# First Common Ancestor of a Binary Search Tree

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 v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

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

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

## Solution

This problem can be solved by using BST property, i.e., left < parent < right for each node. There are 3 cases to handle.

## Code

``````/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
TreeNode m = root;

if(m.val > p.val && m.val < q.val){
return m;
}else if(m.val>p.val && m.val > q.val){
return lowestCommonAncestor(root.left, p, q);
}else if(m.val<p.val && m.val < q.val){
return lowestCommonAncestor(root.right, p, q);
}

return root;
}
}
``````