235. Lowest Common Ancestor of a Binary Search Tree

Description

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

Constraints

• The number of nodes in the tree is in the range [2, 105].

• -109 <= Node.val <= 109

• All Node.val are unique.

• p != q

• p and q will exist in the BST.

Approach

Links

• Binarysearch

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

Examples

Example 1

Input: root = [6, 2, 8, 0, 4, 7, 9, null, null, 3, 5], p = 2, q = 8

Output: 6

Explanation: The LCA of nodes 2 and 8 is 6.

Example 2

Example 3

Solutions

Solution 1

/**
 * Time complexity : O(N), where N is the number of nodes in the BST. 
 *    In the worst case we might be visiting all the nodes of the BST.
 * Space complexity : O(N). This is because the maximum amount of space 
 *    utilized by the recursion stack would be N since the height of a 
 *    skewed BST could be N.
 */

class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if(root == null) {
            return null;
        }
        if(root.val > Math.max(p.val, q.val)) {
            return lowestCommonAncestor(root.left, p, q);
        } else if(root.val < Math.min(p.val, q.val)) {
            return lowestCommonAncestor(root.right, p, q);
        }
        return root;
    }
}

Solution 2

Follow up