230. Kth Smallest Element in a BST

Given a binary search tree, write a function kthSmallest to find the kth smallest element in it.

Note:

You may assume k is always valid, 1 ≤ k ≤ BST's total elements.

Follow-Up:

What if the BST is modified (insert/delete operations) often and you need to find the kth smallest frequently? How would you optimize the kthSmallest routine?

Hint:

Try to utilize the property of a BST.

Solution:

class Solution(object):
    def kthSmallest(self, root, k):
        """
        :type root: TreeNode
        :type k: int
        :rtype: int
        """
        size_map = dict()
        left_size = self.size(root.left, size_map)
        if left_size + 1 == k:
            return root.val
        if left_size + 1 > k:
            return self.kthSmallest(root.left, k)
        return self.kthSmallest(root.right, k - left_size - 1)

    def size(self, root, size_map):
        if not root:
            return 0
        if root in size_map:
            return size_map[root]
        left = self.size(root.left, size_map)
        right = self.size(root.right, size_map)
        size = left + right + 1
        size_map[root] = size
        return size