Introduction

Validate BST means:

  • checking whether
    a binary tree
    follows BST rules

BST Property:

Left subtree values < Root value < Right subtree values

Every node must:

  • satisfy valid range
  • maintain BST ordering

Example:

        5      /   \
     3     7
    / \   / \
   2   4 6   8

Output:
True

Invalid Example:

        5      /   \
     3     7
          /
         4

Output:
False

Explanation:

4 exists inside right subtree of 5 but is smaller than 5.

This problem is one of the most important applications of:

DFS Traversal

Constraints

1 <= Number of Nodes <= 10^5

Approach : Recursive DFS Range Validation

Explanations:

Explanation:

The idea is:

  • recursively validate nodes
    using minimum and maximum limits

Steps:

  1. Visit current node.
  2. Check valid range.
  3. Update maximum for left subtree.
  4. Update minimum for right subtree.
  5. Recursively validate subtrees.

Conditions:

minimum < node.value < maximum

Left subtree:

maximum = current node value

Right subtree:

minimum = current node value

This approach:

  • uses DFS recursion
  • validates BST ordering globally

Dry Run

Visit:5

Range:
(-∞, +∞)

Visit:
3

Range:
(-∞, 5)

Visit:
7

Range:
(5, +∞)

All nodes satisfy BST rules.
Tree is valid.

Practice :

Complexity Analysis :

Time Complexity:- O(n)Explanation :
Every tree node is visited once.

Space Complexity:- O(h)
Explanation :
Recursion stack depends on tree height.

Why This Problem is Important

This problem builds the foundation for:

  • BST validation
  • DFS recursion
  • Range checking
  • Recursive tree traversal
  • Binary search tree analysis

Real-World Applications

BST validation concepts are used in:

  • Database indexing
  • Search engines
  • Ordered storage systems
  • Tree-based caching
  • Hierarchical data processing

Common Beginner Mistakes

  • Checking only direct children
  • Ignoring subtree range violations
  • Incorrect minimum/maximum updates
  • Missing recursion conditions
  • Confusing local and global BST rules

Interview Tip

Interviewers often expect:

  • BST understanding
  • recursion explanation
  • range validation logic
  • subtree constraint discussion

Always explain:

  • valid range propagation
  • recursive subtree validation
  • BST ordering guarantees

Related Questions

  • Kth Smallest Element
  • LCA in BST
  • Insert into BST
  • Binary Search Tree
  • DFS Traversal

Final Takeaway

The Validate BST problem is one of the most important beginner BST problems.

It teaches:

  • BST validation
  • DFS recursion
  • range propagation
  • recursive subtree checking

Understanding this problem builds a strong foundation for:

  • advanced BST problems
  • tree optimization
  • interview-level algorithms.