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Binary Search Tree Kth Smallest Element

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Given the root node of a binary search tree (BST) and an integer k, write a function to find and return the k-th smallest value in the BST. The smallest value in the tree is 1.

The binary tree is represented by a collection of TreeNodes, where each node has optional left and right child nodes, which are also TreeNodes.

A TreeNode has the following interface:

interface TreeNode {
  val: number;
  left: TreeNode | null;
  right: TreeNode | null;
}

Input

  • root: TreeNode: Root node of the tree. Examples display a level-order traversal of the tree
  • k: number: A positive integer

Examples

Input: root = [7,3,10,1,5,8,12], k = 2
Output: 3
Explanation: In this BST, the second smallest value is 3.
Input: root = [1,null,2,null,3,null,4,null,5], k = 4
Output: 4
Explanation: In this right-skewed BST, the fourth smallest value is 4.
Input: root = [8,6,10,5,7,9,12], k = 5
Output: 9
Explanation: In this BST, the fifth smallest value is 9.

Constraints

  • 1 <= k <= Number of nodes <= 1000
  • 1 <= TreeNode.val <= 1,000,000

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