[Leetcode-Tree] Kth Smallest Element in a BST

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.

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?

Hint:

Try to utilize the property of a BST.
What if you could modify the BST node's structure?
The optimal runtime complexity is O(height of BST).

1.解題思路

本題須要找的是第k小的節點值，而二叉搜索樹的中序遍歷正好是數值從小到大排序的，那麼這題就和中序遍歷一個狀況。

public class Solution {
    Stack<TreeNode> s=new Stack<TreeNode>();
    public int kthSmallest(TreeNode root, int k) {
        if(root==null) return 0;
        pushLeft(root);
        while(!s.empty()){
            TreeNode node=s.pop();
            if(--k==0) return node.val;
            if(node.right!=null)
                pushLeft(node.right);
        }
        return 0;
    }
    private void pushLeft(TreeNode root){
        TreeNode node=root;
        while(node!=null){
            s.push(node);
            node=node.left;
        }
    }
}

3.Follow up

若是樹會常常被更改，爲了效率，咱們能夠對樹的構造稍做變動，添加一個屬性，來標明該節點擁有的左子樹的節點數，而這個Number就是比當前值小的節點個數，這樣咱們結合二分法，就很容易找到第k個小的節點值。