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Simplify is_bst.py (#10627)

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* Simplify is_bst.py

* updating DIRECTORY.md

* Update is_bst.py

* Rename is_bst.py to is_sorted.py

* updating DIRECTORY.md

* Update data_structures/binary_tree/is_sorted.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

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Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
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DIRECTORY.md
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* [Flatten Binarytree To Linkedlist](data_structures/binary_tree/flatten_binarytree_to_linkedlist.py)
* [Floor And Ceiling](data_structures/binary_tree/floor_and_ceiling.py)
* [Inorder Tree Traversal 2022](data_structures/binary_tree/inorder_tree_traversal_2022.py)
* [Is Bst](data_structures/binary_tree/is_bst.py)
* [Is Sorted](data_structures/binary_tree/is_sorted.py)
* [Is Sum Tree](data_structures/binary_tree/is_sum_tree.py)
* [Lazy Segment Tree](data_structures/binary_tree/lazy_segment_tree.py)
* [Lowest Common Ancestor](data_structures/binary_tree/lowest_common_ancestor.py)
* [Maximum Fenwick Tree](data_structures/binary_tree/maximum_fenwick_tree.py)

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data_structures/binary_tree/is_bst.py
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"""
Author : Alexander Pantyukhin
Date : November 2, 2022
Task:
Given the root of a binary tree, determine if it is a valid binary search
tree (BST).
A valid binary search tree is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
Implementation notes:
Depth-first search approach.
leetcode: https://leetcode.com/problems/validate-binary-search-tree/
Let n is the number of nodes in tree
Runtime: O(n)
Space: O(1)
"""
from __future__ import annotations
from dataclasses import dataclass
@dataclass
class TreeNode:
data: float
left: TreeNode | None = None
right: TreeNode | None = None
def is_binary_search_tree(root: TreeNode | None) -> bool:
"""
>>> is_binary_search_tree(TreeNode(data=2,
... left=TreeNode(data=1),
... right=TreeNode(data=3))
... )
True
>>> is_binary_search_tree(TreeNode(data=0,
... left=TreeNode(data=-11),
... right=TreeNode(data=3))
... )
True
>>> is_binary_search_tree(TreeNode(data=5,
... left=TreeNode(data=1),
... right=TreeNode(data=4, left=TreeNode(data=3)))
... )
False
>>> is_binary_search_tree(TreeNode(data='a',
... left=TreeNode(data=1),
... right=TreeNode(data=4, left=TreeNode(data=3)))
... )
Traceback (most recent call last):
...
ValueError: Each node should be type of TreeNode and data should be float.
>>> is_binary_search_tree(TreeNode(data=2,
... left=TreeNode([]),
... right=TreeNode(data=4, left=TreeNode(data=3)))
... )
Traceback (most recent call last):
...
ValueError: Each node should be type of TreeNode and data should be float.
"""
# Validation
def is_valid_tree(node: TreeNode | None) -> bool:
"""
>>> is_valid_tree(None)
True
>>> is_valid_tree('abc')
False
>>> is_valid_tree(TreeNode(data='not a float'))
False
>>> is_valid_tree(TreeNode(data=1, left=TreeNode('123')))
False
"""
if node is None:
return True
if not isinstance(node, TreeNode):
return False
try:
float(node.data)
except (TypeError, ValueError):
return False
return is_valid_tree(node.left) and is_valid_tree(node.right)
if not is_valid_tree(root):
raise ValueError(
"Each node should be type of TreeNode and data should be float."
)
def is_binary_search_tree_recursive_check(
node: TreeNode | None, left_bound: float, right_bound: float
) -> bool:
"""
>>> is_binary_search_tree_recursive_check(None)
True
>>> is_binary_search_tree_recursive_check(TreeNode(data=1), 10, 20)
False
"""
if node is None:
return True
return (
left_bound < node.data < right_bound
and is_binary_search_tree_recursive_check(node.left, left_bound, node.data)
and is_binary_search_tree_recursive_check(
node.right, node.data, right_bound
)
)
return is_binary_search_tree_recursive_check(root, -float("inf"), float("inf"))
if __name__ == "__main__":
import doctest
doctest.testmod()

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data_structures/binary_tree/is_sorted.py Normal file
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"""
Given the root of a binary tree, determine if it is a valid binary search tree (BST).
A valid binary search tree is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
In effect, a binary tree is a valid BST if its nodes are sorted in ascending order.
leetcode: https://leetcode.com/problems/validate-binary-search-tree/
If n is the number of nodes in the tree then:
Runtime: O(n)
Space: O(1)
"""
from __future__ import annotations
from collections.abc import Iterator
from dataclasses import dataclass
@dataclass
class Node:
data: float
left: Node | None = None
right: Node | None = None
def __iter__(self) -> Iterator[float]:
"""
>>> root = Node(data=2.1)
>>> list(root)
[2.1]
>>> root.left=Node(data=2.0)
>>> list(root)
[2.0, 2.1]
>>> root.right=Node(data=2.2)
>>> list(root)
[2.0, 2.1, 2.2]
"""
if self.left:
yield from self.left
yield self.data
if self.right:
yield from self.right
@property
def is_sorted(self) -> bool:
"""
>>> Node(data='abc').is_sorted
True
>>> Node(data=2,
... left=Node(data=1.999),
... right=Node(data=3)).is_sorted
True
>>> Node(data=0,
... left=Node(data=0),
... right=Node(data=0)).is_sorted
True
>>> Node(data=0,
... left=Node(data=-11),
... right=Node(data=3)).is_sorted
True
>>> Node(data=5,
... left=Node(data=1),
... right=Node(data=4, left=Node(data=3))).is_sorted
False
>>> Node(data='a',
... left=Node(data=1),
... right=Node(data=4, left=Node(data=3))).is_sorted
Traceback (most recent call last):
...
TypeError: '<' not supported between instances of 'str' and 'int'
>>> Node(data=2,
... left=Node([]),
... right=Node(data=4, left=Node(data=3))).is_sorted
Traceback (most recent call last):
...
TypeError: '<' not supported between instances of 'int' and 'list'
"""
if self.left and (self.data < self.left.data or not self.left.is_sorted):
return False
if self.right and (self.data > self.right.data or not self.right.is_sorted):
return False
return True
if __name__ == "__main__":
import doctest
doctest.testmod()
tree = Node(data=2.1, left=Node(data=2.0), right=Node(data=2.2))
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")
assert tree.right
tree.right.data = 2.0
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")
tree.right.data = 2.1
print(f"Tree {list(tree)} is sorted: {tree.is_sorted = }.")