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230. Kth Smallest Element in a BST

Medium

Given the root of a binary search tree, and an integer k, return the kth smallest value (1-indexed) of all the values of the nodes in the tree.

Example 1:

Input: root = [3,1,4,null,2], k = 1

Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 3

Output: 3

Constraints:

• The number of nodes in the tree is n.
• 1 <= k <= n <= 104
• 0 <= Node.val <= 104

Follow up: If the BST is modified often (i.e., we can do insert and delete operations) and you need to find the kth smallest frequently, how would you optimize?

Solution

/*
 * Definition for a binary tree node.
 * class TreeNode {
 *     val: number
 *     left: TreeNode | null
 *     right: TreeNode | null
 *     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
 *         this.val = (val===undefined ? 0 : val)
 *         this.left = (left===undefined ? null : left)
 *         this.right = (right===undefined ? null : right)
 *     }
 * }
 */
function kthSmallest(root: TreeNode | null, k: number): number {
    let cur = root
    while (cur !== null) {
        if (cur.left !== null) {
            const left = cur.left
            cur.left = null
            let rightmost = left
            while (rightmost.right !== null) rightmost = rightmost.right
            rightmost.right = cur
            cur = left
        } else if (--k !== 0) {
            cur = cur.right
        } else {
            break
        }
    }
    return cur.val
}

export { kthSmallest }

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