【Lowest Common Ancestor of a Binary Tree】cpp

题目：

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.

代码：

/**
 * 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 || root==p || root==q ) return root;
            TreeNode* l = Solution::lowestCommonAncestor(root->left, p, q);
            TreeNode* r = Solution::lowestCommonAncestor(root->right, p, q);
            if ( l && r )
            {
                return root;
            }
            else
            {
                return l ? l : r;
            }
    }
};

tips：

直接学习大神的思路（http://bookshadow.com/weblog/2015/07/13/leetcode-lowest-common-ancestor-binary-tree/），确实很巧妙。

总体来说，就是分叉找；终止条件是到了叶子或者找到p和q的一个就返回了。

这里有个思维误区，为啥找到p或q的一个就返回了，如果先找到p而q在p的下面呢？那就正好了，反正这俩点如果q在p的下面，那么根据定义p就是p和q的公共祖先。