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 allowa 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.

题意：对于一棵BST树，给出树上的两个节点，找出它们的最接近的共同祖先节点。

分类：二叉树

解法1：因为题目给出的是BST树。依据BST树的性质。对于某个节点，其左子树上的全部节点的值都比它小。右子树上的全部节点的值都比它大。

对于根节点root而言。假设p,q两个相比root,一大一小。说明root就是它们的LCA

假设都在比root小。说明它们的LCA在root的左子树上。假设都比root大，说明它们的LCA在root的右子树上。

假设它们有当中一个跟root相等。说明这个就是LCA

依据这个思路，我们非常快写出代码：

/**
 * 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) {
        if(root==null) return null;
        if(p.val<root.val&&root.val<q.val){//假设一左一右
            return root;
        }else if(p.val>root.val&&root.val>q.val){//假设一左一右
            return root;
        }else if(p.val<root.val&&root.val>q.val){//假设都在左边，递归查找左子树
            return lowestCommonAncestor(root.left,p,q);
        }else if(p.val>root.val&&q.val>root.val){//假设都在右边，递归查找右子树
            return lowestCommonAncestor(root.right,p,q);
        }else if(p.val==root.val){//假设和root相等
            return p;
        }else if(q.val==root.val){//假设和root相等
            return q;
        }
        return null;
    }
}

/**
 * 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) {
        if(root==null) return null;
        if(p.val<root.val&&root.val>q.val){//假设都在左边。递归查找左子树
            return lowestCommonAncestor(root.left,p,q);
        }else if(p.val>root.val&&q.val>root.val){//假设都在右边。递归查找右子树
            return lowestCommonAncestor(root.right,p,q);
        }else{//其余情况
            return root;
        }
    }
}