Inorder Successor in Binary Search Tree

Given a binary search tree and a node in it, find the in-order successor
of that node in the BST.
If the given node has no in-order successor in the tree, return null

Notice
It's guaranteed p is one node in the given tree.
(You can directly compare the memory address to find p)

Example
Given tree = [2,1]
and node = 1
  2
 /
1
return node 2

Given tree = [2,1,3]
and node = 2
 2
 / \
1  3
return node 3

我通常能直接想到的办法都是Straightforward的方法，大多数人应该也都这样。这样的方法好处是好理解，能通用；坏处是时间复杂度空间复杂度通常不是最优的。这道题我首先想到的就是先求出Binary tree inorder traversal,然后找到给出的p,返回p的下一个节点就可以了。
但我的作法并没有利用到BST的特性

//do inorder traversal of a binary search tree, and then search in the 
//resultsting list

public class Solution {
    public TreeNode inorderSuccessor(TreeNode root, TreeNode p) {
        // write your code here
        List res = inorderTraversal(root);
        for (int i = 0; i < res.size(); i++){
            if (res.get(i) == p && i + 1 < res.size()){
                return res.get(i+1);
            }
        }
        return null;
    }
    
    private List inorderTraversal(TreeNode root){
        ArrayList inOrder = new ArrayList<>();
        if (root == null){
            return inOrder;
        }
        TreeNode curt = root;
        Stack stack = new Stack<>();
        while (curt != null){
            stack.push(curt);
            curt = curt.left;
        }
        while (!stack.isEmpty()){
            TreeNode node = stack.pop();
            inOrder.add(node);
            curt = node.right;
            while (curt != null){
                stack.push(curt);
                curt = curt.left;
            }
        }
        return inOrder;
    }

另一种解法：O(logN) 利用了BST的性质：节点左边的节点val比该节点的val小，右边的节点比该节点的val大

class Solution {
    public TreeNode inorderSuccessor(TreeNode root, TreeNode p) {
        if (root == null){
            return null;
        }
        
        //if p has right children, its successor will be the left most node 
        //in its right subtree, which is also the smallest. This is due to 
        //the property of BST. 
        if (p.right != null){
             return findMin(p.right);
        } else {
        //if current node has no right children, its successor will be one of
        //its ancestors, which has the deepest depth and current node is in its           
        //left side.
        TreeNode ancestor = root;
        TreeNode successor = null;
           while (ancestor != null){
                //if node's val is less than ancestor, we know node is in the left     
                //side of ancestor. But we are not sure if it is the closet to node, 
                //or in other words the one has the deepest depth, so we move
                //left to update ancestor.
                if (p.val < ancestor.val){
                    successor = ancestor;
                    ancestor = ancestor.left;
                } else {
                    //if node's val is larger than ancestor, we know that node is 
                    //in the right side of ancestor. So we move ancestor to the right
                    ancestor = ancestor.right;
                }
            } 
            return successor;  
        }
    }    
    
    private TreeNode findMin(TreeNode root){
        if (root == null){
            return null;
        }
        while (root.left != null){
            root = root.left;
        }
        return root;
    }
}

helpful resources
Inorder Successor in a binary search tree