LeetCode: Lowest Common Ancestor of a Binary Search Tree二叉搜索树最近公共祖先

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本文介绍了一种在二叉搜索树(BST)中寻找两个给定节点的最低公共祖先(LCA)的有效方法。通过递归地遍历BST，利用BST的特性确保找到的公共祖先既是最小的，也位于目标节点的路径上。示例展示了输入为特定BST及目标节点时，如何依据定义得出正确答案。

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试题：
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]

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.
代码：
如果存在公共祖先，那么这个祖先必然大于左边，小于右边。三种情况互相对立，直接返回结果就行。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if(root==null) return null;
        if(root.val>p.val && root.val>q.val){
            return lowestCommonAncestor(root.left, p, q);
        }else if(root.val<p.val && root.val<q.val){
            return lowestCommonAncestor(root.right, p, q);
        }{
            return root;        
        }
    }
}