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Kth Smallest Element in a BST

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to implement the KthSmallest function, which finds the kth smallest element in a Binary Search Tree (BST). The function should take the root of a BST and an integer k, and return the kth smallest element in the tree.

Example 1
    
  
  • Input: root = [3,1,4,null,2], k = 1
    • 
  
  • Output: 1
    • 
  
  • Explanation: 
    
      
      
    • Tree structure:
      3
       / \
      1 4
       \
      2
      • 
      
    • The smallest element in this BST is 1.
      • 
    
    
  
    •
Example 2
    
  
  • Input: root = [5,3,6,2,4,null,null,1], k = 3
    • 
  
  • Output: 3
    • 
  
  • Explanation: 
    
      
      
    • Tree structure:
      5
       / \
      36
       / \
      2 4
      
        /
      
        1
      • 
      
    • The elements in ascending order are [1,2,3,4,5,6] and the 3rd element is 3.
      • 
    
    
  
    •
Constraints
    
  
  • The number of nodes in the tree is n, where 1 ≤ n ≤ 10^4
    • 
  
  • 0 ≤ Node.val ≤ 10^4
    • 
  
  • 1 ≤ k ≤ n
    • 
  
  • Time Complexity: O(h + k) where h is the height of the tree
    • 
  
  • Space Complexity: O(h) for recursion stack
    •
TreeGoldman SachsSwiggy
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Hint
Solution

Solution Hints

    
  
  • Use an in-order traversal to visit nodes in ascending order
    • 
  
  • Keep a counter to track the position of the current node
    • 
  
  • When the counter equals k, you've found the kth smallest element
    • 
  
  • Try both recursive and iterative solutions
    • 
  
  • Optimize by stopping the traversal once the kth element is found
    •

Steps to solve by this approach:

 Step 1: Implement an in-order traversal using a stack (iterative approach)
 Step 2: Initialize a counter to keep track of the number of nodes visited
 Step 3: Push all left nodes onto the stack first (following BST property that left subtree contains smaller values)
 Step 4: Process nodes in the stack one by one, incrementing the counter for each node
 Step 5: When the counter equals k, return the value of the current node as the kth smallest
 Step 6: If the current node has a right child, traverse its left subtree next
 Step 7: Continue this process until either the kth element is found or all nodes are visited

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