[Leetcode] Binary tree level order traversal二叉树层次遍历

Given a binary tree, return the level order traversal of its nodes' values. (ie, from left to right, level by level).

For example:
Given binary tree{3,9,20,#,#,15,7},

    3
   / 
  9  20
    /  
   15   7

return its level order traversal as:

[
  [3],
  [9,20],
  [15,7]
]

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}".

 

二叉树的层次遍历一般是利用队列结构，先将root入队，然后在队列变空之前反复的迭代。迭代部分：首先是取出队首节点并访问，左孩子入队，然后右孩子入队。

方法一：@牛客网NBingGee

因为这题是以每层的形式输出，不是整体。所以需要一个中间变量levelNode来存放每层的节点，关键在于如何层与层之间的节点分开。可以用两个计数器，一个存放当前层的节点个数（levCount），一个存放下一层的节点个数(count)。如果levCount==0，则将当前层的节点存入res中，更新levCount并进入下一行。过程中，二叉树层次遍历的整体思想不变，只不过在循环体的最后加了一段判断是否存入res的代码。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<vector<int> > levelOrder(TreeNode *root) 
    {
        vector<vector<int>> res;
        vector<int> levelNode;
        queue<TreeNode *> Q;
        if(root) Q.push(root);
        int count=0;         //下一层元素的个数
        int levCount=1;   //当前层元素个数，初始为第一层
        while( !Q.empty())
        {
            TreeNode *cur=Q.front();
            levelNode.push_back(cur->val);
            Q.pop();
            levCount--;
            if(cur->left)
            {
                Q.push(cur->left);
                count++;
            }
            if(cur->right)
            {
                Q.push(cur->right);
                count++;
            }
            if(levCount==0)
            {
                res.push_back(levelNode);
                levCount=count;
                count=0;
                levelNode.clear();  //清空levelNode，为下层
            }
        }
        return res;
    }
};

方法二：

 思路：遍历完一层以后，队列中节点的个数就是二叉树下一层的节点数。实时更新队列中节点的个数，每层的遍历。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<vector<int> > levelOrder(TreeNode *root) 
    {
        vector<vector<int>> res;
        queue<TreeNode *> Q;
        if(root)    Q.push(root);

        while( !Q.empty())
        {
            int count=0;
            int levCount=Q.size();
            vector<int> levNode;
            
            //遍历当前层
            while(count<levCount)
            {
                TreeNode *curNode=Q.front();
                Q.pop();
                levNode.push_back(curNode->val);
                if(curNode->left)
                    Q.push(curNode->left);
                if(curNode->right)
                    Q.push(curNode->right);
                count++;
            }
            res.push_back(levNode);
        }
        return res;    
    }
};

 方法三：

利用队列，在每一层结束时向栈中压入NULL， 则遇到NULL就标志一层的结束，就可以存节点了。

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<vector<int> > levelOrder(TreeNode *root) 
    {
        vector<vector<int>> res;
        queue<TreeNode *> Q;
        if(!root)    return res;    
        Q.push(root);
        Q.push(NULL);
        vector<int> levNode;       //存放每层的结点的值
     
        while( !Q.empty())
        {
            TreeNode *cur=Q.front();
            Q.pop();
            if(cur)
            {
                levNode.push_back(cur->val);
                if(cur->left)   
                    Q.push(cur->left);
                if(cur->right)
                    Q.push(cur->right);
            }
            else
            {
                res.push_back(levNode);
                levNode.clear();
                if( !Q.empty())
                    Q.push(NULL);
            }
        }
        return res;    
    }
};