LeetCode.230 Kth Smallest Element in a BST

最新推荐文章于 2020-11-27 18:02:08 发布

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最新推荐文章于 2020-11-27 18:02:08 发布

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分类专栏： LeetCode算法编程

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本文介绍了一种寻找二叉搜索树中第K小元素的方法，通过中序遍历实现了简单有效的查找过程，并讨论了当二叉树频繁变动时如何优化查找效率。

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?

Credits:
Special thanks to @ts for adding this problem and creating all test cases.

example:

/ \

2 6

/ \ / \

1 3 5 7

分析：

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int kthSmallest(TreeNode root, int k) {
        //给定一颗从左到右的按顺序的二叉树，找出其中第k小的数
        //思路：因为从左到右依次增大的树，那么中序遍历即可满足条件
        List<Integer> list=new ArrayList<>();
        backtrace(root,list,k);
        return list.get(k-1);
    }
    //中序递归
    public void backtrace(TreeNode root,List<Integer> list,int k){
        //出口
        if(list.size()>=k){
            return ;
        }
        if(root.left!=null){
            backtrace(root.left,list,k);
        }
        list.add(root.val);
        if(root.right!=null){
            backtrace(root.right,list,k);
        }
    }
}