Lowest 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

/**
 * 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) {
        if (root == null) return null;
        if (p.val > q.val) return lowestCommonAncestor(root, q, p);

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