First 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

This problem can be solved by using BST property, i.e., left < parent < right for each node. There are 3 cases to handle.

Complexity

时间复杂度 O(n)，空间复杂度 O(h)

Code

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