[leetcode] 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 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).”

Given binary search tree:  root = [6,2,8,0,4,7,9,null,null,3,5]

        _______6______
       /              
    ___2__          ___8__
   /              /      
   0      _4       7       9
         /  
         3   5

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:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself 
             according to the LCA definition.

Note:

• All of the nodes' values will be unique.
• p and q are different and both values will exist in the BST.

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 分析：题目意思也很清楚，解释一下如下：给定一个二叉搜索树，要求找两个节点的最小的父亲。注意到这里时二叉搜索树。也就是说一个节点左子树的值一定小于右子树的值。这是一个核心点，找到这个点我们就可以来写递归代码了。

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);
        else return root;
    }
}