Lowest Common Ancestor of 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.

思路：找A与B的LCA，有两种可能 1. A或B是另一个点得祖先。比如3，2的LCA就是2。

　　　　　　　　　　　　　　　　2. 一个TreeNode，它的左右子树一个包含A，一个包含B。

　　　这种思路是对于binary tree与binary search tree都适用的，还有一种方法，利用了BST得特点，通过对数值的运算确定了，这个LCA是在root的左子树还是右子树，还是root本身。在leetcode的disscusion中有人提到了。两种的代码如下：

 1 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q）{
 2         if (root == null || root == p || root == q) {
 3             return root;
 4         }
 5         TreeNode left = lowestCommonAncestor(root.left, p, q);
 6         TreeNode right = lowestCommonAncestor(root.right, p, q);
 7         
 8         if (left != null && right != null) {
 9             return root;
10         }
11         if (left != null) {
12             return left;
13         }
14         if (right != null) {
15             return right;
16         }
17         return null;
18 }

1 public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
2         while((root.val - p.val) * (root.val - q.val) > 0) {
3             root = (root.val - p.val) > 0 ? root.left : root.right;
4         }
5         return root;
6 }