[leetcode] 230. Kth Smallest Element in a BST 找出二叉搜索树中的第k小的元素

题目大意

https://leetcode.com/problems/kth-smallest-element-in-a-bst/description/

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.

Example 1:

Input: root = [3,1,4,null,2], k = 13/ \1 4\2 Output: 1

Example 2:

Input: root = [5,3,6,2,4,null,null,1], k = 35/ \3 6/ \2 4/1 Output: 3

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?

 

给定一棵二叉搜索树（BST），编写一个函数kthSmallest找出其中第k小的元素。

注意：
你可以假设k总是有效的， 1 ≤ k ≤ BST的元素总数。

进一步思考：
如果BST的修改（插入/删除）操作十分频繁，并且需要频繁地找出第k小的元素，应该怎样优化kthSmallest函数？

 

解题思路

BST具有如下性质：

• 左子树中所有元素的值均小于根节点的值
• 右子树中所有元素的值均大于根节点的值

因此采用中序遍历（左 -> 根 -> 右）即可以递增顺序访问BST中的节点，从而得到第k小的元素，时间复杂度O(k)

Python代码：

# Definition for a binary tree node. class TreeNode(object):def __init__(self, x):self.val = xself.left = Noneself.right = Noneclass Solution(object): def kthSmallest(self, root, k): # 52 ms""":type root: TreeNode:type k: int:rtype: int"""stack = []node = rootwhile node:stack.append(node)node = node.leftx = 1while stack and x <= k:node = stack.pop()x += 1right = node.rightwhile right:stack.append(right)right = right.leftreturn node.val

 

递归方式：

class Solution(object):def kthSmallest(self, root, k):""":type root: TreeNode:type k: int:rtype: int"""cnt = []self.helper(root, cnt, k)return cnt[k - 1]def helper(self, node, cnt, k):if not node:return Noneself.helper(node.left, cnt, k)cnt.append(node.val)if len(cnt) == k: # 56 ms <= 96msreturn Noneself.helper(node.right, cnt, k)

 

进一步思考：
如果BST节点TreeNode的属性可以扩展，则再添加一个属性leftCnt，记录左子树的节点个数

记当前节点为node 当node不为空时循环： 若k == node.leftCnt + 1：则返回node 否则，若k > node.leftCnt：则令k -= node.leftCnt + 1，令node = node.right 否则，node = node.left

上述算法时间复杂度为O(BST的高度)

 

参考

http://bookshadow.com/weblog/2015/07/02/leetcode-kth-smallest-element-bst/

https://leetcode.com/problems/kth-smallest-element-in-a-bst/discuss/63660/3-ways-implemented-in-JAVA-(Python):-Binary-Search-in-order-iterative-and-recursive

转载于:https://www.cnblogs.com/bymo/p/9667337.html

总结

以上是生活随笔为你收集整理的[leetcode] 230. Kth Smallest Element in a BST 找出二叉搜索树中的第k小的元素的全部内容，希望文章能够帮你解决所遇到的问题。

如果觉得生活随笔网站内容还不错，欢迎将生活随笔推荐给好友。