Added the validate bst function (#2696)

* Added the validate bst function

* Added the validate bst function

---------

Co-authored-by: Piyush Goel <[email protected]>

Author: PiyushGoel0612

algorithms/tree/bst/validate_bst.py

@@ -0,0 +1,90 @@
+# ===============================================================================
+# Validate Binary Search Tree
+'''
+To check if the given binary tree is a valid binary search tree (BST), we need to ensure that:
+    1. The left subtree of a node contains only nodes with keys less than the node's key.
+    2. The right subtree of a node contains only nodes with keys greater than the node's key.
+    3. Both the left and right subtrees must also be binary search trees.
+'''
+# ===============================================================================
+
+# Tree class definition
+class TreeNode:
+
+    def __init__(self, value):
+
+        self.val = value
+        self.left = None
+        self.right = None
+
+# Function to validate if a binary tree is a BST
+def validate_bst(node):
+    '''
+    Validate if a binary tree is a binary search tree (BST).
+    Input params : Tree Node to be validated
+    Returns : Tuple (
+        is_bst: bool, 
+        min_value: int | None, 
+        max_value: int | None
+    )
+    '''
+
+    # Base case: An empty tree is a valid BST
+    if not node: 
+        return (True, None, None)
+
+    # Validate the left and right subtrees
+    valid_left, minn_left, maxx_left = validate_bst(node.left)
+    valid_right, minn_right, maxx_right = validate_bst(node.right)
+
+    # If either subtree is not valid, the whole tree is not a valid BST
+    if not valid_left or not valid_right:
+        return (
+            False, 
+            minn_left if minn_left else node.val, 
+            maxx_right if maxx_right else node.val
+        )
+
+    # Check the current node's value against the max of the left subtree
+    if maxx_left is not None and maxx_left > node.val:
+        return (
+            False, 
+            minn_left if minn_left else node.val, 
+            maxx_right if maxx_right else node.val
+        )
+
+    # Check the current node's value against the min of the right subtree
+    if minn_right is not None and minn_right < node.val:
+        return (
+            False, 
+            minn_left if minn_left else node.val, 
+            maxx_right if maxx_right else node.val
+        )
+
+    # If all checks pass, the tree/subtree is a valid BST
+    return (
+        True, 
+        minn_left if minn_left is not None else node.val, 
+        maxx_right if maxx_right is not None else node.val
+    )
+
+# Example usage
+if __name__ == "__main__":
+    # Constructing a simple binary tree
+    root = TreeNode(10)
+    root.left = TreeNode(5)
+    root.right = TreeNode(15)
+    root.right.left = TreeNode(12)
+    root.right.right = TreeNode(20)
+
+    '''
+          10
+         /  \
+        5    15
+            /  \
+           12   20
+    '''
+
+    # Validate if the constructed tree is a BST
+    is_bst, _, _ = validate_bst(root)
+    print(f"The tree is a valid BST: {is_bst}")