https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/
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.
 

像這種返回一個node 的東西，結果要不就從左邊來， 要不就從右邊來，否則就是null
凡事遍歷的點，先查一下自己滿足不滿足，不滿足的話，稍微pruning 一下，大膽往左右兩邊丟，然後等答案返回來
check bal. tree height, path sum i 都是這樣

 1 // the goal is to find the root that would sit in the middle
 2     public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
 3         //base case
 

 4         if (root == null) return null ;
 5         int min = Math.min(p.val, q.val) ;
 6         int max = Math.max(p.val, q.val) ;
 7         //pre order：看看當前點是不是滿足的值
 8         if (root.val>=min && root.val <= max) return root ;
 9         //the left: branch pruning > max, then go left： 左邊返回就一層層往上返回
10         if (root.val > max){
11            return lowestCommonAncestor(root.left, p, q) ;
12         }
13         //the right: branch pruning: <min: then go right： 右邊返回就一層層往上返回
14         if (root.val < min){
15           return lowestCommonAncestor(root.right, p, q) ;
16         }
17         //不從左邊，也不從右邊的話，就是NULL
18         return null;
19     }

這道題首先要明確題目背景---二叉搜索樹。也正是因為是二叉搜索樹，所以我們可以利用二叉搜索樹從小到大排好序的特性來做。

對於一個root和另外兩個Node來說，它們的值會有以下幾種情況：

1. root.val < p.val && root.val < q.val 此時，兩個node的值都比root大，說明這兩個值在root右邊的subtree裏，且他們的最小公共頂點不可能是當前root

2. root.val > p.val && root.val > q.val 此時，兩個node的值都比root小，說明這兩個值在root左邊的subtree裏，且他們的最小公共頂點不可能是當前root

3. else,此時 root的值在p，q之間（或等於p，q中的某一個），此時，當前root即為公共頂點

LC.235.Lowest Common Ancestor of a Binary Search Tree