Kth Smallest Element in a BST

二叉搜索树中第k个最小的数

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.

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?

解析重点

1.看图中的树，我们以中序遍历就可以得到从小到大的排列。
2.然后，我们要找到第k个数，那么我们中序遍历的时候，记录下自己当前遍历到的位置，当当前位置等于k时，即为我们需要的值。

java代码

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    
    private static int number = 0;
    private static int count = 0;
    
    public int kthSmallest(TreeNode root, int k) {
        count=k;
        kSmallest(root);
        return number;
    }
    
    private void kSmallest(TreeNode root){
        if(root.left!=null) kSmallest(root.left);
        count--;
        if(count==0){
            number=root.val;
            return;
        }
        if(root.right!=null) kSmallest(root.right);
    }
}