Introduction

Validate BST means:

  • checking whether
    a binary tree
    follows BST properties

BST Property:

Left subtree values < Root value < Right subtree values

Goal:

  • verify every node
    maintains BST ordering

Example:

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

Output:
True

Explanation:

All nodes satisfy BST ordering rules, so tree is valid.

This problem is one of the most important applications of:

DFS Traversal

Constraints

DFS Traversal

Approach : DFS with Range Validation

Explanations:

Explanation:

The idea is:

  • each node must lie
    inside valid range
  • update boundaries
    during DFS traversal

Steps:

  1. Start from root node.
  2. Maintain minimum boundary.
  3. Maintain maximum boundary.
  4. Validate current node.
  5. Traverse left subtree.
  6. Traverse right subtree.

Conditions:

node.value <= minimum → invalid BSTnode.value >= maximum → invalid BSTminimum < node.value < maximum → valid node

This approach:

  • validates entire tree
  • efficiently checks BST ordering

Dry Run

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

Node 5:
Valid range:
(-∞ , +∞)

Node 3:
Valid range:
(-∞ , 5)

Node 7:
Valid range:
(5 , +∞)

All nodes valid.

Answer:
True

Practice :

Complexity Analysis :

Time Complexity:- O(n)Explanation :
Every 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
  • Recursive DFS traversal
  • Tree boundary checking
  • Ordered tree structures
  • Binary search trees

Real-World Applications

BST validation concepts are used in:

  • Database indexing
  • Ordered storage systems
  • Search engines
  • File indexing
  • Data validation systems

Common Beginner Mistakes

  • Checking only immediate children
  • Ignoring subtree ranges
  • Incorrect boundary updates
  • Missing null handling
  • Using local comparisons only

Interview Tip

Interviewers often expect:

  • BST property understanding
  • range validation explanation
  • recursive DFS discussion
  • complexity clarity

Always explain:

  • why subtree ranges matter
  • minimum/maximum boundaries
  • recursive validation logic

Related Questions

  • Search in BST
  • Insert into BST
  • Recover BST
  • Kth Smallest Element
  • Delete Node in BST

Final Takeaway

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

It teaches:

  • BST validation
  • DFS traversal
  • range-based recursion
  • ordered tree processing

Understanding this problem builds a strong foundation for:

  •  advanced BST problems
  • tree algorithms
  • interview-level data structures.