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)。

解法1

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/binary-tree/bst/kth-smallest-element-in-a-bst.html