Program to find the kth smallest element in a Binary Search Tree in Python

Suppose we have a binary search tree, and another integer k we have to find the kth smallest value in the tree.

So, if the input is like

k = 3, then the output will be 7

To solve this, we will follow these steps −

• stack := an empty stack

• i := 0

• ans := -1

• while stack is not empty or root is not null, do

  • while root is not null, do

    • push root into stack

    • root := left of root

  • v := pop element from stack

  • if i is same as k, then

    • ans := value of v

    • come out from loop

  • root := right of v

  • i := i + 1

• return ans

Let us see the following implementation to get better understanding −

Example

class TreeNode:
   def __init__(self, value):
      self.val = value
      self.left = None
      self.right = None

class Solution:
   def solve(self, root, k):
      stack = []
      i = 0
      ans = -1
      while stack or root:
         while root:
            stack.append(root)
               root = root.left
         v = stack.pop()
         if i == k:
            ans = v.val
            break
         root = v.right
         i += 1
      return ans
ob = Solution()
root = TreeNode(5)
root.left = TreeNode(4)
root.right = TreeNode(10)
root.right.left = TreeNode(7)
root.right.right = TreeNode(15)
root.right.left.left = TreeNode(6)
root.right.left.right = TreeNode(8)
print(ob.solve(root, 3))

Input

root = TreeNode(5)
root.left = TreeNode(4)
root.right = TreeNode(10)
root.right.left = TreeNode(7)
root.right.right = TreeNode(15)
root.right.left.left = TreeNode(6)
root.right.left.right = TreeNode(8)
3

Output

7