[LeetCode]Symmetric Tree

Given a binary tree, check whether it is a mirror of itself (ie, symmetric around its center).

For example, this binary tree is symmetric:

    1
   / \
  2   2
 / \ / \
3  4 4  3

 

But the following is not:

    1
   / \
  2   2
   \   \
   3    3

 

Note:
Bonus points if you could solve it both recursively and iteratively.

confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

OJ's Binary Tree Serialization:

The serialization of a binary tree follows a level order traversal, where '#' signifies a path terminator where no node exists below.

Here's an example:

   1
  / \
 2   3
    /
   4
    \
     5

The above binary tree is serialized as "{1,2,3,#,#,4,#,#,5}".

思考：

递归：DFS，两个指针p、q。若p移到左子树，则q移到右子树，然后再比较。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool DFS(TreeNode *p,TreeNode *q)
    {
        if(!p&&!q) return true;
        else if(p&&q)
        {
            if(p->val!=q->val) return false;
            else return DFS(p->left,q->right)&&DFS(p->right,q->left);
        }
        else return false;
    }
    bool isSymmetric(TreeNode *root) {
        TreeNode *p=root;
        TreeNode *q=root;
        return DFS(p,q);
    }
};

另一种繁一点，先复制原树，然后翻转，再跟原树比较。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    void copyandreverse(TreeNode *root,TreeNode *&newroot,TreeNode *p,bool flag)
    {
        if(root)
        {
            TreeNode *node=new TreeNode(root->val);
            if(newroot==NULL)
            {
                newroot=p=node;
            }
            else
            {
                if(flag) p->right=node;
                else p->left=node;
                p=node;
            }
            copyandreverse(root->left,newroot,p,true);
            copyandreverse(root->right,newroot,p,false);
        }
    }
    bool DFS(TreeNode *root,TreeNode *newTree)
    {
        if(!root&&!newTree) return true;
        else if(root&&newTree)
        {
            if(root->val!=newTree->val) return false;
            else return DFS(root->left,newTree->left)&&DFS(root->right,newTree->right);
        }
        else return false;
    }
    bool isSymmetric(TreeNode *root) {
        if(root==NULL) return true;
        TreeNode *newTree=NULL;
        TreeNode *p=newTree;
        copyandreverse(root,newTree,p,true);
        return DFS(root,newTree);
    }
};