add algorithm to check binary search tree

data_structures/binary_tree/is_bst.py

@@ -0,0 +1,121 @@
+"""
+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 BST 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
+
+
+class TreeNode:
+ def __init__(
+ self,
+ data: float = 0,
+ left: TreeNode | None = None,
+ right: TreeNode | None = None,
+ ) -> None:
+ self.data = data
+ self.left = left
+ self.right = right
+
+
+def is_bst(root: TreeNode | None) -> bool:
+ """
+ >>> is_bst(TreeNode(2, TreeNode(1), TreeNode(3)))
+ True
+
+ >>> is_bst(TreeNode(0, TreeNode(-11), TreeNode(3)))
+ True
+
+ >>> is_bst(TreeNode(5, TreeNode(1), TreeNode(4, TreeNode(3))))
+ False
+
+ >>> is_bst(TreeNode('a', TreeNode(1), TreeNode(4, TreeNode(3))))
+ Traceback (most recent call last):
+ ...
+ ValueError: Each node should be type of TreeNode and data should be float.
+
+ >>> is_bst(TreeNode(2, TreeNode([]), TreeNode(4, TreeNode(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('not a float'))
+ False
+
+ >>> is_valid_tree(TreeNode(1, TreeNode('123')))
+ False
+ """
+ if node is None:
+ return True
+
+ if not isinstance(node, TreeNode):
+ return False
+
+ try:
+ float(node.data)
+ except ValueError:
+ return False
+ except TypeError:
+ 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_bst_internal(
+ node: TreeNode | None, left_bound: float, right_bound: float
+ ) -> bool:
+ """
+ >>> is_bst_internal(None)
+ True
+ """
+
+ if node is None:
+ return True
+
+ return (
+ (node.data > left_bound)
+ and (node.data < right_bound)
+ and is_bst_internal(node.left, left_bound, node.data)
+ and is_bst_internal(node.right, node.data, right_bound)
+ )
+
+ return is_bst_internal(root, -float("inf"), float("inf"))
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()