Leetcode 222

Author: wuqinqiang

201-250/222.md

@@ -0,0 +1,112 @@
+## :pencil2:Leetcode之PHP版题目解析（221. Maximal Square)
+**2020-05-18 吴亲库里 库里的深夜食堂**
+****
+### :pencil2:描述
+**给定一棵完全二叉树,求此完全二叉树的节点个数**
+****
+### :pencil2:题目实例
+<a href="https://github.com/wuqinqiang/">
+​    <img src="https://github.com/wuqinqiang/Lettcode-php/blob/master/images/222.png">
+</a> 
+****
+
+### :pencil2:题目分析
+**可以使用递归一个个的计算节点,一行代码干净,但是时间复杂度在O(n),需要全遍历一遍**
+    
+### :pencil2:代码实现1
+          
+```php
+    /**
+     * @param TreeNode $root
+     * @return Integer
+     */
+    function countNodes($root) {
+        return $root !=null ?1+$this->countNodes($root->left)+$this->countNodes($root->right):0;
+    }
+```
+****
+
+**再想想,题目给的是完全二叉树,完全二叉树的特点是什么?除了最后一层(暂且称之为K),其他每层的节点都是满的,并且最后一层的节点全部靠左**
+**也就是说我们其实是在求最后一层的节点数是多少,因为前面0到K-1层的节点是满的,那么利用此树的特性,除最后一层外的所有节点数就是2^d-1(d表示树的高度),对于最后一层我们可以通过二分查找的方式解决,因为最后一层都是靠左的,我只要检查第index 个节点存不存在,存在就向右靠,不存在即右边已经没有了,像左靠.具体看代码**
+
+### :pencil2:代码实现1
+```php
+/**
+ * Definition for a binary tree node.
+ * class TreeNode {
+ *     public $val = null;
+ *     public $left = null;
+ *     public $right = null;
+ *     function __construct($val = 0, $left = null, $right = null) {
+ *         $this->val = $val;
+ *         $this->left = $left;
+ *         $this->right = $right;
+ *     }
+ * }
+ */
+
+
+
+
+class Solution {
+    
+
+    /**
+     * @param TreeNode $root
+     * @return Integer
+     */
+    function countNodes($root) {
+        if(!$root) return 0;
+        $dep=$this->depthNodes($root);
+        if($dep==0) return 1;
+        $left=1;$right=pow(2,$dep)-1;
+        while($left<=$right){
+            $middle=$left+floor(($right-$left)/2);
+            if($this->hasNode($middle,$dep,$root)){
+                $left=$middle+1;
+            }else{
+                $right=$middle-1;
+            }
+        }
+        return pow(2,$dep)-1+$left;
+        
+    }
+    
+    function depthNodes($node)
+    {
+        $dep=0;
+        while($node->left !=null){
+            $node=$node->left;
+            ++$dep;
+        }
+        return $dep;
+    }
+    
+    function hasNode($middle,$d,$node)
+    {
+        $left=0;$right=pow(2,$d)-1;
+        for($i=0;$i<$d;++$i){
+            $pow=$left+floor(($right-$left)/2);
+            if($middle<=$pow){
+                $node=$node->left;
+                $right=$pow;
+            }else{
+                $node=$node->right;
+                $left=$pow+1;
+            }
+        }
+        return $node !=null;
+    }
+}
+```
+
+### 联系
+
+<a href="https://github.com/wuqinqiang/">
+​    <img src="https://github.com/wuqinqiang/Lettcode-php/blob/master/qrcode_for_gh_c194f9d4cdb1_430.jpg" width="150px" height="150px">
+</a> 
+   
+    
+    
+    
+

README.md

@@ -181,6 +181,7 @@
 - [Leetcode217](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/217.md)
 - [Leetcode219](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/219.md)
 - [Leetcode221](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/221.md)
+- [Leetcode222](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/222.md)
 - [Leetcode225](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/225.md)
 - [Leetcode226](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/226.md)
 - [Leetcode228](https://github.com/wuqinqiang/Lettcode-php/blob/master/201-250/228.md)