# 235-lowest-common-ancestor-of-a-binary-search-tree


Try it on <a href='https://leetcode.com/problems/235-lowest-common-ancestor-of-a-binary-search-tree'>leetcode</a>

## Description
<div class="description">
<div><p>Given a binary search tree (BST), find the lowest common ancestor (LCA) node of two given nodes in the BST.</p>

<p>According to the <a href="https://en.wikipedia.org/wiki/Lowest_common_ancestor" target="_blank">definition of LCA on Wikipedia</a>: “The lowest common ancestor is defined between two nodes <code>p</code> and <code>q</code> as the lowest node in <code>T</code> that has both <code>p</code> and <code>q</code> as descendants (where we allow <strong>a node to be a descendant of itself</strong>).”</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/14/binarysearchtree_improved.png" style="width: 200px; height: 190px;">
<pre><strong>Input:</strong> root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
<strong>Output:</strong> 6
<strong>Explanation:</strong> The LCA of nodes 2 and 8 is 6.
</pre>

<p><strong>Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/14/binarysearchtree_improved.png" style="width: 200px; height: 190px;">
<pre><strong>Input:</strong> root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.
</pre>

<p><strong>Example 3:</strong></p>

<pre><strong>Input:</strong> root = [2,1], p = 2, q = 1
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[2, 10<sup>5</sup>]</code>.</li>
	<li><code>-10<sup>9</sup> &lt;= Node.val &lt;= 10<sup>9</sup></code></li>
	<li>All <code>Node.val</code> are <strong>unique</strong>.</li>
	<li><code>p != q</code></li>
	<li><code>p</code> and <code>q</code> will exist in the BST.</li>
</ul>
</div>
</div>

## Solution(Python)
```Python
# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        if root is None:
            return None
        val = root.val
        pval = p.val
        qval = q.val
        
        if val > pval and val > qval:
            return self.lowestCommonAncestor(root.left, p, q)
        if val < pval and val < qval:
            return self.lowestCommonAncestor(root.right, p, q)
        
        return root
        
        
```