230.kth-smallest-element-in-a-bst.md

题目地址

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

题目描述

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.

Example 1:

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

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

思路

由于‘中序遍历一个二叉查找树（BST）的结果是一个有序数组’ ，因此我们只需要在遍历到第k个，返回当前元素即可。 中序遍历相关思路请查看binary-tree-traversal

关键点解析

• 中序遍历

代码

/*
 * @lc app=leetcode id=230 lang=javascript
 *
 * [230] Kth Smallest Element in a BST
 */
/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {TreeNode} root
 * @param {number} k
 * @return {number}
 */
var kthSmallest = function(root, k) {
    const stack = [root];
    let cur = root;
    let i = 0;

    function insertAllLefts(cur) {
        while(cur && cur.left) {
            const l = cur.left;
            stack.push(l);
            cur = l;
        }
    }
    insertAllLefts(cur);

    while(cur = stack.pop()) {
        i++;
        if (i === k) return cur.val;
        const r = cur.right;

        if (r) {
            stack.push(r);
            insertAllLefts(r);
        }
    }

    return -1;

    
};

扩展

这道题有一个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?

大家可以思考一下。