LeetCode #235 Lowest Common Ancestor of a Binary Search Tree

Easy

Problem

Given a binary search tree (BST), find the lowest common ancestor (LCA) 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).”

Given binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

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.w

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the BST.

Solution

By comparing with root, p and q, we can decide next root or just return root as result.

Complexity

Because we move current from root to a leaf. It’s time complexity will be O(h) if h denotes to the length of longest path from root to leaves in this tree. Or you can say O(logn) because h is bounded by logn.

It’s trivial that it uses O(1) extra space.