235. 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.

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/**
 * 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) {
        /*
        Solution 1: Space O(n)
        if (root == null || p == root || q == root) {
            return root;
        }
        
        // Devide
        TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeNode right = lowestCommonAncestor(root.right, p, q);
        
        // Conquer
        if (left != null && right != null) {
            return root;
        } else if (left == null) {
            return right;
        } else {
            return left;
        }
        */
        // Solution 2: Space O(1), since it's a binary search tree.
        if (root == null || p == null || q == null) {
            return root;
        }
        
        TreeNode node = root;
        
        if (p.val < root.val && q.val < root.val) {
            node = lowestCommonAncestor(root.left, p, q);
        }
        if (p.val > root.val && q.val > root.val) {
            node = lowestCommonAncestor(root.right, p, q);
        }
        
        return node;
    }
}
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