【Leetcode】：230. Kth Smallest Element in a BST 问题 in JAVA

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?

题目要求找到第k小的数，好在给的是一个BST树，可以比较简单的找到。

解题思路：计算root节点的左边有多少个节点，

情况1：如果左边的节点数》=k，那么第k小的元素一定在左边，

情况2：如果左边的节点数等于k-1，那么root就是要找的节点，

情况3：否则第k小的元素一定在左边，去右边找

该函数的作用是计算node下有多少个节点，包括node自己

private int countNode(TreeNode node)
/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public int kthSmallest(TreeNode root, int k) {
int num = countNode(root.left);
if (num + 1 == k) {
return root.val;
} else if (num >= k) { //在左边找
return kthSmallest(root.left, k);
} else { //在右边找
return kthSmallest(root.right, k - num - 1);
}
}

private int countNode(TreeNode node) {
if (node == null) {
return 0;
}
return countNode(node.left) + countNode(node.right) + 1;
}
}