Lowest Common Ancestor of a Binary Tree

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

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).”

_______3______
/ \
___5__ ___1__
/ \ / \
6 _ 2 0 8
/ \
7 4
For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

给定一个二叉树，找到他们的最近公共祖先，之前我们做过一道题目是从一个二叉搜索树中找两个节点的最近公共祖先，我们可以通过值的比较来找出。对于这道题目，我们设定两个辅助节点left和right，分别从根节点的左子树和右子树中寻找，找到了就返回相应的节点。最后判断left和right两个节点，如果都不为空，则LCA为root, 否则为left == null ? right : left。代码如下：

/**
 * 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 || p == root || q == root) return root;
        TreeNode left = lowestCommonAncestor(root.left, p, q);
        TreeNode right = lowestCommonAncestor(root.right, p, q);
        if(left != null && right != null) 
            return root;
        else 
            return left == null ? right : left;
    }
}