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Validate Binary Search Tree

Certification: Intermediate Level Accuracy: 100% Submissions: 1 Points: 10

Write a Python function to validate if a given binary tree 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.
Algorithm for is_valid_bst(root)
  1. Use a recursive approach to validate each node in the tree.
  2. For each node, track the valid range of values (lower and upper bounds).
  3. Validate that the current node's value falls within the valid range.
  4. Update the valid range when traversing to left and right subtrees.
  5. Return true if all nodes satisfy the BST property, false otherwise.
Example 1
    

  • Input:

     2

    / \
     1 3
    • 

  • Output: true
    • 

  • Explanation: 

      

    • The tree has the following structure:
      • 

    • - Root node with value 2
      • 

    • - Left child with value 1 (less than 2)
      • 

    • - Right child with value 3 (greater than 2)
      • 

    • All BST properties are satisfied.
      • 

    

    •
Example 2
    

  • Input:

    5

     / \

    1 4
     / \

    3 6
    • 

  • Output: false
    • 

  • Explanation: 

      

    • The tree has the following structure:
      • 

    • - Root node with value 5
      • 

    • - Left child with value 1 (less than 5)
      • 

    • - Right child with value 4 (less than 5, which violates BST property)
      • 

    •   - Left child of 4 is 3 (less than 4)
      • 

    •   - Right child of 4 is 6 (greater than 4)
      • 

    • The value 4 is not greater than 5, so this is not a valid BST.
      • 

    

    •
Constraints
    

  • The number of nodes in the tree is in the range [1, 10^4]
    • 

  • -2^31 <= Node.val <= 2^31 - 1
    • 

  • Time Complexity: O(n) where n is the number of nodes
    • 

  • Space Complexity: O(h) where h is the height of the tree
    •
RecursionTreeCapgeminiAirbnb
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Hint
Solution

Solution Hints

    
  
  • Consider using an in-order traversal to check if the values are in ascending order
    • 
  
  • Alternatively, use a recursive approach with upper and lower bounds for each node
    • 
  
  • Remember that each node must be greater than all nodes in its left subtree and less than all nodes in its right subtree
    • 
  
  • Track the valid range for each node as you traverse down the tree
    • 
  
  • Be careful about handling duplicate values according to the problem's definition
    •

Steps to solve by this approach:

 Step 1: Define a recursive helper function that takes a node and the valid range (lower and upper bounds).
 Step 2: If the node is None, return True as an empty tree is a valid BST.
 Step 3: Check if the current node's value is within the valid range. If not, return False.
 Step 4: Recursively validate the left subtree with an updated upper bound (current node's value).
 Step 5: Recursively validate the right subtree with an updated lower bound (current node's value).

Submitted Code :