Kth Smallest Element in a BST
描述
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.
- What if you could modify the BST node's structure?
- The optimal runtime complexity is O(height of BST).
分析
最简单的办法，中序遍历，即可以得到递增序列，从而可以找到第k大的元素。时间复杂度O(k)。
如果能够修改节点的数据结构TreeNode，可以增加一个字段leftCnt，表示左子树的节点个数。设当前节点为root，
- 若
k == root.leftCnt+1, 则返回root - 若
k > node.leftCnt, 则k -= root.leftCnt+1,root=root.right - 否则，
node = node.left
算法复杂度为O(height of BST)。