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.

解題思路L：求樹上兩個節點的最近公共祖先

1、如果兩個節點在一個節點的左右子樹，那麽該節點就是最近公共祖先。

2、如果一個節點在另一個節點的子樹下，那麽另一個節點就是最近公公祖先。

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) {
        if(root==NULL||root==p||root==q)return root;
        TreeNode* left=lowestCommonAncestor(root->left,p,q); //find p,q in left half
        TreeNode* right=lowestCommonAncestor(root->right,p,q);//find p,q in right half
        if(left&&right)return root;//1
        return !left?right:left;//2
    }
};

236. Lowest Common Ancestor of a Binary Tree