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0230.kth-smallest-element-in-a-bst

题目

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?

解题思路

以下是BST的性质:

  1. 若任意节点的左子树不空,则左子树上所有节点的值均小于它的根节点的值;
  2. 若任意节点的右子树不空,则右子树上所有节点的值均大于它的根节点的值;
  3. 任意节点的左、右子树也分别为二叉查找树;
  4. 没有键值相等的节点。

见程序注释