Lowest Common Ancestor of a Binary Search Tree

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 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.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        if (root == NULL) {
            return NULL;
        } else if (root -> val == p ->val ||
                    root -> val == q -> val ||
                    (root -> val > p -> val && root -> val < q -> val) ||
                    (root -> val > q -> val && root -> val < p -> val)) {
            return root;
        } else if (root -> val > p -> val &&
                    root -> val > q -> val) {
            return lowestCommonAncestor(root -> left, p, q);
        } else {
            return lowestCommonAncestor(root -> right, p, q);
        }
    }
};

=== Nicer one ===

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

==== Another one =====

TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        if (root == p || root == q || root == NULL) {
            return root;
        }
        
        if ((p -> val < root -> val && q -> val > root -> val) ||
            (p -> val > root -> val && q -> val < root -> val)) {
            return root;
        } else if (root -> val > p -> val && root -> val > q -> val) {
            return lowestCommonAncestor(root -> left, p, q);
        } else {
            return lowestCommonAncestor(root -> right, p, q);
        }
    }