add algorithm to check binary search tree (#7947)

* add algorithm to check binary search tree

* add tests

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* add TreeNode resolving

* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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* Update data_structures/binary_tree/is_bst.py

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data_structures/binary_tree/is_bst.py

@@ -0,0 +1,131 @@
+"""
+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()