Formatted question description: https://leetcode.ca/all/510.html

# 510. Inorder Successor in BST II

Medium

## Description

Given a binary search tree and a node in it, find the in-order successor of that node in the BST.

The successor of a node p is the node with the smallest key greater than p.val.

You will have direct access to the node but not to the root of the tree. Each node will have a reference to its parent node.

Example 1:

Input:
root = {"$id":"1","left":{"$id":"2","left":null,"parent":{"$ref":"1"},"right":null,"val":1},"parent":null,"right":{"$id":"3","left":null,"parent":{"$ref":"1"},"right":null,"val":3},"val":2} p = 1 Output: 2 Explanation: 1's in-order successor node is 2. Note that both p and the return value is of Node type.  Example 2: Input: root = {"$id":"1","left":{"$id":"2","left":{"$id":"3","left":{"$id":"4","left":null,"parent":{"$ref":"3"},"right":null,"val":1},"parent":{"$ref":"2"},"right":null,"val":2},"parent":{"$ref":"1"},"right":{"$id":"5","left":null,"parent":{"$ref":"2"},"right":null,"val":4},"val":3},"parent":null,"right":{"$id":"6","left":null,"parent":{"$ref":"1"},"right":null,"val":6},"val":5}
p = 6
Output: null
Explanation: There is no in-order successor of the current node, so the answer is null.


Example 3:

Input:
root = {"$id":"1","left":{"$id":"2","left":{"$id":"3","left":{"$id":"4","left":null,"parent":{"$ref":"3"},"right":null,"val":2},"parent":{"$ref":"2"},"right":{"$id":"5","left":null,"parent":{"$ref":"3"},"right":null,"val":4},"val":3},"parent":{"$ref":"1"},"right":{"$id":"6","left":null,"parent":{"$ref":"2"},"right":{"$id":"7","left":{"$id":"8","left":null,"parent":{"$ref":"7"},"right":null,"val":9},"parent":{"$ref":"6"},"right":null,"val":13},"val":7},"val":6},"parent":null,"right":{"$id":"9","left":{"$id":"10","left":null,"parent":{"$ref":"9"},"right":null,"val":17},"parent":{"$ref":"1"},"right":{"$id":"11","left":null,"parent":{"$ref":"9"},"right":null,"val":20},"val":18},"val":15} p = 15 Output: 17  Example 4: Input: root = {"$id":"1","left":{"$id":"2","left":{"$id":"3","left":{"$id":"4","left":null,"parent":{"$ref":"3"},"right":null,"val":2},"parent":{"$ref":"2"},"right":{"$id":"5","left":null,"parent":{"$ref":"3"},"right":null,"val":4},"val":3},"parent":{"$ref":"1"},"right":{"$id":"6","left":null,"parent":{"$ref":"2"},"right":{"$id":"7","left":{"$id":"8","left":null,"parent":{"$ref":"7"},"right":null,"val":9},"parent":{"$ref":"6"},"right":null,"val":13},"val":7},"val":6},"parent":null,"right":{"$id":"9","left":{"$id":"10","left":null,"parent":{"$ref":"9"},"right":null,"val":17},"parent":{"$ref":"1"},"right":{"$id":"11","left":null,"parent":{"$ref":"9"},"right":null,"val":20},"val":18},"val":15}
p = 13
Output: 15


Note:

1. If the given node has no in-order successor in the tree, return null.
2. It’s guaranteed that the values of the tree are unique.
3. Remember that we are using the Node type instead of TreeNode type so their string representation are different.

Could you solve it without looking up any of the node’s values?

## Solution

Since the tree is a binary search tree, there is no need to look up any of the node’s values.

If the node has a right child, then obtain the leftmost node in the current node’s left subtree, which is the in-order success of the current node.

If the node doesn’t have a right child, then the node has an in-order successor if and only if there is another node such that the current node is in another node’s left subtree. Starting from the current node, find each node’s parent. If there exist a (parent, child) pair such that the child is the parent’s left child, then return the parent. If such a parent is not found, return null.

/*
// Definition for a Node.
class Node {
public int val;
public Node left;
public Node right;
public Node parent;
};
*/
class Solution {
public Node inorderSuccessor(Node x) {
if (x.right != null) {
Node successor = x.right;
while (successor.left != null)
successor = successor.left;
return successor;
} else {
Node child = x;
Node parent = x.parent;
while (parent != null && child != parent.left) {
child = parent;
parent = parent.parent;
}
return parent;
}
}
}