

 def traversal_tree(self, traversal_function=None) -> Any:
 """
 This function traversal the tree.
 You can pass a function to traversal the tree as needed by client code
 """
 if traversal_function is None:
 return self.preorder_traverse(self.root)
 else:
 return traversal_function(self.root)

 def inorder(self, arr: list, node: Node | None) -> None:
 """Perform an inorder traversal and append values of the nodes to
 a list named arr"""
 if node:
 self.inorder(arr, node.left)
 arr.append(node.value)
 self.inorder(arr, node.right)

 def find_kth_smallest(self, k: int, node: Node) -> int:
 """Return the kth smallest element in a binary search tree"""
 arr: list[int] = []
 self.inorder(arr, node) # append all values to list using inorder traversal
 return arr[k - 1]


def inorder(curr_node: Node | None) -> list[Node]:
 """
 inorder (left, self, right)
 """
 node_list = []
 if curr_node is not None:
 node_list = [*inorder(curr_node.left), curr_node, *inorder(curr_node.right)]
 return node_list


def postorder(curr_node: Node | None) -> list[Node]:
 """
 postOrder (left, right, self)
 """
 node_list = []
 if curr_node is not None:
 node_list = postorder(curr_node.left) + postorder(curr_node.right) + [curr_node]
 return node_list


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)