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Binary Tree is a Valid BST

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C# program to determine 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 Tree with root node 2

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  • Output: true
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  • Explanation: 
    
      
      
    • The binary tree has root value 2, left child with value 1, and right child with value 3.
      • 
      
    • This forms a valid BST.
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    •
Example 2
    
  
  • Input: 

    Binary Tree with root node 5

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  • Output: false
    • 
  
  • Explanation: 
    
      
      
    • The node with value 4 has a left child with value 3, which is valid.
      • 
      
    • However, it also has a right child with value 6, which is greater than the root value 5.
      • 
      
    • This violates the BST property.
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    •
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
    •
Binary TreeTreeShopifyArctwist
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Hint
Solution

Solution Hints

    
  
  • Use recursion to check each subtree.
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  • Keep track of the valid range for each node.
    • 
  
  • Traverse the tree in-order and check if values are in ascending order.
    • 
  
  • Be careful about edge cases with duplicate values.
    •

Steps to solve by this approach:

 Step 1: Use a recursive helper function that takes a node and the valid range for that node (min and max values).
 Step 2: If the node is null, return true (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 check the left subtree, updating the max value to the current node's value.
 Step 5: Recursively check the right subtree, updating the min value to the current node's value.
 Step 6: Return true only if both the left and right subtrees are valid BSTs.
 Step 7: Use long.MinValue and long.MaxValue as the initial range to handle edge cases with integer boundaries.

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