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Valid Binary Search Tree

Certification: Advanced Level Accuracy: 62.5% Submissions: 8 Points: 15

Write a Python function that checks 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.
Example 1
    

  • Input:

    Binary Search Tree One - Root node with value 2

  • 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:


    Binary Search Tree Two - Root node with value 5

    • 

  • 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
    

  • 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
    •
RecursionBinary TreeGoogleTutorialspoint
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Hint
Solution

Solution Hints

    
  
  • Use inorder traversal and check if values are in ascending order
    • 
  
  • Use a recursive approach with min and max boundary values
    • 
  
  • Check each node's value against valid ranges
    • 
  
  • Handle edge cases like duplicates according to BST definition
    •

Steps to solve by this approach:

 Step 1: Use recursive validation with min and max value constraints.

 Step 2: Initially set min value to negative infinity and max value to positive infinity.

 Step 3: Check if the current node's value is within the valid range.

 Step 4: For the left subtree, update the max constraint to the current node's value.

 Step 5: For the right subtree, update the min constraint to the current node's value.

 Step 6: Return true only if current node and all its subtrees satisfy BST properties.

Submitted Code :