Simplify is_bst.py (#10627)

* 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>

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: 3 people

DIRECTORY.md

@@ -199,7 +199,8 @@
     * [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)

data_structures/binary_tree/is_bst.py

@@ -0,0 +1,97 @@
+"""
+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 = }.")