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).”

  1.         _______6______
  2.        /              \
  3.     ___2__          ___8__
  4.    /      \        /      \
  5.    0      _4       7       9
  6.          /  \
  7.          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:

  1. /**
  2.  * Definition for a binary tree node.
  3.  * public class TreeNode {
  4.  *     int val;
  5.  *     TreeNode left;
  6.  *     TreeNode right;
  7.  *     TreeNode(int x) { val = x; }
  8.  * }
  9.  */
  10. public class Solution {
  11.   public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
  12.     if (root == null)
  13.       return null;
  15.     if (root.val > p.val && root.val > q.val)
  16.       return lowestCommonAncestor(root.left, p, q);
  17.     else if (root.val < p.val && root.val < q.val)
  18.       return lowestCommonAncestor(root.right, p, q);
  19.     else    
  20.       return root;
  21.   }
  22. }