Lowest Common Ancestor of a Binary Search Tree

https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/

Given a binary search tree (BST), find the lowest common ancestor (LCA) node of two given nodes in the BST.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.

Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [2,1], p = 2, q = 1
Output: 2

Solution:

Before we start, let's check the code, and then I will explain the main idea.

  public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
    int min = Math.min(p.val, q.val);
    int max = Math.max(p.val, q.val);
     
    while(true){
      if(root.val < min){
        root = root.right;
      } else if(root.val > max){
        root = root.left;
      } else {
        return root;
      }
    }
  }

Based on the description, we should find a node between p and q. My idea is to use part of the binary search. We find min and max for p and q. Then check the current node. If a current value is lower than the min value, we should go to the right side.

But if the current value is bigger than the max value, we have to go to the left, otherwise current value is the Lowest Common Ancestor.

For better understanding, please check the pictures above and use my code.

It cannot be unclear why otherwise, we return the current element. If p and q are placed in different subtrees, we must find the Root node for these subtrees. And this node will be bigger than the left and smaller than the right.